advanced super conductivity and cryogenics

INDEX

Practical 1: History of superconductivity 1

1.1 The Discovery of Superconduction 2

Practical 2: The Phenomenon of Superconductivity 7

2.1 Zero Electric Resistance 7

2.2 Perfect Diamagnetism 9

2.3 Super Currents 10

Practical 3: Thermodynamic and Optical Properties 15

3.1 Flux Quantization 15

3.2 Josephson Tunneling 16

Practical 4: Development of High Tc Cuparates 19

4.1 Introduction 19

4.2 YBCO 19

4.3 BSCCO 22

4.4 Thallium and mercury based compounds 23

4.5 Summary 24

Practical 5:Preparation of Cuprate Materials 25

5.1 Introduction 25

5.2 Different methods of Preparation of Cuprate Materials 26

5.3 Conclusion 29

Practical 6: Theories of Superconductivity-I 31

6.1 London Equation & Hypothesis: 31

6.2 Penetration Depth & Meissner Effect: 32

6.3 Rigidity of Wave Function: 33

PRACTICAL 7: Theories of Superconductivity-II 36

7.1 GinzburgLandau theory 36

7.2 Simple interpretation 37

7.3 Coherence length and penetration depth 38

Practical 8: Study of Josephson Effect and the BCS theory 39

8.1 Type II superconductivity 39

8.2 Josephson Effect 41

8.3 The BCS theory 42

Practical 9: Application of superconductivity-1 44

9.1 Magnets : 44

9.2 Transportation: 47

Practical 10: Application of Superconductivity-2 49

10.1 Energy-related 49

10.2 Electronics and small devices 51

Advanced Cryogenics & Applied Super Conductiity

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Practical 1: History of superconductivity

In 1911 superconductivity was first observed in mercury by Dutch physicist Heike Kamerlingh

Onnes of Leiden University. When he cooled it to the temperature of liquid helium, 4 degrees

Kelvin (-452F, -269C), its resistance suddenly disappeared.

In 1997 researchers found that at a temperature very near absolute zero an alloy of gold and indium

was both a superconductor and a natural magnet. Conventional wisdom held that a material with

such properties could not exist! Since then, over a half-dozen such compounds have been found.

Recent years have also seen the discovery of the first high-temperature superconductor that does

NOT contain any copper (2000), and the first all-metal perovskite superconductor (2001).

Also in 2001 a material that had been sitting on laboratory shelves for decades was found to be an

extraordinary new superconductor. Japanese researchers measured the transition temperature of

magnesium diboride at 39 Kelvin far above the highest Tc of any of the elemental or binary alloy

superconductors. While 39 K is still well below the Tcs of the warm ceramic superconductors,

subsequent refinements in the way MgB2 is fabricated have paved the way for its use in industrial

applications. Laboratory testing has found MgB2 will outperform NbTi and Nb3Sn wires in high

magnetic field applications like MRI.

The chronology of discoveries of superconductors with higher critical temperatures


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A Brief History of Superconductivity:

1.1 The Discovery of Superconduction

Before the discovery of superconduction, it was already known that cooling a metal increased its

conductivity - due to decreased electron-phonon interactions (detailed in the Theory section).

After the 'discovery' of liquified helium, allowing objects to be cooled to within 4K of absolute

zero, it was discovered (by Onnes, 1911) that when mercury was cooled to 4.15K, its resistance

suddenly (and unexpectedly) dropped to zero (i.e. it went superconducting).

Left: When Onnes

cooled mercury to

4.15K, the resistivity

suddenly dropped to

zero

In 1913, it was discovered that lead went superconducting at 7.2K. It was then 17 years until

niobium was found to superconduct at a higher temperature of 9.2K.

Onnes also observed that normal conduction characteristics could be restored in the presence of a

strong magnetic field.

The Meissner Effect

It was not until 1933 that physicists became aware of the other property of superconductors -

perfect diamagnetism. This was when Meissner and Oschenfeld discovered that a superconducting

material cooled below its critical temperature in a magnetic field excluded the magnetic flux. This

effect has now become known as the Meissner effect.


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Above: The Meissner effect - a superconducting sphere in a constant

applied magnetic field excludes the magnetic flux

The limit of external magnetic field strength at which a superconductor can exclude the field is

known as the critical field strength, Bc.

Type II superconductors have two critical field strengths; Bc1, above which the field penetrates

into the superconductor, and Bc2, above which superconductivity is destroyed, as per Bc for Type

I superconductors.

Theory of Superconduction

Fritz and Heinz London proposed equations to explain the Meissner effect and predict how far a

magnetic field could penetrate into a superconductor, but it was not until 1950 that any great

theoretical progression was made, with Ginzburg-Landau theory, which explained

superconductivity and provided derivation for the London equations.

Ginzburg-Landau theory has been largely superseded by BCS theory, which deals with

superconduction in a more microscopic manner.

BCS theory was proposed by J. Bardeen, L. Cooper and J. R. Schrieffer in 1957 - it is dealt with

in the Theory section. BCS suggests the formation of so-called 'Cooper pairs', and correlates

Ginzburg-Landau and London predictions well.

However, BCS theory does not account well for high temperature superconduction, which is still

not fully understood.


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High Temperature Superconduction

The highest known temperature at which a material went superconducting increased slowly as

scientists found new materials with higher values of Tc, but it was in 1986 that a Ba-La-Cu-O

system was found to superconduct at 35K - by far the highest then found. This was interesting as

BCS theory had predicted a theoretical limit of about 30-40K to Tc (due to thermal vibrations).

Soon, materials were found that would superconduct above 77K - the melting point of liquid

nitrogen, which is far safer and much less expensive than liquid helium as a refrigerant. Although

high temperature superconductors are more useful above 77K, the term technically refers to those

materials that superconduct above 30-40K.

History of superconductivity

Superconductivity was discovered on April 8, 1911 by Heike Kamerlingh Onnes, who was

studying the resistance of solid mercury at cryogenic temperatures using the recently produced

liquid helium as a refrigerant. At the temperature of 4.2 K, he observed that the resistance abruptly

disappeared. In the same experiment, he also observed the superfluid transition of helium at 2.2 K,

without recognizing its significance. The precise date and circumstances of the discovery were

only reconstructed a century later, when Onnes's notebook was found. In subsequent decades,

superconductivity was observed in several other materials. In 1913, lead was found to

superconduct at 7 K, and in 1941 niobium nitride was found to superconduct at 16 K.

Great efforts have been devoted to finding out how and why superconductivity works; the

important step occurred in 1933, when Meissner and Ochsenfeld discovered that superconductors

expelled applied magnetic fields, a phenomenon which has come to be known as the Meissner

effect. In 1935, Fritz and Heinz London showed that the Meissner effect was a consequence of the

minimization of the electromagnetic free energy carried by superconducting current.

London theory

The first phenomenological theory of superconductivity was London theory. It was put forward by

the brothers Fritz and Heinz London in 1935, shortly after the discovery that magnetic fields are

expelled from superconductors. A major triumph of the equations of this theory is their ability to


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explain the Meissner effect, wherein a material exponentially expels all internal magnetic fields as

it crosses the superconducting threshold. By using the London equation, one can obtain the

dependence of the magnetic field inside the superconductor on the distance to the surface.

There are two London equations:

The first equation follows from Newton's second law for superconducting electrons.

Conventional theories (1950s)

During the 1950s, theoretical condensed matter physicists arrived at a solid understanding of

"conventional" superconductivity, through a pair of remarkable and important theories: the

phenomenological Ginzburg-Landau theory (1950) and the microscopic BCS theory (1957).

In 1950, the phenomenological Ginzburg-Landau theory of superconductivity was devised by

Landau and Ginzburg. This theory, which combined Landau's theory of second-order phase

transitions with a Schrdinger-like wave equation, had great success in explaining the macroscopic

properties of superconductors. In particular, Abrikosov showed that Ginzburg-Landau theory

predicts the division of superconductors into the two categories now referred to as Type I and

Type II. Abrikosov and Ginzburg were awarded the 2003 Nobel Prize for their work (Landau had

received the 1962 Nobel Prize for other work, and died in 1968). The four-dimensional extension

of the Ginzburg-Landau theory, the Coleman-Weinberg model, is important in quantum field

theory and cosmology.

Also in 1950, Maxwell and Reynolds et al. found that the critical temperature of a superconductor

depends on the isotopic mass of the constituent element. This important discovery pointed to the

electron-phonon interaction as the microscopic mechanism responsible for superconductivity.

The complete microscopic theory of superconductivity was finally proposed in 1957 by Bardeen,

Cooper and Schrieffer. This BCS theory explained the superconducting current as a superfluid of


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Cooper pairs, pairs of electrons interacting through the exchange of phonons. For this work, the

authors were awarded the Nobel Prize in 1972.

The BCS theory was set on a firmer footing in 1958, when N. N. Bogolyubov showed that the

BCS wavefunction, which had originally been derived from a variational argument, could be

obtained using a canonical transformation of the electronic Hamiltonian. In 1959, Lev Gor'kov

showed that the BCS theory reduced to the Ginzburg-Landau theory close to the critical

temperature.

Generalizations of BCS theory for conventional superconductors form the basis for understanding

of the phenomenon of superfluidity, because they fall into the lambda transition universality class.

The extent to which such generalizations can be applied to unconventional superconductors is still

controversial.

Further history

The first practical application of superconductivity was developed in 1954 with Dudley Allen

Buck's invention of the cryotron. Two superconductors with greatly different values of critical

magnetic field are combined to produce a fast, simple, switch for computer elements.

In 1962, the first commercial superconducting wire, a niobium-titanium alloy, was developed by

researchers at Westinghouse, allowing the construction of the first practical superconducting

magnets. In the same year, Josephson made the important theoretical prediction that a supercurrent

can flow between two pieces of superconductor separated by a thin layer of insulator. This

phenomenon, now called the Josephson effect, is exploited by superconducting devices such as

SQUIDs. It is used in the most accurate available measurements of the magnetic flux quantum

0 = h/(2e), where h is the Planck constant. Coupled with the quantum Hall resistivity, this leads

to a precise measurement of the Planck constant. Josephson was awarded the Nobel Prize for this

work in 1973.


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Practical 2: The Phenomenon of Superconductivity

Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion

of magnetic fields occurring in certain materials when cooled below a characteristic critical

temperature. It was discovered by Dutch physicist Heike Kamerlingh Onnes on April 8, 1911

in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum

mechanical phenomenon. It is characterized by the Meissner effect, the complete ejection

of magnetic field lines from the interior of the superconductor as it transitions into the

superconducting state. The occurrence of the Meissner effect indicates that superconductivity

cannot be understood simply as the idealization of perfect conductivity in classical physics.

2.1 Zero Electric Resistance

H. Kamerlingh Onnes, after having successfully liquefied helium in 1908, investigated the

low temperature resistivity of mercury in 1911. The mercury could be made very pure by

distillation, and this was important because the resistivity at low temperatures tends to be

dominated by impurity effects. He found that the resistivity suddenly dropped to zero at 4.2K, a


8

phase transition to a zero resistance state. This phenomenon was called superconductivity, and the

temperature at which it occurred is called its critical temperature.

THE SUPER CONDUCTOR AS A THERMODYNAYC PHASE

The variation of specific heat with temperature is often a good probe of phase transitions

in matter. Historically, it is Ehrenfest who first classified phase transitions based on the variation

of the thermodynamic free energy with some state variable such as temperature. The order of a

transition was defined as the lowest derivative of free energy (with respect to some variable) that

was discontinuous at the transition. If the first derivative of free energy were discontinuous (such

as the case of a solid-liquid transition where the density is discontinuous), then the transition is

called first order. In the case of ferromagnetic transition of Fe for example, the susceptibility (i.e.,

the second derivative of free energy with field) is discontinuous and one would classify this as a

second order phase transition. However, there are many cases in nature where rather than

discontinuous jumps in thermodynamic variables, there is a divergence such as in the heat capacity

of a superconductor. Over the decades, changes in these criteria have been proposed to

accommodate such cases. The modern classification of phase transitions is based on the existence

or lack thereof of a latent heat. If a phase transition involves a latent heat, i.e., the substance absorbs

or releases heat without a change in temperature, and then it is called an order phase transition. In

the absence of a latent heat, the phase transition is an order transition. Landau gave a theory of

order phase transitions and its application to superconductors will be discussed later in these

lectures. The variation of the enthalpy in the vicinity of a first order phase transition. The variation

of the enthalpy in the vicinity of a non-first order phase transition.

The figure shows the schematic variation of enthalpy in the case of a transition involving a latent

heat. For a type I superconductor, in general, there is an entropy change at the transition


9

temperature (and therefore a latent heat) making the transition order. However, in zero magnetic

field, the entropy change is zero and hence the transition is order. In the normal state, the electronic

contribution to the heat capacity is linear in temperature, as explained in a previous chapter. The

heat capacity exhibits a jump at and at lower temperatures, it falls with an exponential temperature

dependence. The exponential dependence is due to the opening up of a gap in the excitation

spectrum. Signatures of a gap are seen in various other properties such as thermal conductivity,

current-voltage characteristics, etc. Variation of X with temperature for a normal metal & a

Superconducting

1.Entropy 2. Heat capacity 3. Internal Energy 4. Free Energy

The accompanying figures contrast the variation with temperature of some basic thermodynamic

quantities such as the entropy S, the internal energy U, the heat capacity C and the Helmholtz free

energy F.

2.2 Perfect Diamagnetism

Super diamagnetism (or perfect diamagnetism) is a phenomenon occurring in certain materials

at low temperatures, characterized by the complete absence of magnetic permeability (i.e.

a magnetic susceptibility = 1) and the exclusion of the interior magnetic field. Super

diamagnetism established that the superconductivity of a material was a stage of phase transition.


10

Superconducting magnetic levitation is due to super diamagnetism, which repels a permanent

magnet which approaches the superconductor, and flux pinning, which prevents the magnet

floating away. Super diamagnetism is a feature of superconductivity. It was identified in 1933,

by Walther Meissner and Robert Ochsenfeld, but it is considered distinct from the Meissner

effect which occurs when the superconductivity first forms, and involves the exclusion of magnetic

fields that already penetrate the object.

2.3 Super Currents

In the super conductor, due to the resistance is almost zero, the very high currents can be flow

through it without more heat generation. The heat generated is proportional to R2 and that tends

to zero. So, it can have super currents.

Penetration depth

The characteristic length, , associated with the decay of the magnetic field at the surface of a

superconductor is known as the penetration depth, and it depends on the number densityns of

superconducting electrons.

We can estimate a value for by assuming that all of the free electrons are superconducting. If we

set ns = 1029 m3, a typical free electron density in a metal, then we find that


11

The small size of indicates that the magnetic field is effectively excluded from the interior of

macroscopic specimens of superconductors, in agreement with the experimentally observed

Meissner effect.The characteristic length, , associated with the decay of the magnetic field at the

surface of a superconductor is known as the penetration depth, and it depends on the number

density ns of superconducting electrons. We can estimate a value for by assuming that all of the

free electrons are superconducting. If we set ns = 1029 m3, a typical free electron density in a

metal, then we find that The small size of indicates that the magnetic field is effectively excluded

from the interior of macroscopic specimens of superconductors, in agreement with the

experimentally observed Meissner effect.

MAGNETIC PHASE DIAGRAM CRITICAL MAGNETIC FIELD AND

TEMPERATURE

The superconducting state cannot exist in the presence of a magnetic field greater than a critical

value, even at absolute zero.


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This critical magnetic field is strongly correlated with the critical temperature for the

superconductor, which is in turn correlated with the band gap. Type II superconductors show two

critical magnetic field values, one at the onset of a mixed superconducting and normal state and

one where superconductivity ceases.

The critical magnetic field required to destroy the superconducting state is strongly correlated with

the critical temperature for the superconductor


13

Each of these parameters can be viewed as representative of energy which can be supplied to the

material in such a way that it interferes with the superconducting mechanism. This is consistent

with the idea that there is a bandgap between the superconducting and normal states.

INTERMEDIATE STATE

In the intermediate state of a thin type-I superconductor magnetic flux penetrates in a disordered

set of highly branched and fingered macroscopic domains. To understand these shapes, we study

in detail a recently proposed current-loop model @R. E. Goldstein, D. P. Jackson, and A. T.

Dorsey, Phys. Rev. Lett. 76, 3818 1996that models the intermediate state as a collection of tense

current ribbons flowing along the superconducting-normal interfaces and subject to the constraint

of global flux conservation. The validity of this model is tested through a detailed reanalysis of

Landaus original conformal mapping treatment of the laminar state, in which the superconductor-

normal interfaces are flared within the slab, and of a closely related straightlamina model. A

simplified dynamical model is described that elucidates the nature of possible shape instabilities

of flux stripes and stripe arrays, and numerical studies of the highly nonlinear regime of those

instabilities demonstrate patterns like those seen experimentally. Of particular interest is the

buckling instability commonly seen in the intermediate state. The free-boundary approach further

allows for a calculation of the elastic properties of the laminar state, which closely resembles that

of smectic liquid crystals. We suggest several experiments to explore flux domain shape

instabilities, including an Eckhaus instability induced by changing the out-of-plane magnetic field

and an analog of the Helfrich-Hurault instability of smectics induced by an in-plane field

Gibbs free energy

In magnetic field we define a Gibbs free energy as: G = E - TS -M.B, where the M.B term includes

the energy of interaction of the specimen with the external field. Thus:

dG = (dE - TdS - B.dM) - SdT - M.dB = - SdT - M.dB dE = dQ + dW


14

Superconductivity RJ Nicholas HT10 5 At BC the normal and superconducting phases are in

equilibrium, so their Gibbs functions are the same. Thus:

We can deduce the Entropy difference from S = -G/T

At Tc the value of Bc 0 so SN = SS dBc/dT is negative, so SN > SS for T < Tc


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Practical 3: Thermodynamic and Optical Properties

3.1 Flux Quantization

When two superconductors are separated by a very thin insulating layer, quite unexpectedly, a

continuous electric current appears, the value of which is linked to the characteristics of the

superconductors. This effect was predicted in 1962 by Brian Josephson. Since then, this

superconductor-insulator-superconductor sandwich has been called a Josephson junction.

Where does such an effect come from?

When a material becomes superconducting, the electrons form Cooper pairs and condensate in the

shape of a unique collective quantum wave. If the electric insulator separating the two

superconductors is very thin (only a few nanometres), then the wave can somehow spill out of the

superconductor, which enables the electron pairs to go through the insulator thanks to a quantum

effect called tunneling effect. When spontaneously going from one superconductor to the other,

the pairs create an electric current. Each superconductor is characterized by a quantity called phase,

with a subtle signification. The electric current in the junction is a continuous current, the value of

which is proportional to the sine of the phase difference between the two superconductors.

Now, if we apply a constant electric tension difference between the two superconductors, an

alternating electric current appears, in reaction to the phase variations. This effect that links a

continuous voltage to an alternating current is unusual. Especially since the frequency of

alternating currents depends neither on the size of the superconductors, nor on their properties

(critical temperature, chemical composition). This frequency only depends on the applied voltage

and on fundamental permanent features (the electric charge of the electron and Planck quantum of

energy). We can measure a frequency very precisely thanks to atomic clocks, but until this effect

was discovered, we could not precisely measure a voltage. The Josephson Effect enables us to

define a reference value of the voltage that is then used to calibrate the measuring devices and to

make sure that one volt has the same value in France and in Japan.

Josephson effects are very sensitive to the value of the magnetic field, because the phase variation

of a superconductor can be linked to the magnetic flux. It then becomes possible to use this

magnetic field sensitivity to build very accurate magnetic field measuring devices, called squids:

these devices are the most precise means to measure a magnetic field.


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3.2 Josephson Tunneling

So far we have not discussed the magnitude of the maximum Josephson current density Jc. In this

subsection we derive an expression of this quantity for the case of Josephson junction with an

insulating tunneling barrier of thickness d. That is, we consider the supercurrent density across a

superconductor insulator the so-called wave matching method. Here, we solve the Schrdinger

equation in the three regions, namely the two superconducting electrodes and the insulating barrier.

The solutions will contain coefficients that can be determined by matching the solutions at the

boundaries between the three regions.

We first start with the wave function in the superconducting electrodes. The supercurrent density

at the edges of the junction electrodes at the positions x = _d=2 is given by the supercurrent density

equation We already have found the relationship between the current density at the boundary to

the insulator and the phase of the wave functions at each boundary. It is given by the current-phase

relation. In order to derive the magnitude of the maximum Josephson current density Jc we make

the same assumptions as ins. That is, we assume a uniform tunnelling barrier. We further assume

that the junction area L _W is small enough, so that the Josephson current density can be assumed

uniform within the junction area. It will be discussed later, up to which length scale this

approximation is valid.

We start our discussion with the energy-phase relation (1.1.69) for the superconducting electrodes,

which directly follows from the Schrdinger equation. In the absence of any electric and magnetic

field this mechanically the situation is different. Here, the superelectrons can tunnel through the

barrier. In our discussion we consider only elastic processes, that is, the superelectrons maintain

their energy. Therefore, the time evolution of the wave function is the same outside and inside the

barrier and we have to consider only the time independent part. Moreover, since within the barrier

we are in a region of constant potential energy V0, the time dependent Schrdinger-like can be

written as the time independent Schrdinger equation.

Superconductors and Superfluid

In 1908, Heike Kammerling Onnes succeeded in liquefying helium for the first time. At ambient

pressure, helium boils/condenses at 4.22 K, only about 4 degrees above the absolute zero of


17

temperature (Fossheim 2004). A meticulous and continuous effort over many years led to the

determination of the so-called isotherms of helium, and this was a key ingredient in achieving

success.

Superconductors and Superfluid Matter Wave Analogs of the LASER Kammerling Onnes the

Nobel Prize in 1913: The attainment of these low temperatures is of the greatest importance to

physics research, for at these temperatures both the properties of the substances and also the course

followed by physical phenomena, are generally quite different from those at our normal and higher

temperatures, and a knowledge of these changes is of fundamental importance in answering many

of the questions of modern physics. These were truly prophetic words, in view of what was to

come.

In 1938, Pjotr Kapitza found that liquid helium suddenly loses its viscosity when cooled down to

2.17 K (Khalatnikov 1989, Annett 2004). The loss of viscosity is the counterpart in helium to the

loss of electrical resistivity in a metal. This loss of viscosity was called superfluidity. There is a

fascinating analog of the Meissonier effect in helium. Recall that a magnetic field couples to matter

in two ways, either via the spin of a particle or via its charge. It is the coupling to charge which is

important for the Meissner effect. However, helium is a noble gas made up of neutral (uncharged)

and spineless atoms! The analog is as follows:

Superconductors and Superfluids Matter Wave Analogs of the LASER you rotate a bucket of

helium. The superfluid liquid in the bucket remains irrotational if the rotational frequency is not

too large. When it exceeds some critical value, the liquid remains irrotational except along certain

lines parallel to the rotation vector, where specific quanta of rotation appear. These lines are

arranged in a hexagonal pattern in the plane perpendicular to the lines, and are lines of quantized

vorticity, or vortexlines.

The explanation for superfluidity in helium as observed by Kapitza is quite different from the BCS

theory, and in some senses simpler. The helium isotope in Kapitzas fluid has two protons and two


18

neutrons in the nucleus, and is a boson. Bosons have the intrinsic property of preferring to

macroscopically occupy one and the same single-particle state at low temperatures. This is called

Bose-Einstein condensation. (Fermions such as electrons are quite the opposite. Two of them

cannot possibly occupy the same single-particle state).

Superfluidity

in bosonic helium is simply Bose- Einstein condensation in a strongly interacting bosonic fluid.

However, helium has another isotope with two protons and one neutron, which is a fermion.

Superfluidity in this liquid, now in the mille-Kelvin regime, was discovered in 1972. The discovery

was awarded the Nobel Prize in 1997. The theory for this is much more elaborate than for bosonic

helium.

Superconductors and Superfluids Matter Wave Analogs of the LASER pairs by some interaction

(which has to be different in origin from the lattice-mediated interactions for the metals described

above). The wave function for these Cooper pairs turns out to be a monster with no fewerthan nine

complex components, compared with one in the BCS theory of superconductivity. The phase

coherence in such rich and complex matter waves will continue to intrigue researchers for many

decades to come.


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Practical 4: Development of High Tc Cuparates

4.1 Introduction

Until 1986, the record transition temperature for a superconductor was 23 K. In that year, Bednorz

and Muller synthesized the compound La2CuO4 which remains superconducting up to 30 K, and

soon afterwards other superconducting cuprate materials were discovered with even higher

transition temperatures. YBa2Cu3O7- (YBCO) has a Tc of 92 K , which is significant because it

is greater than the boiling point of liquid nitrogen at atmospheric pressure. Bi-Sr-Ca-Cu-O, Tl-Ba-

Ca-Cu-O and Hg-Ba-Ca-Cu-O compounds have higher critical temperatures as shown in table 4.1.

Table 4.1 Transition temperatures of some high Tc superconducting compounds

Material Tc (K)

YBa2Cu3O7- 92

Bi2Sr2CaCu2O8 85

Bi2Sr2Ca2Cu3O10 110

TlBa2Ca2Cu3O9 123

HgBa2Ca2Cu3O8 135

All these high temperature superconductors have highly anisotropic crystal structures, containing

layered CuO2 planes in which the superconducting charge carriers are thought to be localized.

4.2 YBCO

The unit cell of YBCO is based on a stack of three perovskite cells as shown in figure 4.2 and the

lattice type is either tetragonal or orthorhombic, depending on the oxygen content. The central

perovskite cell contains a Y atom, sandwiched between CuO2 planes. Adjacent to the CuO2 planes

are layers of BaO2 and at the top and bottom of the cell there are Cu-O chains which have variable

oxygen content, dependent upon the overall oxygenation level of the material.

The HTS compounds can be described using a four number naming scheme, the numbers

representing :

1) The number of insulating layers between CuO2 planes (for YBCO, 1, the basal plane)


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Figure 4.2 Unit cell of a) YBa2Cu3O7 and b) YBa2Cu3O7-. The dashed circles indicate

oxygen sites which are partially filled

2) The number of spacing layers between blocks of CuO2 planes (for YBCO, 2, the BaO2 layers)

3) The number of separating layers within each block of CuO2 planes (for YBCO, 1, the Y layer)

4) The number of CuO2 layers in each block (for YBCO, 2)

Thus the crystal structure may be represented as in figure 4.3. Each square based pyramid has O

atoms at its apices and a Cu atom at the center of the base. The square Cu-O sheets have an O atom

at each corner and a Cu atom at the center. Note that in order to show two complete blocks of

CuO2 planes, the origin of figure 1.3 is shifted by (0,0,) relative to the conventional cell shown

in figure 4.2.

Figure 4.3 The crystal structure of YBCO. The pyramids have O atoms at the apices and

Cu atoms at the centre of the base.


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The variation of the oxygen content in YBa2Cu3O7- is extremely important in determining the

superconducting properties. The effect of reducing the oxygen content below 7 atoms per unit cell

is shown in figure 4.4. An optimum Tc of 93 K is obtained for =0.08, but if more oxygen is

removed from the structure, Tc falls rapidly and for >0.56, YBa2Cu3O7- is not superconducting.

Also important for the superconducting properties of YBCO is the existence of chains of Cu-O

atoms, which have metal-like electrical properties and reduce the anisotropy of the superconductor.

Figure 4.4 The effect of oxygen content on the Tc of YBa2Cu3O7- . Adapted from .

The variation of the unit cell parameters of YBCO with oxygen content is shown in figure 4.5,

which demonstrates the tetragonal-orthorhombic transition at around =0.6. Although the

superconducting phase of YBCO is orthorhombic, in practice it is not possible to distinguish a and

b directions in a macroscopic sample due to twinning on a fine scale.

Figure 4.5 The unit cell parameters of YBCO as a function of the oxygen content.


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The large anisotropy of the crystal structure has consequences for the physical properties as the

effective mass of the electrons moving in the a-b plane, mab, is different from that in the c direction,

mc. This difference is characterised by an anisotropy parameter, , such that 2=mc/mab. The

anisotropy parameter is a measure of the ratio of the coherence length and the penetration depth in

the a-b plane and c-direction. For YBCO, is approximately 5-7 as demonstrated by the values

shown in table 4.2.

Table 4.2 Anisotropy of and in YBCO (T=0 K) .

The large Ginzburg-Landau parameter (=/) means that YBCO is very strongly type II. The

lower critical field Bc1 is around 10 mT at 77 K compared with an upper critical field Bc2 of over

800 T for field in the c-direction at T=0 K .

4.3 BSCCO

The superconducting compounds of Bi-Sr-Ca-Cu-O are based on Bi2Sr2CanCun+1O6+2n, where

n is an integer. The structures of the n=1 and n=2 compounds, generally known as Bi-2212 and

Bi-2223 are shown in figure 4.6.

Figure 4.6 The crystal structures of Bi-2212 and Bi-2223.


23

BSCCO-2223 is an extremely anisotropic material, the value of being at least an order of

magnitude greater than that in YBCO. Values of the coherence length and penetration depth are

difficult to measure accurately and there is significant variation in the data reported in the literature,

though some estimates are given in table 4.3.

Table 1.3 Anisotropy of and in BSCCO (T=0 K)

4.4 Thallium and mercury based compounds

There are several families of superconducting materials which incorporate Tl. The

Tl2Ba2CanCun+1O2n+6 system is analogous to the Bi based material with equivalent crystal

structures and similar inter-layer spacings. In addition, the single Tl-O layer TlBa2Can

1CunO2n+3 and TlSr2Can-1CunO2n+3 are superconducting. The n=1 and n=2 structures are

shown in figure 4.7.

Figure 4.7 Crystal structures of 1212 and 1223


24

The TSCCO compounds can be difficult to synthesise unless the Tl is partially substituted by Pb

or Bi and the critical temperatures are generally lower than those of TBCCO, although they may

be increased to 100 K with appropriate doping. The superconducting properties of the Tl

compounds are less sensitive to oxygen stoichiometry than YBCO and in terms of anisotropy,

they lie somewhere between YBCO and BSCCO.

Of all the high Tc materials fabricated to date, those with the highest transition temperatures are

the Hg based compounds. HgBa2Ca2Cu3O8, which has the same crystal structure as Tl-1223, has

a Tc of 135 K, which can be increased by application of pressure. Due to the fact that the Hg

compounds are closely related to the Tl materials in terms of their crystal structures, they have

similar superconducting properties.

4.5 Summary

The high Tc materials have highly anisotropic crystal structures which leads to anisotropic physical

properties. This anisotropy is related to the spacing between the superconducting Cu O planes. An

additional factor, which makes YBCO much less anisotropic than the other materials is the

presence of Cu-O chains between the cuprate planes.

Table 4.4 Lattice parameters of common high Tc materials .


25

Practical 5:Preparation of Cuprate Materials

5.1 Introduction

Slynthesis and processing of superconducting alloys and other metallic systems is

relatively straightforward and one uses known metallurgical techniques for this purpose. This

is, however, not true of the cuprate superconductors. Complex oxides such as the cuprates are

ordinarily made by the ceramic method (mix, grind and heat), which involves thorough mixing

of the various oxides and/or carbonates (or some other salt) in the Hesired proportion, and

heating the mixture (preferably in pellet form) at a high temperature; this mixture is ground

again after some time, and reheated until the desired product is formed as indicated by x-ray

diffraction. Since this method may not always yield the product in the desired structure or punty,

variants of the method are often employed. For example, decomposing a mixture of nitrates has

been found by some workers to yield a better product in the case of 123 compounds; some

others prefer to use Ba02 in place of BaC03 for the synthesis.

1. Sol-gel method

It has been employed for the synthesis of 123 compounds. This method provides a

homogeneous dispersion of the various component metals, when a solution containing the metal

ions is transformed into a gel by adding an organic solvent such as an alcohol. The gel is then

decomposed at relatively low temperatures to obtain the desired oxide, generally in a particulate

form. Materials prepared by such low-temperature methods may need to be annealed or heated

under suitable conditions in order to obtain the desired oxygen stoichiometry as well as the

characteristic high Tc

One of the problems in the case of the 123 compounds is that they lose oxygen easily.

It therefore becomes necessary to heat the material in an oxygen atmosphere at an appropriate

temperature. Large-scale preparation of ceramic powders of 123 cuprates and related materials

is itself not easy: the processing parameters involved in the synthesis of ceramic materials are

not well understood. This, in addition to the difficulty faced with the oxygen stoichiometry,

makes large-scale synthesis of 123 cuprates quite challenging. Oxygen stoichiometry is,

however, not a problem in the bismuth cuprates. The problem with bismuth cuprates is the

difficulty in obtaining phasic purity (minimizing the intergrowth of the different layered phases.


26

2. Glass or the melt route yields good materials

Many other techniques have been used to synthesize cuprates superconductors. In the

case of bismuth cuprates, the glass or the melt route yields good materials. The method involves

preparing a glass by quenching the melt; the glass is then crystallized by heating it above the

crystallization temperature. Thallium cuprates are best prepared in sealed tubes (gold or silver).

Heating T1203 with a matrix of the other oxides (already heated to 1100 -1200 K) in a sealed

tube is preferred by some workers. It is important that thallium cuprates are not prepared in

open furnaces since Tl203, which sublimes readily, is highly toxic.

Heating oxidic materials under high oxygen pressures or in flowing oxygen, often becomes

necessary to obtain the required oxygen stoichiometry. Thus, La2Cu04 and La2CaSr2Cu206

heated under high oxygen pressure become superconducting, with Tcs of 40 and 80 K,

respectively. The 124 superconductors were first prepared under high oxygen pressures. It was

later found that heating the oxide or nitrate mixture in the presence of Na2O2 in flowing oxygen,

is sufficient to obtain 124 compounds. In the case of the electron superconductor Nd2 x CexCu04,

it is necessary to ensure that there is no oxygen excess; otherwise, the electron given by Ce will

merely go into giving an oxygen-excess material. For this purpose, it is recommended that Nd2

x CexCu04 first be prepared by a suitable method, and then reduced with hydrogen.

3. Single crystals of cuprate superconductors

Single crystals of cuprate superconductors are necessary to make good physical

measurements. Crystals of 123 compounds and bismuth cuprates have been grown using an

appropriate flux. However, it is rather difficult to grow large crystals of these materials.

5.2 Different methods of Preparation of Cuprate Materials

Superconducting materials for electronic applications have to be prepared in the form of

films. Thin film prepared by a variety of techniques such as electron- beam evaporation, radio-

frequency sputtering, magnetron sputtering, microwaved plasma, plasma spray and chemical

vapour deposition.


27

1. Electron- beam evaporation

Fig.1 Rotating crucible with pellets of oxide materials for electron- beam

evaporation

Fig. 2 Multi-target evaporation using an effusion cell for evaporating the

materials

A technique of making superconducting cuprate films is shown in Fig. 1 and 2. Such thin

films are deposited on a sutabile substrate. In order to make films of metallic alloys by evaporation

techniques, targets of the different metals involved can be used to obtain the required


28

compositions. In the case of oxide materials, multi-metallic films are oxidised to obtain the desired

material. The target of the oxide can also be used directly to obtain films.

2. High-pressure oxygen sputtering system

Fig. 3 High-pressure oxygen sputtering system

The process of High-pressure oxygen sputtering system is shown in Fig. 3. In this

system oxygen bombarded to the target. In the chemical vapour deposition technique,

organometallic derivatives are employed to deposit the required quantities of the metals on a

given film which is then processed to give the desired produce of cuprates, oxidation of the

organometallics is carried out. High-pressure sputtering is especially useful in preparing

stoichiometric oxide superconductor films.


29

3. Laser ablation method

Laser ablation method has become quite successful in preparing film superconductors.

The working process of Laser ablation method is shown in Fig. 4. Formula units (e.g.

YBa2Cu3O7 of the cuprates can be deposited directly onto the substrate by using an excimer

laser.

Fig. 4 Laser ablation method

The substrates used for cuprates are generally oxides (e.g. SrTi03). Employing single-

crystal substrates, one can get oriented, epitaxial films. Once a film is prepared, its composition is

determined by techniques such as Rutherford back- scattering, Auger spectroscopy and

Photoelectron spectroscopy. In Fig. 5, the resistivity and critical current behavior of a film of

YBa2Cu3O7 illustrates the excellent quality of films that have been obtained.

5.3 Conclusion

If the superconducting materials are to be used in magnet or power applications, it becomes

necessary to make them in the form of wires or tapes. Drawing wires, in the case of metals and

alloys (even if somewhat brittle as in some of the Nb alloys), is not very difficult. The situation is,

however, altogether different with oxide ceramics such as the cuprates. However, altogether

different with oxide ceramics such as the cuprates. Various ways of making wires and tapes have


30

been developed for these materials. To draw wires, one generally packs a silver or a copper tube,

open at one end, with the cuprate. The packed tube is sealed and then drawn into wire form by

extrusion. In the case of the 123 cuprates, oxygen treatment becomes necessary after the wire is

drawn to obtain the desired stoichiometry. Reasonably good tapes (oriented, in some cases) of 123

cuprates as well as of Bi cuprates have been made.


31

Practical 6: Theories of Superconductivity-I

6.1 London Equation & Hypothesis:

The London equations, developed by brothers Fritz and Heinz London in 1935, relate

current to electromagnetic fields in and around a superconductor.

Arguably the simplest meaningful description of superconducting phenomena, they form

the genesis of almost any modern introductory text on the subject. A major triumph of the

equations is their ability to explain the Meissner effect, wherein a material exponentially expels

all internal magnetic fields as it crosses the superconducting threshold.

There are two London equations when expressed in terms of measurable fields:

Here is the superconducting current density, E and B are respectively the electric and

magnetic fields within the superconductor, is the charge of an electron & proton, is electron

mass, and is a phenomenological constant loosely associated with a number density of

superconducting carriers.

On the other hand, if one is willing to abstract away slightly, both the expressions above

can more neatly be written in terms of a single "London Equation" in terms of the vector

potential A:


32

The last equation suffers from only the disadvantage that it is not gauge invariant, but is

true only in the Coulomb gauge, where the divergence of A is zero. This equation holds for

magnetic fields that vary slowly in space

6.2 Penetration Depth & Meissner Effect:

If the second of London's equations is manipulated by applying Ampere's law,

Then, the result is the differential equation

Thus, the London equations imply a characteristic length scale, over which external

magnetic fields are exponentially suppressed. This value is the London penetration depth.

Simple example geometry is a flat boundary between superconductors within free space

where the magnetic field outside the superconductor is a constant value pointed parallel to the

superconducting boundary plane in the z direction. If x leads perpendicular to the boundary then

the solution inside the superconductor may be shown to be

From here the physical meaning of the London penetration depth can perhaps most easily

be discerned.


33

6.3 Rigidity of Wave Function:

The defining property of a solid object is its rigidity, or resistance to mechanical

deformation. A superconductor is characterized by an analogous rigidity, but in a more abstract

quantity, namely the phase of its wave function.

The superconducting state is well-described by a complex wave function yexp[iq(r)] that

exists throughout the superconducting region. (The amplitude y, which measures the density of

superconducting of electrons in the sample, is not important for this discussion.) In the absence

of currents, the phase q(r) strongly resists deformation (it prefers to be uniform

throughout). Experiments that manipulate the phase, however, can reveal many interesting

phenomena that are highly specific to the superconducting state.

In a solid, rigidity implies that potential energy is stored when the solid is bent. A dramatic

consequence is the mechanical resonance in which the potential energy oscillates 180o out-of-

phase with the kinetic energy of the vibrating sub-components. In a tuning fork or a gong, the

resonant oscillation can persist for a very long time (high Q-factor).

A very important property of the superconducting state is that, when a super

current Js flows (say, parallel to z), the phase advances at a rate proportional to the magnitude

of Js, viz. dq/dz ~ Js. In the figure above, the value of q(r) at each point r is indicated by the arrow

on the dial. In the direction of Js, the phase advances in an anticlockwise sense viewed from the

left. (If Js is absent, all the dials will show the same value, selected spontaneously.) By

increasing Js, one may increase the pitch of the phase winding (and the energy stored), much as

one winds up a watch.

Fig. 5.1 Supercurrent and phase difference


34

The cuprate superconductors grow as a stack of copper-oxide layers. In this layered

structure, the phase stiffness is highly anisotropic. Within each layer, the phase stiffness is so large

that the phase may be assumed to be uniform. Between layers, however, the phase stiffness is

much weaker, so q(r) may fluctuate between layers with less cost. (The solid analog is a stack of

plates connected by soft springs.) If the phase difference between adjacent layers is dq, the cost

incurred (per unit area) is written as

For simplicity, we consider just two layers (blue squares in figure). We have a parallel-

plate capacitor that allows a weak supercurrent Js (green arrow) to flow between the layers. From

the discussion above, Js leads to a phase difference dq between the layers (compare yellow dials),

which produces the potential energy Uf. Since it transfers Cooper pairs, Js also leads to a charge

unbalance dQ, which increases the electrostatic energy by

(C is the capacitance per unit area). The charging energy UQ oscillates out-of-phase with

the potential energy Uf. The total energy (Hamiltonian) of the system is

Where, we have written dQ = 2ne as the number n of Cooper pairs transferred (with e the

elementary charge). The second term is the stiffness energy Ufvalid for large phase deviation.

6.4 Flux Quantization:

Flux quantization is a quantum phenomenon in which the magnetic field is quantized in

the unit of , also known variously as flux quanta, fluxoids, vortices or fluxons.

Flux quantization occurs in Type II superconductors subjected to a magnetic field. Below

a critical field Hc1, all magnetic flux is expulsed (force out of body) according to the [Meissner

effect] and perfect diamagnetism is observed, exactly as in a Type I superconductor. Up to a second


35

critical field value, Hc2, flux penetrates in discrete units while the bulk of the material remains

superconducting. Both critical fields are temperature dependent, and tabulated values are the zero-

temperature extrapolation unless otherwise noted.

This quantization of the magnetic flux is observed in superconductors. Superconductivity

is theorized to be due to a special correlation between pairs of electrons that extends over the whole

body of the superconductor.

When a Type I superconductor is placed in a magnetic field and cooled below its critical

temperature, it excludes all magnetic flux from its interior. This is called the Meissner effect. If

there is a "hole" in the superconductor, then flux can be trapped in this hole. The flux trapped in

the hole must be quantized. It has been experimentally verified that the trapped flux is quantized

in units of elementary flux quanta, thus verifying that the charge carriers in superconductors are

indeed correlated electron pairs of charge 2e.

A possible solution is A=eM(1-cosq)/(rsinq) in the f-direction. But A is singular on the

negative z-axis at q=p. If we consider A just a device for obtaining B, then we can construct a pair

of vector potentials.


36

Practical 7: Theories of Superconductivity-II

7.1 GinzburgLandau theory

In physics, GinzburgLandau theory, named after Vitaly Lazarevich Ginzburg and Lev Landau,

is a mathematical physical theory used to describe superconductivity. In its initial form, it was

postulated as a phenomenological model which could describe type-I superconductors without

examining their microscopic properties.

Based on Landau's previously-established theory of second-order phase

transitions, Ginzburg and Landau argued that the free energy, F, of a superconductor near the

superconducting transition can be expressed in terms of a complex order parameter field, , which

is nonzero below a phase transition into a superconducting state and is related to the density of the

superconducting component, although no direct interpretation of this parameter was given in the

original paper. Assuming smallness of || and smallness of its gradients, the free energy has the

form of a field theory.

where Fn is the free energy in the normal phase, and in the initial argument were treated as

phenomenological parameters, m is an effective mass, e is the charge of an electron, A is

the magnetic vector potential, and is the magnetic field. By minimizing the free

energy with respect to variations in the order parameter and the vector potential, one arrives at

the GinzburgLandau equations

where j denotes the dissipation-less electrical current density and Re the real part. The first

equation which bears some similarities to the time-independent Schrdinger equation, but is

principally different due to a nonlinear term determines the order parameter, . The second

equation then provides the superconducting current.


37

7.2 Simple interpretation

Consider a homogeneous superconductor where there is no superconducting current and the

equation for simplifies to:

This equation has a trivial solution: = 0. This corresponds to the normal state of the

superconductor, that is for temperatures above the superconducting transition temperature,T>Tc.

Below the superconducting transition temperature, the above equation is expected to have a non-

trivial solution (that is 0). Under this assumption the equation above can be rearranged into:

When the right hand side of this equation is positive, there is a nonzero solution for (remember

that the magnitude of a complex number can be positive or zero). This can be achieved by assuming

the following temperature dependence of : (T) = 0 (T - Tc) with 0 / > 0:

Above the superconducting transition temperature, T > Tc, the expression (T) / is

positive and the right hand side of the equation above is negative. The magnitude of a

complex number must be a non-negative number, so only = 0 solves the Ginzburg

Landau equation.

Below the superconducting transition temperature, T < Tc, the right hand side of the

equation above is positive and there is a non-trivial solution for . Furthermore

that is approaches zero as T gets closer to Tc from below. Such a behaviour is typical for a second

order phase transition.

In GinzburgLandau theory the electrons that contribute to superconductivity were proposed to

form a superfluid. In this interpretation, ||2 indicates the fraction of electrons that have condensed

into a superfluid.


38

7.3 Coherence length and penetration depth

The GinzburgLandau equations predicted two new characteristic lengths in a superconductor

which was termed coherence length, . For T > Tc (normal phase), it is given by

While for T < Tc (superconducting phase), where it is more relevant, it is given by

It sets the exponential law according to which small perturbations of density of superconducting

electrons recover their equilibrium value 0. Thus this theory characterized all superconductors by

two length scales. The second one is the penetration depth, . It was previously introduced by the

London brothers in their Lonrdon theory. Expressed in terms of the parameters of Ginzburg-

Landau model it is

where 0 is the equilibrium value of the order parameter in the absence of an electromagnetic field.

The penetration depth sets the exponential law according to which an external magnetic field

decays inside the superconductor.

The original idea on the parameter "k" belongs to Landau. The ratio = / is presently known as

the GinzburgLandau parameter. It has been proposed by Landau that Type I

superconductors are those with 0 < < 1/2, and Type II superconductors those with > 1/2.

The exponential decay of the magnetic field is equivalent with the Higgs mechanism in high-

energy physics.


39

Practical 8: Study of Josephson Effect and the BCS theory

8.1 Type II superconductivity

Superconductors made from alloys are called Type II superconductors. Besides being

mechanically harder than Type I superconductors, they exhibit much higher critical magnetic

fields. Type II superconductors such as niobium-titanium (NbTi) are used in the construction of

high field superconducting magnets.

Type-II superconductors usually exist in a mixed state of normal and superconducting regions.

This is sometimes called a vortex state, because vortices of superconducting currents surround

filaments or cores of normal material.

Fig. Behavior of type II super conductors

Type II superconductors usually exist in a vortex state with normal cores surrounded by

superconducting regions. This allows magnetic field penetration. As their critical temperatures are

approached, the normal cores are more closely packed and eventually overlap as the

superconducting state is lost.

At the lower of the two critical magnetic fields in a Type II superconductor, magnetic fields begin

to penetrate through cores of normal material surrounded by superconducting current vortices. As

long as these vortices are stationary (pinned), the magnetic fields can penetrate while still

maintaining zero electric resistivity paths through the material. While the Meissner effect is

modified to allow magnetic fields through the normal cores, magnetic fields are still excluded from

the superconducting regions.


40

Fig. Vortex state of type II super conductors

As the temperature or the external magnetic field is increased, the normal regions are packed closer

together. The vortices feel a force when current flows, and if they move, the superconducting state

is lost.

Abrikosov found that the interface energy is negative in a class of Superconductors above a certain

external magnetic field, and that the magnetic field penetrates in form of quantized flux tubes. The

flux associated with each tube is given by

0 = = 2

To see how this results arises, consider the superconductor penetrated by a flux tube which is

cylindrical, with the axis along the field direction. The field is maximum along the axis and

decreases to zero along the radius (in the plane perpendicular to the axis) in a distance of the order

of the penetration depth. Also shown in the order parameter which is zero along the axis (the field

being highest there) and which rises to its equilibrium value in radial distance 0.

Fig. a superconductor with a hole


41

The interface energy or the energy of flux tube is roughly the sum of two terms: the

superconductivity energy loss due to a region of volume 20 per unit length of tube becoming

normal, and the magnetic field energy gain due to volume 2 (per unit tube length again) admitting

the field B. the total flux tube energy or the normal-superconducting interface energy per unit tube

length works out to be

=

2

800

2 2

802

The vortex state has zero electrical resistivity if the flux tubes are prevented from moving in

response to an external electric field, if they move the normal core regions of vortex also move,

this would roughly be like pieces of the normal metal electrons drifting in an external field. Such

a drift or current causes ohmic heat loss; the system has nonzero electrical resistance. Flux tubes

can be prevented from moving if there are specific regions where it is energetically favorable for

them to be. The flux tube are then stuck or pinned to this regions. This is called flux pinning. In

technologically important type II superconductors, critical current densities of the order of 106

A/cm2 are possible, especially in good quality thin films or single crystal.

8.2 Josephson Effect

When two superconductors are separated by a very thin insulating layer, quite unexpectedly, a

continuous electric current appears, the value of which is linked to the characteristics of the

superconductors. This effect was predicted in 1962 by Brian Josephson. Since then, this

superconductor-insulator-superconductor sandwich has been called a Josephson junction.

When a material becomes superconducting, the electrons form Cooper pairs and condensate in the

shape of a unique collective quantum wave. If the electric insulator separating the two

superconductors is very thin (only a few nanometers), then the wave can somehow spill out of the

superconductor, which enables the electron pairs to go through the insulator thanks to a quantum

effect called tunneling effect. When spontaneously going from one superconductor to the other,

the pairs create an electric current. Each superconductor is characterized by a quantity called phase,

with a subtle signification. The electric current in the junction is a continuous current, the value of

which is proportional to the sine of the phase difference between the two superconductors.


42

Now, if we apply a constant electric tension difference between the two superconductors, an

alternating electric current appears, in reaction to the phase variations. This effect that links a

continuous voltage to an alternating current is unusual. Especially since the frequency of

alternating currents depends neither on the size of the superconductors, nor on their properties

(critical temperature, chemical composition). This frequency only depends on the applied voltage

and on fundamental permanent features (the electric charge of the electron and Planck quantum of

energy). We can measure a frequency very precisely thanks to atomic clocks, but until this effect

was discovered, we could not precisely measure a voltage. The Josephson Effect enables us to

define a reference value of the voltage that is then used to calibrate the measuring devices and to

make sure that one volt has the same value in France and in Japan.

Josephson effects are very sensitive to the value of the magnetic field, because the phase variation

of a superconductor can be linked to the magnetic flux. It then becomes possible to use this

magnetic field sensitivity to build very accurate magnetic field measuring devices, called squids:

these devices are the most precise means to measure a magnetic field.

8.3 The BCS theory

In 1957, more than 40 years after the discovery of superconductivity, three physicists, Bardeen,

Cooper and Schrieffer, finally found the correct explanation to superconductivity in metals. In a

theoretical model (that has since been called BCS, after their initials), they proposed the

following explanation: electrons form a collective quantum state made up of pairs of electrons of

opposite spin and momentum. This remarkable state, called a pair condensate, explained all known

superconducting properties and made possible the prediction of new ones. It helps predict

the behavior of characteristic lengths. This BCS theory has since been proven by numerous

experiments in metals and alloys. But it cannot apply straightforward in the case of some new

superconductors such as cuprates or pnictides, and scientists are still working on finding new

explanations for these materials.

The main idea of the BCS theory relies on the quantum nature of electrons. In a metal, electrons

are waves. Each of these electrons is relatively independent and follows its own path independent

of other electrons. In a superconductor, the majority of these electrons merge in order to form a

large collective wave. In quantum physics, we call it macroscopic quantum wave function,

or condensate. When the collective wave is formed, it requires each member to move at the same


43

speed. In a metal, an individual electron is easily diverted by a flaw or an atom that is too big. In

a superconductor however, this same electron can be diverted only if, at the same time, all the

other electrons of the collective wave are diverted in the exact same manner. The flaw in a single

atom surely cannot do that; the wave will not be diverted, and, thus, not slowed down. It

superconducts!


44

Practical 9: Application of superconductivity-1

The major focus of this practical is application of superconductivity on magnets and transportation.

It describes how superconductivity is applied in magnets & speed-up the transportation.

9.1 Magnets :

In the case of magnets it is applicable to following aspects.

High field Magnet applications

Nuclear magnetic resonance (NMR), medical diagnostics and spectroscopy.

Ore refining ( magnetic separators )

Magnetic levitation

Magnetic shielding

Large physics machines

Nuclear magnetic Resonance:

Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy, is a

research technique that exploits the magnetic properties of certain atomic nuclei. It determines the

physical and chemical properties of atoms or the molecules in which they are contained. It relies

on the phenomenon of nuclear magnetic resonance and can provide detailed information about the

structure, dynamics, reaction state, and chemical environment of molecules. The intramolecular

magnetic field around an atom in a molecule changes the resonance frequency, thus giving access

to details of the electronic structure of a molecule.

Magnetic Separators:

Another application related to production of magnetic fields is in magnetic separation.

Ordinary electromagnets have long been used for the processing of coal and other mineral raw

materials to remove impurities. By passing the solid crushed materials through a magnetic field,

magnetic particles in the materials can be diverted and collected. With high-strength magnetic

fields, this technique can also be used in other processes such as the removal of toxic metals from

water and the recovery of metallic crystals from chemical reactors.


45

In the recent past the problem of removing the deleterious iron particles from a process stream had

a few alternatives. Magnetic separation was typically limited and moderately effective. Magnetic

separators that used permanent magnets could generate fields of low intensity only. These worked

well in removing ferrous tramp but not fine paramagnetic particles. Thus high-intensity magnetic

separators that were effective in collecting paramagnetic particles came into existence. These focus

on the separation of very fine particles that are paramagnetic.

The current is passed through the coil, which creates a magnetic field, which magnetizes the

expanded steel matrix ring. The matrix material being paramagnetic behaves like a magnet in the

magnetic field and thereby attracts the fines. The ring is rinsed when it is in the magnetic field and

all the non-magnetic particles are carried with the rinse water. Next as the ring leaves the magnetic

zone the ring is flushed and a vacuum of about 0.3 bars is applied to remove the magnetic

particles attached to the matrix ring.

Fig.2 Magnetic Separator


46

Magnetic Levitation:

Magnetic levitation, maglev, or magnetic suspension is a method by which an object

is suspended with no support other than magnetic fields. Magnetic force is used to counteract the

effects of the gravitational and any other accelerations. The two primary issues involved in

magnetic levitation are lifting force: providing an upward force sufficient to counteract gravity,

and stability: ensuring that the system does not spontaneously slide or flip into a configuration

where the lift is neutralized

Magnetic levitation is used for maglev trains, contactless melting, and magnetic bearings and for

product display purposes.

Magnetic Shielding:-

Electromagnetic shielding is the practice of reducing the electromagnetic field in a space by

blocking the field with barriers made of conductive or magnetic materials. Shielding is typically

applied to enclosures to isolate electrical devices from the 'outside world', and to cables to isolate

wires from the environment through which the cable runs. Electromagnetic shielding that

blocks frequency electromagnetic is also known as RF shielding.

Fig.3 A superconductor levitating a permanent magnet

The shielding can reduce the coupling of radio waves, electromagnetic fields and electrostatic

fields. A conductive enclosure used to block electrostatic fields is also known as a Faraday cage.

The amount of reduction depends very much upon the material used, its thickness, the size of the

shielded volume and the frequency of the fields of interest and the size, shape and orientation of

apertures in a shield to an incident electromagnetic field.


47

9.2 Transportation:

In case of transportation it is applicable to following aspects.

High-speed trains

Ship-drive systems.

High-speed trains:-

An efficient production of high strength field for holds promise for applications in transportation,

the most important one being in magnetically levitated rail transportation. Maglev transportation

uses magnetic repulsion to lift and hold a train a short distance above the track, thus eliminating

traction resistance and leaving only the wind resistance to be overcome by the moving train.

Maglev (derived from magnetic levitation) is a transport method that uses magnetic levitation to

move vehicles without touching the ground. With maglev, a vehicle travels along a guide way

using magnets to create both lift and propulsion, thereby reducing friction and allowing higher

speeds.

The Shanghai Maglev Train, also known as the Transrapid, is the fastest commercial train currently

in operation and has a top speed of 430km/h. The line was designed to connect Shanghai Pudong

International Airport and the outskirts of central Pudong, Shanghai. It covers a distance of 30.5

kilometres in 8 minutes.

Maglev trains move more smoothly and more quietly than wheeled mass transit systems. They are

relatively unaffected by weather. The power needed for levitation is typically not a large

percentage of its overall energy consumption most goes to overcome drag, as with other high-


48

speed transport. Maglev trains hold the speed record for rail transportation. Vacuum tube

train systems might allow maglev trains to attain still higher speeds, though to date no such vacuum

tubes have been built commercially.

Compared to conventional trains, differences in construction affect the economics of maglev

trains. For high-speed wheeled trains, wear and tear from friction along with the "hammer effect"

from wheels on rails accelerates equipment wear and prevents higher speeds conversely, maglev

systems have been much more expensive to construct, offsetting lower maintenance costs.

Ship-drive systems:-

The second application would be in magnetic ship propulsion. Here there are no moving parts. A

superconducting magnets creates a magnetic field on-board and the surrounding water gets

charged with an electric current from the ship. The current creates its own magnetic field and the

interaction between the two fields drives the ship forward. The use of conventional propellers in

ship gives rise to an inherent limitation in the speed. Because of cavitation, the rapid formation

and collapse of vapour speeds can, in theory, be attained. HTSCs offer the possibility of drastically

reducing the weight of the propelling equipment.

Within the past 20 years, ship designers have begun to adopt electric propulsion systems.

This shift has been characterized as the most important change in ship design since the adoption

of diesel engines in the 1920s. Electric propulsion systems enable new, more flexible arrangements

and the more efficient integration of a ships energy-using systems, because they allow the same

power plant to support propulsion as well as other requirements. As a result, ships can be

redesigned to provide more space below deck, whether for passengers, cargo or, in the case of

naval applications, weapons and weapon systems. Among large commercial ocean-going vessels,

nearly 100% of all new ships are electrically propelled, including many large cruise ships, such as

the Queen Mary 2. Electric propulsion offers other advantages for naval applications, and in 2000,

the U.S. Navy announced that it would migrate toward an all-electric fleet.


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Practical 10: Application of Superconductivity-2

10.1 Energy-related

Several applications of superconductivity in the electric power sector have undergone extensive

evaluation and even prototype development: e.g., fusion magnets, generators, superconducting

magnetic energy storage (SMES), and AC transmission lines. An overview of the impact of

superconductivity on these applications is provided in table 3-1. Other applications not discussed

here include magneto hydrodynamic power generation, transformers, motors, and power

conditioning electronics.

Fusion Magnets

Magnetic fusion requires confinement of a heated plasma in a magnetic field long enough to get it

to igniteabout 1 second. Superconducting magnets are considered essential for the continuous,

high field operation that would be necessary for a commercial fusion reactor. Like particle

accelerator magnets, Federal fusion magnet programs have provided a significant government

market that has driven the development of superconducting magnet technology. As a result, there

are no major unsolved technical problems in the fabrication of large fusion magnets. The lack of

follow through on these programs can be attributed to technical, economic, and political issues

affecting fusion technology. Because magnet refrigeration costs are less than 1 percent of total

construction costs, the advent of HTS is not expected to change the outlook for fusion.

Superconducting Generators

Superconducting generators enjoy three potential benefits over conventional generators. They

offer better system stability against frequency changes due to transients on the grid. Because they

can operate at higher magnetic fields (5 to 6 tesla), the size can be reduced up to 50 percent; this

in turn could reduce capital costs significantly. Finally, efficiency could be increased by 0.5

percent (a reduction in losses of around 50 percent). Even this small efficiency increase could

result in fuel savings that would pay back the capital costs of the generator over its lifetime.14

Although several prototype superconducting generators were designed and constructed at the

Massachusetts Institute of Technology, General Electric Co., and Westinghouse Electric Corp.

during the 1960s to the early 1980s,15 these were never commercialized because there was no

perceived demand for new generating capacity.lb Today, the United States has no significant


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ongoing commercial LTS generator program, although programs are continuing in West Germany,

Japan, and the Soviet Union. Siemens in West Germany is proceeding with plans for an 850

megawatt (MW) commercial system, and tests of prototype components are expected to begin in

1990.17 A consortium of Japanese companies is developing a 200 MW generator for the late

1990s.

Superconducting Magnetic Energy Storage (SMES)

In an SMES system, electric power is stored in the magnetic field of a large superconducting

magnet, and can be retrieved efficiently at short notice. Power conditioning systems are required

to convert the DC power in the magnet to AC for the grid when discharging the SMES, and vice

versa when recharging. SMES has several potential applications in electric utilities. Large units

(above 1 GW-hr capacity) could be used for diurnal storage and load leveling. Smaller units may

provide a number of operating benefits: e.g., spinning reserve, automatic generation control, black

start capability, and improved system stability.

SMES is also of interest to the military because it can deliver large quantities of pulsed power to

weapon systems such as ground-based lasers for ballistic missile defense. The Strategic Defense

Initiative Organization (SDIO) is presently supporting the development of a 20 MW-hr/400 MW

engineering test model (ETM), which could begin tests by 1993.20 Because the military design

and the utility design are similar except for the power conditioning system (weapons must receive

large amounts of power quickly and may drain the SMES in a very short time; utilities must have

a constant reliable supply from which smaller amounts of power are withdrawn on a daily basis),

utilities are providing a small percentage of the funding through the Electric Power Research

Institute.

Power Transmission Lines

Interest in superconducting power transmission lines dates back to the 1960s, when demand for

electricity was doubling every 10 years. There was great concern about where large new power

plants could be sited safely--specially nuclear plants and about how such large amounts of power

could be transmitted to users without disrupting the environment. Overhead lines often cut swathes

through wooded areas and spoil scenery. Underground lines, a solution to environmental concerns,

have other problems. Conventional underground cables are about 10 times more expensive than


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overhead lines, and consequently account for only 1 percent of the transmission lines in the United

States. Moreover, because of heat dissipation and line impedance problems, these lines are limited

to small capacities and short distances.

10.2 Electronics and small devices

Superconducting circuits offer several advantages over conventional semiconducting devices,

including higher switching speeds, lower power dissipation, extreme detection sensitivity, and

minimal signal distortion. There has been a long history of LTS R&Din electronic devices in the

United States, primarily sponsored by the Department of Defense with some support from the

National Bureau of Standards (now the National Institute of Standards and Technology). As a

result of this effort, several LTS electronic devices are now readily available, including SQUID

magnetometers, Josephson voltage standards, millimeter wave mixers, and fast data sampling

circuits

Digital Devices and Computers

Digital devices are those that manipulate information with discrete levels ( 1s or Os) rather

than over a continuous range, as does an analog device. Present superconducting digital circuits

rely on the on/off switching of Josephson Junctions (JJs) to create these discrete levels, unlike

semiconductor digital circuits, which use transistors. Development of a practical superconducting

transistor remains a major research goal, but such a device has not yet been invented.

Computer applications of superconductors include logic gates , memories , and interconnects. In

principle, a computer based on JJs could be several times faster and 100 times smaller than present

computers, though this application is somewhat speculative (see below). Meanwhile, the same

devices required for JJ computer circuits can also be used in less demanding, smaller scale

applications, e.g., fast analog-to-digital converters, shift registers, and memories, as well as circuits

to perform arithmetic operations.

Thus, a role for HTS in computers is possible in the future, but it is somewhat uncertain. Much

depends on the development of technologies for controlling the properties of surfaces and

junctions, which are still fairly primitive for HTS.


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Analog Devices

Analog circuits provide a continuous range of signal level, in contrast to the discrete nature of

digital circuits. Analog devices that have already been fabricated with LTS include SQUIDS,

microwave and millimeter wave components for detection, amplification, and processing of

signals in the 10 to 200 GHz range, voltage standards, and infrared detectors.

SQUIDS are considered to be one of the most promising HTS devices in the near term. Magnetic

field sensors based on SQUIDS potentially have wide applications in

advanced super conductivity and cryogenics

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