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A thin flake of ordinary carbon, just one atom thick, lies behind this year’s Nobel Prize in Physics. Andre Geim and Konstantin Novoselov have shown that carbon in such a flat form has exceptional properties that originate from the remarkable world of quantum physics.

A d G i K t ti N lAndre GeimBorn: 1958, Sochi, Russia University of Manchester

Konstantin NovoselovBorn: 1974, Nizhny Tagil, RussiaUniversity of Manchester

Prize motivation: "for groundbreaking experiments regarding the two-dimensional material graphene"

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1 Department of Physics, University of Manchester, Manchester M13 9PL, UK.2 Institute for Microelectronics, Technology, 142432 Chernogolovka, Russia.* To whom correspondence should be addressed. E-mail: geim@man.ac.uk

We describe monocrystalline graphitic films which are a few atoms thick but are nonetheless stableWe describe monocrystalline graphitic films, which are a few atoms thick but are nonetheless stable under ambient conditions, metallic, and of remarkably high quality. The films are found to be a two-dimensional semimetal with a tiny overlap between valence and conductance bands, and they exhibit a strong ambipolar electric field effect such that electrons and holes in concentrations up to 1013 per square centimeter and with room-temperature mobilities of ~10,000 square centimeters per volt-second can be induced by applying gate voltage.

What is Graphene?

The term “graphene” was first used in 1987, referring to a single layer of graphite within a larger compound (Mouras, 1987)

(A) Allotropes of carbon

http://earthobservatory.nasa.gov/Features/CarbonCycle/carbon_cycle4.php

Carbon is the most important element in the ecosystem (12th

most abundant

element).

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Carbon can form structures from zero to three-dimensions

Diamond

Dimensionality is one of the most defining material parameters. The various structural forms of carbon (polymorphism) give carbon a unique variety of properties and applications.

(B) Graphene

G h i i l l f Graphene is a single layer of carbon packed in a hexagonal (honeycomb) lattice, with a carbon-carbon distance of 0.142 nm. It is the first truly two-dimensional crystalline material.

Graphene is a basic building block for graphitic materials of all otherdimensionalities

Graphene

Bilayer graphitic films

GraphiteGraphite

“Graphene is stronger and stiffer than diamond, yet can be stretched by a quarter of its length, like rubber. Its surface area is the largest known for its weight.” - Andre Geim

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(C) Bonding in graphene

Electronic configuration: 1s22s22p2

Orbital HybridizationOrbital Energy

In graphene, sp2 hybridized orbitalsare responsible for bonding in the x-y plane, while the remaining 2p orbital exists perpendicular to the plane, contributing 1 conduction electron per C atom.

(D) Crystal lattice of graphene

Direct lattice

R i l l ttiReciprocal lattice

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Why is Graphene Interesting and Significant?

Graphene is the first truly 2-dimensional material that is stable at room temperature. It is believed that graphene will bring revolutionary changes in microelectronics, material science and theoretical physics.

Imagine a piece of paper but a million times thinner. This is how thick graphene is.

Imagine a material stronger than diamond. This is how strong graphene is (in the plane).

Imagine a material more conducting than copper. This is how conductive graphene is

A quote from Andre Geim:

graphene is. Imagine a machine that can test the same physics that scientists test in, say,

CERN, but small enough to stand on top of your table. Graphene allows this to happen.

Having such a material in hand, one can easily think of many useful things that can eventually come out. As concerns new physics, no one doubts about it already…

Landau (1937) and Peierls (1935) argued that strictly 2D crystals were thermodynamically unstable and could not exist. Their theory pointed out that a divergent contribution of thermal fluctuations in low-dimensional crystal lattices should lead to such displacements of atoms that they become comparable to interatomic distances at any finite t t

(A) The difficulties of obtaining 2-dimensional crystals

temperature.

The argument was later extended by Mermin (1968) and is strongly supported by many experimental observations.

The melting temperature of thin films rapidly decreases with decreasing thickness, and the films become unstable (segregate or decompose) at a thickness of, typically, dozens of atomic layers.

Before Geim’s team observed the single atomic layer graphene, it was believed that true 2D materials could never exist, because it was thought that any atomic monolayer would have to roll or fold in order to achieve its lowest potential energy. `

p ) , yp y, y

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- Using electron microscopy it has been observed that within graphenemonolayers small ripples exist. These imperfections are believed to prevent graphene from rolling and also help to suppress thermal vibrations.

Why is monolayer graphene stable?

- The strong interatomic bonds ensure that thermal fluctuations cannot lead to the generation of dislocations or other crystal defects even at room temperature.

(B) The electronic configuration of graphene

The unique electrical properties of graphenecome from its electronic configuration, which is rather different from usual three-dimensional materials.

Its Fermi surface is characterized by six double cones In intrinsic (undoped) graphene the

Conduction band (empty)

Fermi level

Since the density of states of the material is zero at the Fermi level, the electrical conductivity of intrinsic graphene is quite low.

The Fermi level can however be changed by an

cones. In intrinsic (undoped) graphene the Fermi level is situated at the connection pointsof these cones.

kxValence band (full)

Fermi level

electric field so that the material becomes either n-doped (with electrons) or p-doped (with holes) depending on the polarity of the applied field.

The electrical conductivity for doped graphene is potentially quite high. Valence band

Conduction band

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Graphene’s electrical conductivity is unparalleled at room temperature, higher than silver (the least resistive metallic material).

Bi-layer graphene has a tunable band gap. Using an electrical field, bi-layer graphene can be changed from a conductor to a semiconductor.

= 0

Quantum mechanical tunneling in graphene

“Normal’ electrons:mass = mcannot reach the speed of lightkinetic energy =(1/2)mv2.

Massless elementary particles ( h t t i )

Classical particles: cannot propagate through potential barriers

Quantum particles: can propagate

(photon, neutrino):mass =0, speed = c

Electrons in graphenemass = 0speed cg ~ 106 m/s (constant)kinetic energy = cg p

- Mimicking relativistic behavior, but at a much lower speed c ~ c/300Quantum particles: can propagate

(tunnelling) but probability decays exponentially with barrier height and width

Ultrarelativistic quantum particles: can propagate with the probability of order of unity (Klein paradox)

at a much lower speed cg ~ c/300

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(C) Optical properties of graphene

Graphene is practically transparent. In the visible region it absorbs only 2.3% of the light. This number is given by πα,where, α=e2/(hc)=1/137, is the fine structure constant that sets the strength of the electromagnetic force.

-

(D) Thermal properties of graphene

The thermal conductivity of graphene is very high (much higher than that of silver).

Thermal conductivity measurement on graphene

Temperature is measured by micro-Raman spectroscopy

Diamond 900 – 2320

Aluminum 250Silver 429

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Graphene is the strongest known material. The extraordinary strength comes from the strong covalent carbon-carbon bond as well as the absence of defects in the 2-dimensional crystal.

(D) Elastic properties of graphene

Elastic property measurement on grapheneYoung’s modulus

- Graphene is much stronger than steel, very stretchable and can be

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used as a flexible conductor.

- The intrinsic strength of graphene can be considered as an 'upper bound' for the strength of materials that could serve as a goal for engineers who design materials.

- The measured mechanical properties of graphene can also serve as a benchmark to validate various theories and computer models.

How is Graphene Prepared?

The most commonly used method for obtaining single layer graphene is peeling from high quality graphite.

3 4 Å

Highly Ordered Pyrolytic Graphite

Graphene layers in graphite are held 3.4 Å

Single-layer graphene has delocalized electrons on each side. These electrons act as a barrier that prevents graphene from binding each other too tightly In the meantime these electrons can help graphene’s binding

together by weak van der Waals forces. Therefore, it is easy to peel layers off the bulk sample.

too tightly. In the meantime, these electrons can help graphene s binding to other surfaces.

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(A) Making graphene samples by mechanical exfoliationBy repeated peeling of flakes of highly oriented pyrolytic graphite, single and multiple layered graphene samples are obtained.

HOPG flakes Peel HOPG

Transfer graphenePieces to the substrate

Identify graphene samples under optical microscope

Peeling graphite with tapes has been done for a long time, but the peeled pieces have a wide range of thicknesses. An efficient technique to screen the samples for graphene was critical.

The breakthrough in getting single layer graphene was the observation that graphene becomes visible in an optical microscope with the color correlating to the number of layers (Novoselov et al. 2004). The sample was placed on top of a Si wafer with a carefully chosen thickness of SiO2, and the visibility comes from a feeble interference-like contrast with respect to an empty wafer.

The thickness of the SiO2 coating is critical, a 5% difference in the thickness can make single-layer graphene completely invisible.

Other (inefficient but can be more accurate) techniques that can be used to indentify single-layer graphene are AFM, SEM, TEM, Raman, and QHE.

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AFM image of graphene TEM image of graphene

SEM image of graphene. Two edge geometies

A step-by-step guide for preparing graphene samples

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(B) Making suspended graphene samples

What Are the Special Properties of Graphene?

The remarkable properties of graphene are due to several facts:

G h i l f t 2D t l Th f d i i d

Graphene has shown some extremely interesting properties that have not yet observed in any other materials.

- Graphene is a nearly perfect 2D crystal. The error-free ordering is due to the strong bonding of the carbon atoms. At the same time, the bonds are flexible (can be stretched to 120%). The lattice also enables electrons to travel long distances.

- The Fermi surface of graphene is situated at the connection points between conduction band and valence band. The Fermi level can be tuned by the application of an electric field.

- The electrons in graphene behave like massless particles, traveling at a constant speed. This opens up the possibility of studying certain phenomena more easily on a smaller scale, i.e. without the use of a large particle accelerator

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(A) Tunable electrical conductivityDensity of states

Graphene’ displays ambipolar electric field effect such that charge carriers can be tuned continuously between

l d h lelectrons and holes.

The charge carrier mobilities weakly depend on temperature. Even at 300 K the mobilities are still limited by impurity scattering.

Klaus von KlitzingNobel Prize 1985

(B) Quantum hall effect (QHE) in graphene

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The Quantum Hall Conductivity

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The QHE is an example of a quantum phenomenon occurring on a macroscopic scale. The QHE is exclusive to two-dimensional (2D) metals and has elucidated many important aspects of quantum physics and deepened our understanding of interacting systems.

As many other quantum phenomena, the observation of QHE usually requires very low temperatures T ~ 1 K.

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In graphene, QHE can be observed at room temperature. This is due to the highly unusual nature of charge carriers in graphene, which behave as massless relativistic particles (Dirac fermions) and move with little scattering under ambient conditions .

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What Are the Potential Applications of Graphene?

Graphene is a very attractive material for a wide range of applications due to its unusual properties: mechanically very strong, transparent, flexible, electrical conductivity tunable over a large range either by chemical doping or electric field.

(A) Electronic applications

- Super-Small Transistors : 1-nanometer graphene transistor is possible (one atom thick and 10 atoms across. The absolute physical limit of Moore’s Law). Graphene has the potential of replacing silicon as a semiconductor and becomes the base material for integrated circuits, ultra capacitors, and future electronic devices.

- High frequency electronic devices: The charge carrier mobilities of graphene are very high.

- Graphene based quantum computation: Low spin-orbit coupling in graphene may make it a ideal q-bit.

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(B) Material applications

- New composite materials: Composite materials based on graphenewill have great strength and low weight, which can be used for gasoline tanks, plastic containers, sports’ equipment, aircraft and automobile parts, wind turbines, and medical implants.

- Screens and coatings: Graphene is a transparent conductor, it can be d t t d ti l t d f t h li ht used as transparent conducting electrodes for touch screens, light

panels, solar cells, and organic light emitting devices.

- Energy storage: Graphene is capable of absorbing a large amount of hydrogen due to the large surface area, and it is possible to make energy storage devices based on graphene. Graphene powder can also be used in electric batteries, replacing graphite. The large surface-to-volume ratio and high conductivity can lead to improvements in the efficiency of batteriesimprovements in the efficiency of batteries.

(C) Sensing applications

- Gas sensors: Graphene can be an excellent material for solid-state gas detection. Its 2D structure, ability to store high amounts of hydrogen, and change in local electrical resistance makes molecule detection much easier.

(D) Fundamental physics applications

- Electrical resistance calibration: The quantum Hall effect in graphenecould also possibly contribute to an even more accurate resistance standard in metrology.

I ti t h i l h i t di i l - Investigate physical phenomena in two-dimensional space

- Provide experimental support for theoretical models of 2D systems.

- Investigate properties of high energy particles on desktop.

What Are the Challenges for Graphene Applications?

- High-quality, large area graphene sheets suitable for industrial g q y, g g papplications still remain to be demonstrated.

- Accurate control of individual features in graphene devices is still difficult. Such control will be necessary to provide sufficient reproducibility in their performance.

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