physics in 2d materials - université paris-saclay · 14 from two equations k k e e this can be...

Physics in 2D Materials

Taro WAKAMURA (Université Paris-Saclay)

Lecture 3

Today’s Topics

Lecture 3: Transition metal dichalcogenides (TMDCs)1

2.3 Graphene spintronics

3.1 Semiconducting TMDCs

3.2 Superconducting TMDCs

First of all... What is “spintronics”?

Electronics and Spintronics

Electron has: charge e Electronics

Electron has: spin 1/2 Spintronics

Spintronics in our daily lives

Magnetoresistive Random Access Memory

(MRAM)

Hard Disc Drive

(HDD)

How was spintronics born?

Spin polarized current

Ie ( = I↑ + I↓) ≠ 0

IS ( = I↑－I↓) ≠ 0

＝

Flow of charge and spinI↑： ↑spin current

I↓： ↓spin current

：Charge ：Spin

Spin-dependent transport

Currents

in ferromagnets

Birth of Spintronics

Giant Magneto-Resistance (GMR) effect

Peter Grunberg

Albert Fert

Nobel Prize in Physics in 2007

Nonmagnetic metal

Spin polarized current

Ie ( = I↑ + I↓) ≠ 0

IS ( = I↑－I↓) ≠ 0

＝

Flow of charge and spin

Pure spin current

＝IS ( = I↑－I↓) ≠ 0

Flow of spin only

I↑： ↑spin current

I↓： ↓spin current

：Charge ：Spin

Spin-dependent transport

Currents

in ferromagnets

?

Nonlocal spin injection and detectionEasiest way: lateral spin valves

charge current

+ spin current

spin accumulation

spin current

F side N side

Spin Polarized CurrentPure Spin Current

Spin Current

Lateral Spin Valve (LSV) structure

↑

↓

N F

VP

VAP

DV

-500 0 500

-1

0

Magnetic field [Oe]

DV

/I [

m

]

DR

V

Nonlocal spin injection and detection

10

-500 0 500

-1

0

Magnetic field [Oe]

DV

/I [

m

]

DR

Fitting equation

where

PI: spin polarization of tunneling

junction

lX: spin diffusion length of X

T. Wakamura et al., Appl. Phys. Exp. 4, 063002 (2011).

Nonlocal spin injection and detectionData evaluation

Key points of spin transport

Spin can transfer information

Spin transport in a long distance is preferable

However

Spins (to a certain quantized axis) are not conserved

Charges are conserved on the contrary.

Therefore, it is important to choose materials with long spin relaxation length or

spin relaxation time.

Then how does spin relaxation occur in materials?

Spin relaxation mechanismSpin relaxation mechanism

A: Elliot-Yafet mechanism

Periodic ion scattering containing

phonon contribution

B: D’yakonov-Perel’ mechanism

Spin precesses along an effective

magnetic field during momentum

scattering.J. Fabian and S. Das Sarma, J. Vac. Sci. Technol. B 17, 1708 (1999).

e.g. Metals, Graphene…

e.g. Semiconductors, Graphene…

Two mechanisms show different dependence of ts on tp.

ts: spin relaxation time, tp: momentum relaxation time

13

A: Elliot-Yafet mechanism

Basic idea: impurity or phonon scattering + spin-orbit interaction

B: D’yakonov-Perel mechanism

Spin tilts a little every time the electron

experiences momentum scattering.

ps tt

Basic idea: spin precession by random magnetic fields

The system lack of inversion symmetry:

kkEE

Kramer’s theorem: if Hamiltonian is time-reversal symmetric

J. Fabian and S. Das Sarma, J. Vac. Sci. Technol. B 17, 1708 (1999).

kkEE

Spin relaxation mechanism

14

From two equations

kkEE

This can be regarded as a spin split caused by an effective

k-dependent magnetic field (k):

)(2

1)( kΩk Η

J. Fabian and S. Das Sarma, J. Vac. Sci. Technol. B 17, 1708 (1999).

Electrons change their momentum after

each momentum scattering process

Random magnetic field between

the scattering processes

The smaller tp, the smaller the net magnetic field for spin becomes.

(motional narrowing)

Thusps tt 1

Spin relaxation mechanism

Role of graphene in spintronics

The biggest advantage of graphene for spin transport

Intrinsic spin-orbit interaction(SOI) is small for

graphene due to small atomic number (~24 eV [1]).

[1] M. Gmitra et al., Phys. Rev. B 80, 235431 (2009).

Small spin relaxation = long-range spin transport

is possible!

Theoretically, lsf ~ 100 m, tsf ~ 100 ns are possible.

Much larger than other materials!

Atomic Number

Typical metallic materials with low SO (Cu, Ag, Al) have m spin diffusion

length and less than 1 ns spin diffusion time.

First experimental demonstration

N. Tombros et al., Nature 448, 571 (2008).

Lateral spin valve structure with graphene

Co/Al2O3/graphene lateral spin valve (figure)

Nonlocal spin valve signals are observed!

Spin diffusion length: between 1.5 ~ 2 m

L eB B

S

Larmor precession

NM

a 0 rotation

NM

B

b

B = 0

p/2 rotation

NM

B

c p rotation

V/I

B

0

0

VI

Hanle effectAnother way to estimate tsf and D: the Hanle effect

N

B=0V

Time t

t=0

44 46 48

P (

arb

.)

Time (ps)

DN

= 500 cm2/s

t = 40 ps

0

( )cosPV

dt tI

t

21( ) exp e p

4x

4 sfNN

LP t

D t

t

D t

p t

Diffusion Spin-flip

( )P t

F. J. Jedema et al, Nature 416, 713 (2002).

Hanle effectEstimation of tp and D by the Hanle effect

First experimental demonstration

N. Tombros et al., Nature 448, 571 (2008).

Hanle curves clearly demonstrate that

measured voltages are spin currents origin

However, the observed spin diffusion length

is much shorter than theoretically predicted.

Because of low mobility (2000 cm2V-1s-1)?

Low quality tunneling layer?

Spin injection efficiency: 10 %

Spin diffusion time: less than 200 ps

For efficient spin injection

Impedance mismatch problem

“Spin resistance” of material X is defined as 𝑅𝑋𝑠 = 𝜌𝑋

𝜆𝑠𝑓𝑋

𝐴𝑁

Spin impedance mismatch

Large mismatch of the spin resistance for

two different materials prevents efficient spin

transfer between the two materials

How to overcome?

Inserting spacer (tunneling layer) between

ferromagnet and nonmagnet can reduce the

impedance mismatch.S. Takahashi and S. Maekawa, Phys. Rev. B 67, 052409 (2003).

AN: Cross-sectional area of X

For efficient spin injection

In the case of graphene and ferromagnetic metal contacts

𝑅𝑋𝑠 = 𝜌𝑋

𝜆𝑠𝑓𝑋

𝐴𝑁

Contact resistance:

Graphene Large r (a few hundred ~ kilo Ohm/sq), large lsf (more than m)

Ferromagnetic metal

Small r (a few ten microOhm cm), small lsf (less than 10 nm)

Huge impedance mismatch emerges at the interface between

ferromagnets and graphene.

Spin injection through direct contact between F and Gr

Direct contact of Co to graphene

Spin injection efficiency 1.3 %

Spin diffusion length 1.5 m

W. Han et al., Appl. Phys. Lett. 94, 222109 (2009).

Spin currents are not

efficiently injected into

graphene with transparent

contacts!

Spin injection through h-BN into graphene

Hexagonal boron nitride (h-BN)

Two dimensional van der Waals insulator

Atomically flat, small lattice mismatch with graphene

Good candidate for tunnel barrier between

graphene and ferromagnetic metals!

Co/h-BN/graphene tunnel junction

M. V. Kamalakar et al., Sci. Rep. 4, 6146 (2014).

h-BN mono ~ a few layer

Mobility of graphene 2000 cm2V-1s-1


Data from five devices:

h-BN0 Transparent contact between Co and graphene

(no h-BN tunneling layer)

h-BN1~4 Co/h-BN/graphene with different thickness of

h-BN



Nonlocal spin valve signals (DRNL) are clearly enhanced

with h-BN tunneling layer (contact resistance (RA)).

The thicker h-BN is, the larger the value of DRNL.


Efficient spin injection into graphene!

Spin transport in graphene

B. Dlubak et al., Nat. Phys. 8, 557 (2012).

Epitaxial graphene on SiC

Flatter than exfoliated graphene

= less ripples, which induce gauge

fields that enhance spin relaxation

High mobility (17000 cm2V-1s-1)

Co/Al2O3/graphene local spin valve

Longer spin diffusion length is expected!



“Mega-Ohm” magnetoresistance signals are observed.

Local spin valve measurements

Magnetoresistance (MR) ratio of 12 % is observed.



Mega Ohm magnetoresistance can be achieved

when the contact (barrier) resistance (Rb) is

more than 1 M.

Al2O3 tunnel barrier should be high quality

lsf > 150 m for graphene on SiC!

tsf > 100 ns!

Considering the observed magnetoresistance

value and the distance between the contacts (L),

the fitting for the experimental data shows the

spin diffusion length lsf is more than 150 m.

Physics in TMDC

What are TMDCs?

TMDC (Transition Metal DiChalcogenides)

2D materials (like graphene)

Composition is MX2

M: Mo, W, Nb, V, Cr, etc.

X: Te, Se, S, etc.

Semiconductors, Semimetals, Metals, Superconductors,

Ferromagnets...

What are TMDCs?

Structural difference

WSe2, WS2, MoS2, etc.NbSe2, NbS2, TaS2, etc.

X. Qian et al., Science 346, 1344 (2014). J. Ribeiro-Soares et al., Phys. Rev. B 90, 155438 (2014).

What are TMDCs?

X. Qian et al., Science 346, 1344 (2014). J. Ribeiro-Soares et al., Phys. Rev. B 90, 155438 (2014).

Semiconducting TMDC

(Examples: WSe2, WS2, MoSe2, MoS2 etc.)

Thickness-dependent properties

Difference between monolayer and bulk

Bulk (crystal): Indirect band-gap semiconductor

Monolayer: Direct band-gap semiconductor

Band gap is located at the K (K’) point.

Slight difference of the lattice constant

(bulk 3.135 A, monolayer 3.193 A)

H. Terrones et al., Sci. Rep. 3, 1549 (2013).

Transition metal dichalcogenides (TMDs)

Similar to graphene with Dirac cones

at K (K’) points


Indirect to direct band gap transition in MoS2

Photoluminescence for 1-6 layers MoS2

Spectrum A: c1 to v1 at K

Spectrum B: c1 to v2 at K

Direct transition between the band edges

Spectrum I: Indirect transition between c1 and v1

Strong suppression of spectra except A

Signature of indirect-to-direct transition

from 2-layer to 1-layer MoS2

K. F. Mak et al., Phys. Rev. Lett. 105, 136805 (2010).


Indirect to direct band gap transition in MoS2

Photoluminescence for 1-6 layers MoS2

Spectrum A: c1 to v1 at K

Spectrum B: c1 to v2 at K

Direct transition between the band edges

Strong suppression of spectra except A

Signature of indirect-to-direct transition

from 2-layer to 1-layer MoS2

K. F. Mak et al., Phys. Rev. Lett. 105, 136805 (2010).

Spectrum I: Indirect transition between c1 and v1

Electronic properties

High-mobility FET with monolayer MoS2

Monolayer MoS2 on SiO2: mobility 0.5-3 cm2V-1s-1

Screening of charged impurities by a material with

high dielectric constant may increase the mobility

Device with top & bottom gate

HfO2: k=25

(e.g. SiO2: k=4)

B. Radisavljevic et al., Nat. Nanotech 6, 147 (2011).



Carrier-type:n-type

Mobility: = 217 cm2V-1s-1




High on-off ratio (108 current modulation)

4 orders of magnitude larger than conventional

Si-based transistor

Steep increase of current by Vg


Valley-Zeeman Coupling

Broken inversion symmetry

Effective inplane electric field

Heavy transition metal (Mo, W)

Strong spin-orbit interaction

𝐵 ∝ 𝑣 × 𝐸Direction of spin is locked by an effective

out-of-plane magnetic field

Time reversal symmetry requires

opposite spin directions at K and – K points

Valley-Zeeman couplingD. Xiao et al., Phys. Rev. Lett. 108, 196802 (2012).

J. M. Riley et al., Nat. Phys. 10, 835 (2014).

40

Strong anisotropy in induced SOI may be

relevant to “Valley-Zeeman Coupling”


Electrical control of VZ coupling

VZ coupling in bulk TMDCs: Due to the inversion

symmetry, the splitting is opposite at K (or K’)

in the adjacent layer

Layer 1 Layer 2

Spin-degenerated bands

Applying strong out-of-plane electric fields, broken out-of-plane symmetry

H. Yuan et al., Nat. Phys. 9, 563 (2013).


Electric-double-layer transistor (EDLT)

Large interfacial electric field Extremely high carrier density @ the interface

Rxx vs T curves: From insulating to metallic dependence (more carriers can be

doped in Hole-doped regime)




Crossover from weak localization (WL) to weak antilocalization (WAL) with the gate

Electrical modulation of SOI

SOI increases as a function of carrier density




Band structure of bulk WSe2: Valence band maximum at G

(Valence bands at K with slightly lower energy)

Out-of-plane electric field E shifts the valence

band maximum from G to K

Broken inversion symmetry by E induces the

spin-splitting at K

Monolayer WSe2 is not affected by E


Valley Hall effect in TMDCs

D. Xiao et al., Phys. Rev. Lett. 108, 196802 (2012).

Spin Hall effect: Electrons are deflected depending

on the spin index

Valley Hall effect: Electrons are deflected depending

on the valley index

Origin: Valley-dependent anomalous velocity

Figure: Carriers at the valley K (filled circles)

Carriers at the valley K’ (empty circles)


Electronic structure of graphene

C・ O

General form of the Berry phase (when circulates back to at )

R

:Berry connection

:Berry curvature

Vector potential

Magnetic field

Concept of anomalous velocityAnomalous velocity

Effect of the Berry curvature in the equation of motion

Anomalous velocity (normal to the electric field)

Berry curvature defined as

Defines “how much the band bends” Periodic part of the Bloch wave function

Effect of anomalous velocityAnomalous velocity

Equation of motion including the Berry curvature

When the electron moves, it feels the bending of the band.

Electron Wave packet

The center of the wave packet is determined by the interference of the

waves close to a certain wave number k. When the Berry curvature is not

zero, it affects the interference during the motion of the electron and causes

the shift of the center of the wave packet.

Effect of the Berry curvature

“Berry curvature acts as an effective magnetic field”


Berry curvature in the conduction band

Valley index

In the valence band

Berry curvature is “valley-dependent”

Equation of motion including the Berry curvature

Carriers at different valleys (K or -K) are

deflected to the opposite direction! Figure: Carriers at the valley K (filled circles)

Carriers at the valley K’ (empty circles)



When an electric field is applied, the same number of

electrons (or holes) at K and -K are accumulated

at both edges

Optical excitation of carriers

Electrical detection of the valley Hall effect (VHE)

impossible

Selective excitation of carriers at K (or -K) by

the circularly-polarized light

Coupling strength of carriers at K (or -K) to + (-) lights

Valley index D. Xiao et al., Phys. Rev. Lett. 108, 196802 (2012).


Excitation by +, d & -, u

↓ spin electron and ↑ spin hole both at K and -K

No charge Hall effect, no spin Hall effect, finite VHE

Excitation by linearly polarized light with u

↑ spin electron and ↓ spin hole at K &

↓ spin electron and ↑ spin hole at -K

No charge Hall effect,

finite spin Hall effect

finite VHE



Experimental observation of VHE in monolayer MoS2

Longitudinal conductivity: n-doped behavior as a function of Vg

Carriers are electrons

K. F. Mak et al., Science 344, 1489 (2014).


Longitudinal conductivity is measured with a longitudinal electric field and

shining a circularly polarized light

Rapid increase of conductivity

Longitudinal conductivity owing to

a photocurrent

A



At the resonance (A point), the Hall voltage is measured

R-L: Clockwise, L-R counterclockwise

s-p: Linear polarization

Opposite sign of VH for the opposite polarization Valley Hall effect



No valley Hall effect for bilayer MoS2

Monolayer MoS2

Inversion

asymmetric

Bilayer MoS2

Inversion

symmetric

Photocarriers are created at opposite

valley for each layer, so the valley Hall

effect is canceled out.D. Xiao et al., Phys. Rev. Lett. 108, 196802 (2012).X. Qian et al., Science 346, 1344 (2014).

J. Ribeiro-Soares et al., Phys. Rev. B 90, 155438 (2014).


Superconducting TMDC

Superconducting TMDCs

Superconducting TMDCs: Note

TMDCs like MoS2, MoSe2, WS2, WSe2.......

Semiconducting, and not superconducting intrinsically

TMDCs like NbS2, NbS2, TaS2...

Metallic, and superconducting intrinsically at low T

TMDCs like WTe2

Metallic or semiconducting, and superconducting intrinsically for monolayers


Superconductivity in doped MoS2

Electric-double-layer transistor (EDLT) Strong carrier doping

Superconducting transition @ 9.5K

Y. Saito et al., Nat. Phys. 12, 144 (2016).


Magnetic field dependence of superconductivity

Out-of-plane field Inplane field

Superconductivity is robust against inplane fieldY. Saito et al., Nat. Phys. 12, 144 (2016).



Superconductivity is broken by

Cooper pair is composed by a ↑ electron at K

and ↓ electron at K’

For out-plane-field: Orbital + spin effect

For inplane-field: Spin effect

Strong valley-Zeeman coupling creates

robust Cooper pairs for inplane field

Orbital effect

Orbital broken by Lorenz force

Spin effect

Spin-singlet broken by the Zeeman effect


Superconductivity in monolayer NbSe2

2H-NbSe2: Superconducting TMDC (Bulk Tc~ 7 K)

NbSe2 in monolayer limit Spin-valley locking due to inversion symmetry breaking

(similar to MoS2)

Tc of monolayer NbSe2: 3.0 K

Note: NbSe2 is unstable

in atmosphere

X. Xi et al., Nat. Phys. 12, 139 (2016).


Superconductivity is highly robust against inplane magnetic field

X. Xi et al., Nat. Phys. 12, 139 (2016).


Temperature vs Magnetic field

X. Xi et al., Nat. Phys. 12, 139 (2016).

MoS2 case

Critical magnetic field goes over “Pauli limit”

HC

2/H

PPauli limit: The magnetic field where the condensation energy is

equal to the Zeeman energy

NbSe2


Superconductivity in 1T’-WTe2

1T-WTe2 covered by h-BN

Exhibits a superconductivity in

the electron-doped region (Tc ~ 0.65 K)

V. Fatemi et al., Science 362, 926 (2018).


When the back gate voltage (Vbg) < 0.75 V, R increases as T decreases

Metal-insulator transitionV. Fatemi et al., Science 362, 926 (2018).


By the gate voltage modulation, a wide range of resistance (from

superconductivity to insulating state) is obtained



1T-WTe2: Quantum spin Hall insulator (2D topological insulator)

In one sample QSHI phase and superconducting phase

can be both observed

Inplane critical field exceeds the Pauli limit



Similar measurements from another group

Superconducting transition

h-BN/mono-WTe2/h-BN with top &

bottom gates

E. Sajadi et al., Science 362, 922 (2018).


Superconducting transition occurs at highly doped region (~20 x1012 cm-2)

Tc ~ 0.5 K

150 mT perpendicular field is enough to suppress superconductivity, but

superconductivity persists up to 3.5 T when the field is inplane



Even for non-perfect superconducting state, resistance saturates @LT

Resistance gradually increases as a function of perpendicular magnetic field

By contrast, Resistance rapidly increases with inplane magnetic field

Interesting features


Summary for today

TMDCs become superconducting even at a monolayer limit, and Cooper pairs

are robust against inplane field owing to the Ising paring

Semiconducting TMDCs are good candidates for 2D electric-field transistors

In terms of spin properties, valley-Zeeman SOI is specific for semiconducting

TMDCs

Valley-related phenomena, such as valley Hall effect are useful for future valley-

tronics

Graphene is an ideal material for spin transport owing to the small spin-orbit

interaction

physics in 2d materials - université paris-saclay · 14 from two equations k k e e this can be...

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