Physics in 2D Materials - Université Paris-Saclay · 2019. 6. 27. · Physics in 2D Materials Taro...

Physics in 2D Materials

Taro WAKAMURA (Université Paris-Saclay)

Lecture 4

Today’s Topics

Lecture 4:TMDCs 2

4.1 Magnetic 2D materials

4.2 Topologically nontrivial TMDCs

Magnetic TMDCs

Introduction of magnetism

Different magnetic states

(a) Ferromagnetism (b) Anti-

ferromagnetism(c) Ferrimagnetism (d) Paramagnetism

Many examples in 3D materials, but not in 2D

Magnetic 2D materials

Mermin-Wagner theorem: No long-ranger order can exist in 1D & 2D at finite T

At a finite energy there is always a spin wave mode

At a finite temperature ferromagnetic ground state

(long-range order) is impossible


Mermin-Wagner theorem: No long-ranger order can exist in 1D & 2D at finite T

Is it possible to have a gap for the spin wave excitation?

k

E

Yes! By introducing a uniaxial magnetic anisotropy!

Energy gap


Spin dimensionality

Ising model XY model Heisenberg model

Infinitesimally small rotation of a spin is possible

Finite energy gap

is possibleM. Gibertini et al., Nat. Nanotech. 14, 408 (2019).


Magneto-optical Kerr effect (MOKE)

M. Gibertini et al., Nat. Nanotech. 14, 408 (2019).

Linearly-polarized light incident to the surface

Reflected with rotation of the main axis

depending on the magnetization

Useful method to measure macroscopic

magnetization

cf. Similar effect: Faraday effect

(For transmission)

Rotation angle Magnetization


Field-induced ferromagnetism in Cr2Ge2Te6

Long-range ferromagnetic order in 2D

Magnetic anisotropy is essential due to

Mermin-Wagner theorem

Ferromagnetism emerges down to bilayer limit

under weak out-of-plane field (0.075 T)

TC ~ 15 K

However, without external field almost no

ferromagnetic signatures are observed for bilayers

C. Gong et al., Nature 546, 265 (2017).


Field-induced ferromagnetism in Cr2Ge2Te6

Bulk: Intrinsically ferromagnetic

Thin layers: No ferromagnetism without external magnetic fields

C. Gong et al., Nature 546, 265 (2017).


Ferromagnetic 2D materials: CrI3

Bulk CrI3

Ferromagnetic insulator with perpendicular spin anisotropy

Bulk

Clear hysteresis of the Kerr rotation angle

as a function of magnetic field

Monolayer

B. Huang et al., Nature 546, 270 (2017).


Ferromagnetic 2D materials: CrI3

Monolayer CrI3

Bulk

Clear hysteresis of the Kerr rotation angle

as a function of magnetic field Ferromagnetic!

Monolayer

Curie temperature (Tc) ~ 45 K



Thickness dependence of magnetic properties

Monolayer CrI3: Clear hysteresis for H

Bilayer CrI3: No hysteresis for |H| < 0.65 T,

at -0.65 & 0.65 T there is a sharp jump

Trilayer CrI3: Clear hysteresis for H

Antiferromagnetic coupling between the two layers?

Parallel alignment of spins between the two layers

Sharp jump


Monolayer

Bilayer

Trilayer


Metallic 2D ferromagnet Fe3GeTe2

Hall

resis

tan

ce

1.5 K 100 K

Bulk crystal: Metallic, Monolayer: Insulating behavior

Magnetic properties can be measured via

the anomalous Hall effect (AHE)

AHE is observed even at 100 K for monolayer

Y. Deng et al., Nature 563, 94 (2018).


Variation of Tc for different thickness



Room temperature ferromagnetism by ionic liquid gating

Trilayer sample shows signatures of magnetism even

at 240 K by strongly doping with ionic gate



Ferromagnetism @ RT

AHE is observed even at room temperature for a four-layer sample

Room temperature ferromagnetism for 2D materials!



Ferromagnetism in CrTe2

Perpendicular ferromagnetism above RT

Metallic behavior

D. C. Freitas et al., J. Phys. Cond. Mat. 27, 176002 (2015).


RT Ferromagnetism in VSe2

Bulk VSe2: Nonmagnetic material

Monolayer or less VSe2 grown on HOPG or

MoS2 by molecular beam epitaxy (MBE)

Ferromagnetic even at RT

VSe2/HOPG


VSe2/HOPG

Inplane magnetic anisotropy Different from other 2D ferromagnets

Ferromagnetism is also observed on MoS2

M. Bonilla et al., Nat. Nanotech. 13, 289 (2018).

VSe2/MoS2


Ferromagnetism seems stronger for VSe2/MoS2 than VSe2/HOPG

Substrates play important rolesM. Bonilla et al., Nat. Nanotech. 13, 289 (2018).


Ferromagnetism disappears as the number of layer increases

Effects from the substrate (e.g. strain) may be important

Note: Exfoliated monolayer VSe2 does not show ferromagnetism

AHE


Controlling magnetism of CrI3 by electrostatic doping

Monolayer CrI3 (ferromagnetic)

By changing the gate voltage, the saturation

magnetization and coercive field are dramatically

modulated

(Shape of the M-H curve does not change so much)

S. Jiang et al., Nat. Nanotech. 13, 549 (2018).



Bilayer CrI3 (antiferromagnetic)

The saturation magnetization and remnant magnetization

are not dramatically modulated

The doping effect is the same for the two layers in

the amplitude, but opposite in the direction






Spin-flip field (Hsf) is modulated dramatically

Antiferromagnetic to ferromagnetic transition



Goes to zero




Modulation of interlayer exchange constant

Negative : Antiferromagnetic to ferromagnetic transition



Magnetic 2D materialsS. Jiang et al., Nat. Nanotech. 13, 549 (2018).

Clear phase transition (between antiferro and ferromagnetic) is

observed, induced by electrostatic gating!




Monolayer Bilayer

Magnetization switching by gating

Gate voltage swept under a (small) perpendicular field

B = -0.12 T

Monolayer: Switching occurs only once

Bilayer: Repeatable switching is possible

Giant magnetorestsiance effect

Giant Magneto-Resistance (GMR) effect

Peter Grunberg

Albert Fert

Nobel Prize in Physics in 2007

Nonmagnetic metal


Giant tunneling magnetoresistance (GTMR) in CrI3

Antiferromagnetic coupling between layers in CrI3

High resistance Low resistance Low resistance

Self-organized spin filtering effect is expected for multilayer CrI3!

T. Song et al., Science 360, 1214 (2018).


GTMR in bilayer CrI3


Graphene/CrI3/graphene

magnetic tunneling junction (MTJ)

Tunneling current is enhanced when

a parallel or perpendicular magnetic field

is applied


Dramatic change of tunneling current as a function of a magnetic field

Spin-filtering effect

Larger parallel magnetic field to saturate the magnetic field

Out-of-plane magnetic anisotropy T. Song et al., Science 360, 1214 (2018).

Large TMR ratio ( ) is observed: 530 %!




GTMR in trilayer CrI3

TMR ratio is 3200 %!

Spin-filtering effect is enhanced



GTMR in four-layer CrI3

TMR ratio as high as 19000 %!

Spin-filtering effect is more enhanced


Topologically nontrivial TMDC

Introduction of topological insulatorsExamples where “topology” plays an important role in condensed matter physics

Topological insulators

Bulk (inside the material) is insulating, but at the edge (or surface) it is conductive

Quantum Hall insulator 2D topological insulator

(quantum spin Hall insulator)

These properties derive from distinct “topology”

in momentum space

Electronic structure of graphene

What is the Berry phase?

1) Assume a sphere and a vector tangent to the sphere

2) Assume parallel transport of the vector as 1 → 2 → 3 → 1

3) When there is a curvature on the sphere, the direction of

the vector changes at 1 before/after the parallel transport

1

2 3

This idea is related to differential geometry,

but also applicable to the Hilbert space

Berry phase

Differential geometry

Direction of a vector

Quantum mechanics

Phase of a wave function

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

(Integer) quantum Hall effect

Berry connection

Introduction of topological insulators

Resis

tan

ce

Magnetic field

Chern number (TKNN formula)

In k space

Generic two band Hamiltonian in 2D is described as

where , : Pauli matrix

B

Eigen functions (Bloch waves) depend on the vector:

We can define Berry connection in d space


Therefore a small region dkxdky is projected onto a sphere formed by d

On the sphere, the small area is expressed as

k space d space

Surface area of the r =1 sphere

By using the d vector, Hall conductivity is written as


On the sphere, the small area is expressed as k space d space

Surface area of the r =1 sphere

Thus the Hall conductivity depends on “How many times wraps the sphere

when k vector wraps the whole Brillouin zone”. Winding number


An example in real space: Skyrmions

Skyrmions: Particle-like spin textures

Skyrmion number Nk:

n(r): Unit vector parallel to the magnetization at r

Magnetization vector of a skyrmion covers a whole

surface, thus Nk = ±1.(the sign depends on the direction of the magnetization at the core)

Ferromagnets, antiferromagnets etc. :Nk = 0.

Topologically different

(Integer) quantum Hall effect

Berry connection


Re

sis

tan

ce

Magnetic field

Chern number = Winding number

Quantum Hall states with different

Chern numbers Topologically different

Is it possible to construct quantum Hall states (topologically

protected) without magnetic field?

Rule: Between two topologically different states, energy gap has to be closed

Emergence of edge states

- Yes! With strong spin-orbit interaction!


2D Topological insulator or

quantum spin Hall insulator

Model system: HgxCd1-xTe/HgTe quantum wells


where , : Pauli matrix


In k space Generic Hamiltonian in 2D is described as

e.g. BHZ model (the model for 2D topological insulator)

“Mass term” M determines the topology in momentum space

M < 0

“Ferromagnetic”

configuration

0 < M < 4B

“Skyrmionic”

configuration

“Winding number”

=0


=1

d vector map


M < 0

“Ferromagnetic”

configuration

0 < M < 4B

“Skyrmionic”

configuration


=0


=1

d vector map

Winding number means “whether d vector wraps the sphere when k vector wraps the

whole Brillouin zone”.


Example in a real material: HgTe/CdHgTe quantum wells

In BHZ model: M/B < 0 In BHZ model: M/B > 0

Mass term is related to the band gap.

Parity change is related to the topological transition

Introduction of topological insulatorsEdge states as a signature for the quantum spin Hall effect

Edge states emerge!

In the quantum spin Hall insulator state,

the band inversion occurs and the parity

of the conduction bands changes.

Parity of the bands can be used to

define the topological state in the

system

We can define Z2 topological number

(−1)𝜈=

Product of the parity of the filled bands at

time-reversal symmetric points in the Brillouin zone.

Gan=0 :Non topological

n=1 :Topological

Quantum spin Hall effect in WTe2

Theoretical prediction on QSH state in TMDs


Theoretical prediction on QSH state in TMDs

X. Qian et al., Science 346, 1344 (2014).


Band inversion at G point

due to the structural transition

from 1T- to 1T’- phase

Topological phase transition

Band gap opens due to strong

spin-orbit interaction



Edge states Large 2d is important to realize

QSHE experimentally

1T’- state is stable only for WTe2...


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).

Quantum spin Hall effect in WTe2C

on

du

cta

nce

Trilayer Bilayer monolayer

Gate voltage dependence of resistance

Strong suppression for mono and bilayer WTe2 with decreasing T

Z. Fei et al., Nat. Phys. 13, 677 (2017).


Quantum spin Hall insulator

Characterized by edge currents

Two current paths: Bulk + Edge

Strong suppression of the conductance

when the edge is grounded

Evidence of edge current

Edge current contribution does not depend on Vg

Edge current is strongly suppressed by

inplane field



Conductance should be e2/h, but lower values are observed

Conducta

nce

Edge length

Due to imperfect edge (Potential puddles, magnetic scattering etc.)



Structural transition from 1T- to 1T’- state

provoke the band inversion at G-point

Parity switching in the valence band

at G-point

Transition from topologically trivial

to topologically nontrivial state

S. Tang et al., Nat. Phys. 13, 683 (2017).


Angular-resolved photoemission

spectroscopy (ARPES) measurements

demonstrate the topological gap between

valence and conduction bands.



Scanning tunneling spectroscopy (STS) measurements

Bulk

Conductance

En

erg

y

Subgap conductance is observed at the edge

Energy gap is observed around zero energy in the bulk

&

Signatures of bulk insulator & edge states!



STM measurements of MBE-grown 1T’-WTe2

30 nm

Conductance is dramatically suppressed for

monolayer 1T’-WTe2

Z. -Y. Jia et al., Phys. Rev. B 96, 041108 (2017).


Spatial map of conductance for mono WTe2

Ingap (between -0.5 V and +0.5 V) conductance increases

near the step edge.

Z. -Y. Jia et al., Phys. Rev. B 96, 041108 (2017).


Spatial map of conductance for mono WTe2

Microwave impedance microscopy (MIM)

measurements

Measuring real and imaginary part of

admittance

Y. Shi et al., Sci. Adv. 5, eaat8799 (2019).Clear signatures of the edge states


Y. Shi et al., Sci. Adv. 5, eaat8799 (2019).

Edge states exist

only on the protected

region, around

bubbles, cracks...

Contacts may not be

well connected to the

edge states...


Device combined with global top gate

& local bottom gates

Sweeping the top gate with floating the bottom gates

Conductance plateau is observed, but the value

varies depending on contact properties

S. Wu et al., Science 359, 76 (2018).

Better electrical measurements


By using a local bottom gate, carriers in WTe2 is

locally depleted

(other regions are highly doped by the top gate)

Device combined with global top gate

& local bottom gates

S. Wu et al., Science 359, 76 (2018).


Conductance quantization

(2 ballistic channels in parallel)

S. Wu et al., Science 359, 76 (2018).


Conductance quantization

(independent of the channel length)

Characteristic length of the edge states: ~100 nm (rather short)S. Wu et al., Science 359, 76 (2018).

Quantum spin Hall effect in WTe2Conductance evolution with perpendicular magnetic field

Helical edge states cross at the Dirac point

Magnetic field lift up the spin degeneracy

and the Zeeman gap opens

= Strong suppression of conductance with B

Strong suppression

S. Wu et al., Science 359, 76 (2018).


Conductance quantization upto 100 K (much higher than other systems)!S. Wu et al., Science 359, 76 (2018).

Superconducting TMDCs

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 TMDCs

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

Green curve: Superconductivity is

suppressed, but not the

edge states

Orange curve: Superconductivity + Edge

states both suppressed

The same conductance difference in low

and highly doped region

Signature of parallel conduction of

the edge states

Summary for today

Bulk WTe2 was predicted to be a Weyl semimetal, and later a high-order topological

insulator (HOTI).

Semiconducting and metallic 2D magnetic materials can be exploited for

tunneling-magnetoresistance (TMR) devices, exhibiting surprisingly high TMR

ratio

Quantum spin Hall state was predicted and experimentally demonstrated for

monolayer 1T’-WTe2

2D magnetic materials are ideal systems as Ising magnets

Physics in 2D Materials - Université Paris-Saclay · 2019. 6. 27. · Physics in 2D Materials Taro...

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