Physics in 2D Materials - Université Paris-Saclay · 2019. 6. 27. · Physics in 2D Materials Taro...
Transcript of 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
Magnetic 2D materials
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
Magnetic 2D materials
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).
Magnetic 2D materials
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
Magnetic 2D materials
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).
Magnetic 2D materials
Field-induced ferromagnetism in Cr2Ge2Te6
Bulk: Intrinsically ferromagnetic
Thin layers: No ferromagnetism without external magnetic fields
C. Gong et al., Nature 546, 265 (2017).
Magnetic 2D materials
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).
Magnetic 2D materials
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
B. Huang et al., Nature 546, 270 (2017).
Magnetic 2D materials
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
B. Huang et al., Nature 546, 270 (2017).
Monolayer
Bilayer
Trilayer
Magnetic 2D materials
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).
Magnetic 2D materials
Variation of Tc for different thickness
Y. Deng et al., Nature 563, 94 (2018).
Magnetic 2D materials
Room temperature ferromagnetism by ionic liquid gating
Trilayer sample shows signatures of magnetism even
at 240 K by strongly doping with ionic gate
Y. Deng et al., Nature 563, 94 (2018).
Magnetic 2D materials
Ferromagnetism @ RT
AHE is observed even at room temperature for a four-layer sample
Room temperature ferromagnetism for 2D materials!
Y. Deng et al., Nature 563, 94 (2018).
Magnetic 2D materials
Ferromagnetism in CrTe2
Perpendicular ferromagnetism above RT
Metallic behavior
D. C. Freitas et al., J. Phys. Cond. Mat. 27, 176002 (2015).
Magnetic 2D materials
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
Magnetic 2D materials
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
Magnetic 2D materials
Ferromagnetism seems stronger for VSe2/MoS2 than VSe2/HOPG
Substrates play important rolesM. Bonilla et al., Nat. Nanotech. 13, 289 (2018).
Magnetic 2D materials
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
Magnetic 2D materials
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).
Magnetic 2D materials
Controlling magnetism of CrI3 by electrostatic doping
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
S. Jiang et al., Nat. Nanotech. 13, 549 (2018).
S. Jiang et al., Nat. Nanotech. 13, 549 (2018).
Magnetic 2D materials
Controlling magnetism of CrI3 by electrostatic doping
Bilayer CrI3 (antiferromagnetic)
Spin-flip field (Hsf) is modulated dramatically
Antiferromagnetic to ferromagnetic transition
S. Jiang et al., Nat. Nanotech. 13, 549 (2018).
S. Jiang et al., Nat. Nanotech. 13, 549 (2018).
Goes to zero
Magnetic 2D materials
Controlling magnetism of CrI3 by electrostatic doping
Bilayer CrI3 (antiferromagnetic)
Modulation of interlayer exchange constant
Negative : Antiferromagnetic to ferromagnetic transition
S. Jiang et al., Nat. Nanotech. 13, 549 (2018).
S. Jiang et al., Nat. Nanotech. 13, 549 (2018).
Magnetic 2D materialsS. Jiang et al., Nat. Nanotech. 13, 549 (2018).
Clear phase transition (between antiferro and ferromagnetic) is
observed, induced by electrostatic gating!
S. Jiang et al., Nat. Nanotech. 13, 549 (2018).
Magnetic 2D materials
S. Jiang et al., Nat. Nanotech. 13, 549 (2018).
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
Magnetic 2D materials
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).
Magnetic 2D materials
GTMR in bilayer CrI3
T. Song et al., Science 360, 1214 (2018).
Graphene/CrI3/graphene
magnetic tunneling junction (MTJ)
Tunneling current is enhanced when
a parallel or perpendicular magnetic field
is applied
Magnetic 2D materials
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 %!
Magnetic 2D materials
T. Song et al., Science 360, 1214 (2018).
Magnetic 2D materials
GTMR in trilayer CrI3
TMR ratio is 3200 %!
Spin-filtering effect is enhanced
T. Song et al., Science 360, 1214 (2018).
Magnetic 2D materials
GTMR in four-layer CrI3
TMR ratio as high as 19000 %!
Spin-filtering effect is more enhanced
T. Song et al., Science 360, 1214 (2018).
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
Introduction of topological insulators
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
Introduction of topological insulators
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
Introduction of topological insulators
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
Introduction of topological insulators
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!
Introduction of topological insulators
2D Topological insulator or
quantum spin Hall insulator
Model system: HgxCd1-xTe/HgTe quantum wells
Introduction of topological insulators
Model system: HgxCd1-xTe/HgTe quantum wells
Introduction of topological insulators
where , : Pauli matrix
Introduction of topological insulators
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
“Winding number”
=1
d vector map
Introduction of topological insulators
M < 0
“Ferromagnetic”
configuration
0 < M < 4B
“Skyrmionic”
configuration
“Winding number”
=0
“Winding number”
=1
d vector map
Winding number means “whether d vector wraps the sphere when k vector wraps the
whole Brillouin zone”.
Introduction of topological insulators
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
Quantum spin Hall effect in WTe2
Theoretical prediction on QSH state in TMDs
X. Qian et al., Science 346, 1344 (2014).
Quantum spin Hall effect in WTe2
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
X. Qian et al., Science 346, 1344 (2014).
Quantum spin Hall effect in WTe2
Edge states Large 2d is important to realize
QSHE experimentally
1T’- state is stable only for WTe2...
X. Qian et al., Science 346, 1344 (2014).
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 effect in WTe2
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
Z. Fei et al., Nat. Phys. 13, 677 (2017).
Quantum spin Hall effect in WTe2
Conductance should be e2/h, but lower values are observed
Conducta
nce
Edge length
Due to imperfect edge (Potential puddles, magnetic scattering etc.)
Z. Fei et al., Nat. Phys. 13, 677 (2017).
Quantum spin Hall effect in WTe2
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).
Quantum spin Hall effect in WTe2
Angular-resolved photoemission
spectroscopy (ARPES) measurements
demonstrate the topological gap between
valence and conduction bands.
S. Tang et al., Nat. Phys. 13, 683 (2017).
Quantum spin Hall effect in WTe2
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!
S. Tang et al., Nat. Phys. 13, 683 (2017).
Quantum spin Hall effect in WTe2
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).
Quantum spin Hall effect in WTe2
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).
Quantum spin Hall effect in WTe2
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
Quantum spin Hall effect in WTe2
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...
Quantum spin Hall effect in WTe2
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
Quantum spin Hall effect in WTe2
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).
Quantum spin Hall effect in WTe2
Conductance quantization
(2 ballistic channels in parallel)
S. Wu et al., Science 359, 76 (2018).
Quantum spin Hall effect in WTe2
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).
Quantum spin Hall effect in WTe2
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