recent progress on quantum anomalous hall...
TRANSCRIPT
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Recent Progress on
Quantum Anomalous Hall Effects
Zhenhua Qiao
Department of Physics & ICQD/HFNL
University of Science and Technology of China
Dec. 03, 2019
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Outline
1. Introduction
2. Quantum anomalous Hall effect (QAHE) in graphene
3. Exploration of high-temperature QAHE in topological
insulators and graphene
4. Anderson localization from Berry-curvature interchange
in QAHE systems
5. Summary
• Graphene
• Band gap engineering
Progress on QAHE in graphene from ideal to realistic materials
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3D Hall Effect 3D Anomalous Hall Effect
Quantum Hall Effect
Quantum Spin-Hall Effect/ 2D Topological Insulators (TI)
Quantum Anomalous Hall Effect (QAHE)
Edwin Herbert Hall1879
Spin-Hall Effect
(B field,
Lorenz force)
(2D, Low T, Landau
Quantization)
1975 1980
(Ferromagnetic
material)
1971 2004
2005 2007
ABCs about Hall Effects
Quantum Valley Hall Effect (QVHE)
1988 2013
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ABCs about Hall Effects
2D Topological Insulators
3D Topological Insulators
3D quantum Hall effect
(2019 Experiment)
3D quantum Hall effect
(1987 theory)
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Members of Hall family
5
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Quantum Hall Effect
In the 2D limit, Landau-level quantization
from strong magnetic field leads to quantized
Hall conductance --- zero longitudinal
resistance.
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Edge States of Quantum Hall Effect
Back-scattering
is forbidden!
Characters of QHE
Strong magnetic field
Insulating bulk
-- Landau level
Real topological state
-- Robust edge state
-- Backscattering forbidden
High-precision determination of fine structure
constant
-- IQHE: 𝛼−1 = 137.0360037 27
-- CODATA-2010: 𝛼−1 = 137.035999074(44)
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Fractional Quantum Hall Effect
8
𝜎𝑥𝑦 = 𝑛 𝑒2/ℎ
𝑛=1/3, 2/3, 1/5, …
Electron-electron interaction
Landau quantization
A topological quantum phase of composite fermions with broken time-reversal symmetry
D.C. Tsui, et al., PRL (1982)
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Nobel Prize in Quantum Hall Effect
9
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Topology
10
Möbius strip
Continuous deformation
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Topology in Condensed Matter Physics
11
Material classificationBulk Edge
Trivial gap
Non-trivial gap
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Topology in Condensed Matter Physics
12
D. J. Thouless et al., PRL 1982
Berry curvature:
M. C. Chang and Q. Niu, PRL 1995; PRB 1996
Chern number:
Kubo formula: TKNN number / Chern number
Induce anomalous velocity
perpendicular to external
electric filed!
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The Disadvantage of QHE: Strong B field
QHE: 10000 Gauss
Earth: 0.5 Gauss
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Quantum Hall Effect
Goal of both condensed matter physics
and materials physics:
Quantum Hall effect without magnetic field
Quantum anomalous Hall Effect
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Nobel Prize in Physics 2016
16
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(a) Disordered honeycomb system
(b) HgTe quantum wells
(c) Cold-atom system
(d) Topological insulators
(e) Graphene
(f) Silicene
(g) Kagome lattices
(h) Thin layers containing heavy elements
(i) Organic molecules
(j) ……
Liu et al., PRL 101, 146802 (2008)
Onoda et al., PRL 90, 206601 (2003)
Wu, PRL 101, 186807 (2008)
Yu et al., Science 329, 61 (2010)
Qiao et al., PRB 82, 161414 (2010)
Ezawa, PRL 109, 055502 (2012)
Zhang, JPCM 23, 365801 (2011)
Garrity et al., PRL 110, 116802 (2013)
Wang et al., PRL 110, 196801 (2013)
Proposals for realizing QAHE
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Experimentally
Realized Dirac Systems
Topological insulators
(No magnetism
strong spin-orbit coupling)
Graphene
(No magnetismno spin-orbit coupling)
Spin-orbit coupling
+
Ferro-magnetism
Ferro-magnetism
Requirements
General QAHE Materials
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2010年,方忠、戴希团队
理论首次提出;
2013年,由薛其坤教授领
衔的国际联合团队首次实
验观测到;
2018年,薛其坤教授团队
获得国家自然科学一等奖
Short summary of magnetic topological insulator
based quantum anomalous Hall effect
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2004: the beginning of 2D materials
Graphene-hBN-Silicene-MoS2… …
Why graphene? Era of 2D Materials
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石墨烯材料的优势
1、材料特性:
线性Dirac色散关系引起的
优异的电学、光学特性
2、制备基础:
实验及工业上已经可制备
大面积高质量的石墨烯
石墨烯:拓扑态的理想载体
多种可调自由度
自旋 谷 子晶格
KK’
A
B
Why graphene?
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Engineering band gaps
How?
Degrees of freedom
Real spin Valleys LayersSublattices
KK’
A
Btop
bottom
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Gap opening mechanism (1)
Breaking inversion symmetry.
53 meVG. Giovannetti et al., PRB 76, 073103 (2007)
(a) Placing graphene on top of
hexagonal boron nitride:
(b) Applying an interlayer potential
difference in AB-stacking bilayer
graphene:Y. Zhang et al.,
Nature 459, 820
(2008)
Supporting quantum valley-Hall state
Tunable
band
gap
A
B
top
bottom
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Intervalley scattering.
Doping in 3*3 supercell of graphene.
J. Ding, Z. Qiao* et al., PRB 84,195444 (2011)
Z. Qiao, H. Jiang et al., PRB 85,115439 (2012)
Y. Ren, X. Deng et al, PRB 91,245415 (2015)
Gap opening mechanism (2)
Co doping
KK’
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Intrinsic spin-orbit coupling
Gap opening mechanism (3)
Kane-Mele model
Intrinsic SOCVSO>>Vr
C. Kane et al., PRL 95, 146802 (2005)
Rashba SOCQuantum spin-Hall effect
Y. Yao et al., PRB 75, 041401 (2007)
H. Min et al., PRB 74, 165310 (2006)Extremely weak intrinsic SOC!
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Outline
1. Introduction
2. Quantum anomalous Hall effect (QAHE) in graphene
3. Exploration of high-temperature QAHE in topological
insulators and graphene
4. Anderson localization from Berry-curvature interchange
in QAHE systems
5. Summary
• Graphene
• Band gap engineering
Progress on QAHE in graphene from ideal to realistic materials
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The rise of QAHE in graphene
Zeeman field
Modified Kane-
Mele model
Quantum anomalous-Hall effect
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Qiao, Yang et al,
PRB 82, 161414 (2010)
Ding, Qiao* et al.,
PRB 84,195444 (2011)
Jiang*, Qiao* et al.,
PRL 109,116803 (2012)
Qiao, Ren et al.,
PRL 112,116404 (2014)
Ideal model
Periodic adsorptionExperimental prototype
Roadmap of QAHE in grapheneIm
pro
ved
solu
tion
Deng, Qi, Xu, and Qiao*,
PRB 95, 121410 (2017)
Random adsorptionExperimental prototype
Magnetic substrateExperimental prototype
Codoping adatomsExperimental prototype
Ren, Qiao, Niu,
Rep. Prog. Phys. 112,116404 (2014)
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Band structure: ideal model
Rashba SOC is further
included
With Zeeman field
Pure graphene
Evolution of bulk band structure (Tight-binding):
Z. Qiao et al., PRB 82, 161414(R) (2010)
K’K
Ener
gy
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Edge mode & Berry curvature
Z. Qiao et al., PRB 82, 161414(R) (2010)
Gapless edge mode
AB
CD
(c)
Edge mode
Berry curvature distribution
(d)
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QAHE in graphene: periodic adsorption
Z. Qiao et al., PRB 82, 161414(R) (2010)
J. Ding, Z. Qiao* et al., PRB 84,195444 (2011)
K K’
Adatoms:Sc, Ti, V, Cr, Mn, Fe, Co
Band structure
Berry curvature
Graphene
X X
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Difficulties of periodic adsorption
Z. Qiao, H. Jiang et al., PRB 85,115439 (2012)
J. Ding, Z. Qiao* et al., PRB 84,195444 (2011)
Co doping
Experimental difficulty:
(1) Precise control
(2) Intervalley scattering
3N*3N supercell
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n=1 n=2 n=3
Finite size scaling
3*3 supercell 6*6 supercell
Only intervalley
interaction
Only intrinsic
SOC
Random adsorption
Influence of random :
Slight changeH. Jiang, Z. Qiao* et al., PRL 109,116803 (2012)
n2 adatoms in a
3n*3n supercell
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Intervalley interaction Intrinsic SOC Intervalley interaction
+ intrinsic SOC
Z2=0
Z2=1
Z2=1
Z2=1
Random adsorption
H. Jiang, Z. Qiao* et al., PRL 109,116803 (2012)
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H. Jiang, Z. Qiao* et al., PRL 109,116803 (2012)
Random adsorption
Periodic adsorption
Random adsorption
L RCentral
Scattering
periodic
random
Energy
Two-terminal conductance vs. energy
Topological states are the
ground states!
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Adatom difficulty
Adatoms Clusters
Exploring easily realized substrate.
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Graphene/magnetic insulator
Graphene on top of BiFeO3
Z. Qiao, W. Ren et al., PRL 112, 116404 (2014)
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Graphene/magnetic insulator
Band structure
Z. Qiao, W. Ren et al., PRL 112, 116404 (2014)
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Experimental progresses
Proximity induced ferromagnetism
USTC
Changgan Zeng’s group
UC Irvine
Jing Shi’s group
Large ferromagnetism and weak
spin-orbit coupling
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Experimental progresses
UC Irvine
Jing Shi’s group
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Experimental progresses
UC Irvine
Jing Shi’s group
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Experimental progressesUC Irvine
Jing Shi’s group
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Experimental progressesUC Irvine
Jing Shi’s group
PRL 112,
116404 (2014)
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Codoped Graphene
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47
Outline
1. Introduction
2. Quantum anomalous Hall effect (QAHE) in graphene
3. Exploration of high-temperature QAHE in topological
insulators and graphene
4. Anderson localization from Berry-curvature interchange
in QAHE systems
5. Summary
• Graphene
• Band gap engineering
Progress on QAHE in graphene from ideal to realistic materials
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Magnetic TIs---Zhong Fang and Xi Dai’s group (IOP, CAS 2010)
Topological Insulator Based QAHE: Theory
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Prof. Q.-K. Xue
Tsinghua Univ.
Topological Insulator Based QAHE: Experiment
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Topological Insulator Based QAHE: Experiment
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Topological Insulator Based QAHE: Experiment
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Topological Insulator Based QAHE: Experiment
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Dependence of Realization Temperature
1. Surface band gap of magnetic TI thin films
2. Spatial inhomogeneity of dopants
3. Ferromagnetic Curie temperature
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Why T is so small in the conventional
magnetic doping?
Let’s take the example of doping V atoms in Sb2Te3
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1. Charge compensation, keeping the system an insulator.
2. Tune band gaps of some materials.
Xu et al., NJP 8, 135 (2006) Chen et al., PRB 79,235202 (2009)Zhu et al., PRL 100, 027205 (2008) Zhu et al., PRL 103, 226401 (2009)
Why N-P Codoping?
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V-I Codoped Sb2Te3
Vanadium (V) --------- p-doping and introducing Ferromagnetism
Iodine (I) -------- n-doping and enhancing spin-orbit coupling
V Sb
I Te
V doping: dilute distribution.
(More V doping is required to
get a large ferromagnetism)
V-I codoping: attractive.
(Less doping is required to
get a large ferromagnetism)
Both give rise to ferromagnetism.
S. Qi*, Z. Qiao* et al., arXiv:1507.03218 (2015)
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Band Structures of V-I Codoped Sb2Te3
S. Qi*, Z. Qiao* et al., arXiv:1507.03218 (2015)
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58
Comparison between V and V-I Codoped Sb2Te3
V-doped
V-I codoped
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Ideal Platform for Large Band Gap QAHE
1. Large spin-orbit coupling
2. Ferromagnetic system
3. Insulator
4. Large bulk band gap
S. Qi*, Z. Qiao* et al., arXiv:1507.03218 (2015)
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Realization of QAHE in V-I codoped Sb2Te3
thin films
S. Qi*, Z. Qiao* et al., arXiv:1507.03218 (2015)
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61
Outline
1. Introduction
2. Quantum anomalous Hall effect (QAHE) in graphene
3. Exploration of high-temperature QAHE in topological
insulators and graphene
4. Anderson localization from Berry-curvature interchange
in QAHE systems
5. Summary
• Graphene
• Band gap engineering
Progress on QAHE in graphene from ideal to realistic materials
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How will the QAHE be destroyed in the
presence of disorders?
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Single Dirac-cone model
Lattice model of a
single Dirac-cone
system:
Chern number =
0.5+0.5
(a) Band structure of
a ribbon
(b) Berry curvature
distribution
MODEL
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Disorder Effect on Transport Properties
of QAHE in Mesoscopic Regime
Left lead Right leadDisorder80*80
Nonmagnetic
Spin-flip
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Berr
y c
urv
atu
re d
en
sity
Anom
alo
us H
all
conducta
nce
1. Shrinking
band gap;
2. Separating
Berry
curvature
peaks
Berry curvature and Hall conductance
analysis50*50
Spin-flip disorder
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Be
rry c
urv
atu
re d
en
sity
Anom
alo
us H
all
conducta
nce
1. Gap closing and
reopening;
2. Berry curvature
exchange between
valence and
conduction bands;
3. The Hall
conductance at the
center changes
quickly.
Berry curvature and Hall conductance
analysis Spin-flip disorder
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Phase-diagram
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Phenomenological understanding------ From
topological charge aspect
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SUMMARY
(1) Brief review of the progress on QAHE
in graphene
(2) Pursuing high-temperature QAHE in TI
(3) Localization mechanism of QAHE in
the presence of spin-flip disorders