Anderson Localization from the Berry-Curvature Interchange in Quantum Anomalous Hall Systems

Qiao, Zhenhua; Han, Yulei; Zhang, Lei; Wang, Ke; Deng, Xinzhou; Jiang, Hua; Yang, Shengyuan A.; Wang, Jian; Niu, Qian

doi:10.1103/PhysRevLett.117.056802

Title: Anderson Localization from the Berry-Curvature Interchange in Quantum Anomalous Hall Systems

Authors:: Qiao, Zhenhua; Han, Yulei; Zhang, Lei; Wang, Ke; Deng, Xinzhou; Jiang, Hua; Yang, Shengyuan A.; Wang, Jian; Niu, Qian

Publication Date:: 2016-07-27

Sponsoring Org.:: USDOE

OSTI Identifier:: 1273677

Grant/Contract Number:: FG03-02ER45958

Resource Type:: Publisher's Accepted Manuscript

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Name: Physical Review Letters Journal Volume: 117 Journal Issue: 5; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Citation Formats


                    Qiao, Zhenhua, Han, Yulei, Zhang, Lei, Wang, Ke, Deng, Xinzhou, Jiang, Hua, Yang, Shengyuan A., Wang, Jian, and Niu, Qian. Anderson Localization from the Berry-Curvature Interchange in Quantum Anomalous Hall Systems.  United States: N. p., 2016. 
Web.  doi:10.1103/PhysRevLett.117.056802.

Copy to clipboard


                    Qiao, Zhenhua, Han, Yulei, Zhang, Lei, Wang, Ke, Deng, Xinzhou, Jiang, Hua, Yang, Shengyuan A., Wang, Jian, & Niu, Qian. Anderson Localization from the Berry-Curvature Interchange in Quantum Anomalous Hall Systems.  United States.  https://doi.org/10.1103/PhysRevLett.117.056802

Copy to clipboard


                    Qiao, Zhenhua, Han, Yulei, Zhang, Lei, Wang, Ke, Deng, Xinzhou, Jiang, Hua, Yang, Shengyuan A., Wang, Jian, and Niu, Qian. Wed .  
"Anderson Localization from the Berry-Curvature Interchange in Quantum Anomalous Hall Systems".  United States.  https://doi.org/10.1103/PhysRevLett.117.056802.

Copy to clipboard


                    
@article{osti_1273677,

  title        = {Anderson Localization from the Berry-Curvature Interchange in Quantum Anomalous Hall Systems},

  author       = {Qiao, Zhenhua and Han, Yulei and Zhang, Lei and Wang, Ke and Deng, Xinzhou and Jiang, Hua and Yang, Shengyuan A. and Wang, Jian and Niu, Qian},

  abstractNote = {},

  doi          = {10.1103/PhysRevLett.117.056802},

  journal      = {Physical Review Letters},

  number       = 5,

  volume       = 117,

  place        = {United States},

  year         = {2016},

  month        = {7}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Publisher's Version of Record
https://doi.org/10.1103/PhysRevLett.117.056802

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 5 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance
journal, August 1980

Klitzing, K. v.; Dorda, G.; Pepper, M.
Physical Review Letters, Vol. 45, Issue 6
DOI: 10.1103/PhysRevLett.45.494

Topological insulators and superconductors
journal, October 2011

Qi, Xiao-Liang; Zhang, Shou-Cheng
Reviews of Modern Physics, Vol. 83, Issue 4
DOI: 10.1103/RevModPhys.83.1057

Metallic Phase in Quantum Hall Systems due to Inter-Landau-Band Mixing
journal, November 2001

Xiong, Gang; Wang, Shi-Dong; Niu, Qian
Physical Review Letters, Vol. 87, Issue 21
DOI: 10.1103/PhysRevLett.87.216802

The Quantum Anomalous Hall Effect: Theory and Experiment
journal, March 2016

Liu, Chao-Xing; Zhang, Shou-Cheng; Qi, Xiao-Liang
Annual Review of Condensed Matter Physics, Vol. 7, Issue 1
DOI: 10.1146/annurev-conmatphys-031115-011417

Simple scheme for surface-band calculations. II. The Green's function
journal, May 1981

Lee, D. H.; Joannopoulos, J. D.
Physical Review B, Vol. 23, Issue 10
DOI: 10.1103/PhysRevB.23.4997

Scale-Invariant Quantum Anomalous Hall Effect in Magnetic Topological Insulators beyond the Two-Dimensional Limit
journal, September 2014

Kou, Xufeng; Guo, Shih-Ting; Fan, Yabin
Physical Review Letters, Vol. 113, Issue 13
DOI: 10.1103/PhysRevLett.113.137201

Absence of Diffusion in Certain Random Lattices
journal, March 1958

Anderson, P. W.
Physical Review, Vol. 109, Issue 5
DOI: 10.1103/PhysRev.109.1492

Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
journal, December 2006

Bernevig, B. A.; Hughes, T. L.; Zhang, S.-C.
Science, Vol. 314, Issue 5806, p. 1757-1761
DOI: 10.1126/science.1133734

Disappearance of Integer Quantum Hall Effect
journal, January 1997

Sheng, D. N.; Weng, Z. Y.
Physical Review Letters, Vol. 78, Issue 2
DOI: 10.1103/PhysRevLett.78.318

Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential
journal, February 1982

Halperin, B. I.
Physical Review B, Vol. 25, Issue 4
DOI: 10.1103/PhysRevB.25.2185

Quantum anomalous Hall effect and related topological electronic states
journal, May 2015

Weng, Hongming; Yu, Rui; Hu, Xiao
Advances in Physics, Vol. 64, Issue 3
DOI: 10.1080/00018732.2015.1068524

Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
journal, August 2006

Qi, Xiao-Liang; Wu, Yong-Shi; Zhang, Shou-Cheng
Physical Review B, Vol. 74, Issue 8
DOI: 10.1103/PhysRevB.74.085308

Quantized Hall effect and edge currents
journal, February 1984

MacDonald, A. H.; Středa, P.
Physical Review B, Vol. 29, Issue 4
DOI: 10.1103/PhysRevB.29.1616

The electronic properties of graphene
journal, January 2009

Castro Neto, A. H.; Guinea, F.; Peres, N. M. R.
Reviews of Modern Physics, Vol. 81, Issue 1, p. 109-162
DOI: 10.1103/RevModPhys.81.109

Quantum Anomalous Hall Effect in Graphene Proximity Coupled to an Antiferromagnetic Insulator
journal, March 2014

Qiao, Zhenhua; Ren, Wei; Chen, Hua
Physical Review Letters, Vol. 112, Issue 11
DOI: 10.1103/PhysRevLett.112.116404

Effects of spin-flip scattering on gapped Dirac fermions
journal, August 2011

Yang, S. A.; Qiao, Z.; Yao, Y.
EPL (Europhysics Letters), Vol. 95, Issue 6
DOI: 10.1209/0295-5075/95/67001

Quantized Anomalous Hall Effect in Two-Dimensional Ferromagnets: Quantum Hall Effect in Metals
journal, May 2003

Onoda, Masaru; Nagaosa, Naoto
Physical Review Letters, Vol. 90, Issue 20
DOI: 10.1103/PhysRevLett.90.206601

Real-space observation of a two-dimensional skyrmion crystal
journal, June 2010

Yu, X. Z.; Onose, Y.; Kanazawa, N.
Nature, Vol. 465, Issue 7300
DOI: 10.1038/nature09124

Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions
journal, March 1979

Abrahams, E.; Anderson, P. W.; Licciardello, D. C.
Physical Review Letters, Vol. 42, Issue 10
DOI: 10.1103/PhysRevLett.42.673

Valley-Polarized Quantum Anomalous Hall Effect in Silicene
journal, March 2014

Pan, Hui; Li, Zhenshan; Liu, Cheng-Cheng
Physical Review Letters, Vol. 112, Issue 10
DOI: 10.1103/PhysRevLett.112.106802

Quick iterative scheme for the calculation of transfer matrices: application to Mo (100)
journal, May 1984

Sancho, M. P. Lopez; Sancho, J. M. Lopez; Rubio, J.
Journal of Physics F: Metal Physics, Vol. 14, Issue 5
DOI: 10.1088/0305-4608/14/5/016

The scaling theory of electrons in disordered solids: Additional numerical results
journal, March 1983

MacKinnon, A.; Kramer, B.
Zeitschrift für Physik B Condensed Matter, Vol. 53, Issue 1
DOI: 10.1007/BF01578242

Quantum anomalous Hall effect with tunable Chern number in magnetic topological insulator film
journal, January 2012

Jiang, Hua; Qiao, Zhenhua; Liu, Haiwen
Physical Review B, Vol. 85, Issue 4
DOI: 10.1103/PhysRevB.85.045445

High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator
journal, March 2015

Chang, Cui-Zu; Zhao, Weiwei; Kim, Duk Y.
Nature Materials, Vol. 14, Issue 5
DOI: 10.1038/nmat4204

Topological phases in two-dimensional materials: a review
journal, May 2016

Ren, Yafei; Qiao, Zhenhua; Niu, Qian
Reports on Progress in Physics, Vol. 79, Issue 6
DOI: 10.1088/0034-4885/79/6/066501

Chern Insulators from Heavy Atoms on Magnetic Substrates
journal, March 2013

Garrity, Kevin F.; Vanderbilt, David
Physical Review Letters, Vol. 110, Issue 11
DOI: 10.1103/PhysRevLett.110.116802

Quantum anomalous Hall effect in graphene from Rashba and exchange effects
journal, October 2010

Qiao, Zhenhua; Yang, Shengyuan A.; Feng, Wanxiang
Physical Review B, Vol. 82, Issue 16
DOI: 10.1103/PhysRevB.82.161414

Random-matrix theory of quantum transport
journal, July 1997

Beenakker, C. W. J.
Reviews of Modern Physics, Vol. 69, Issue 3
DOI: 10.1103/RevModPhys.69.731

Theory of Colossal Magnetoresistance in $R_{1 - x} A_{x} {MnO}_{3}$
journal, September 1997

Sheng, L.; Xing, D. Y.; Sheng, D. N.
Physical Review Letters, Vol. 79, Issue 9
DOI: 10.1103/PhysRevLett.79.1710

Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
journal, March 2013

Chang, C. -Z.; Zhang, J.; Feng, X.
Science, Vol. 340, Issue 6129
DOI: 10.1126/science.1234414

Quantum Anomalous Hall Effect in ${Hg}_{1 - y} {Mn}_{y} Te$ Quantum Wells
journal, October 2008

Liu, Chao-Xing; Qi, Xiao-Liang; Dai, Xi
Physical Review Letters, Vol. 101, Issue 14
DOI: 10.1103/PhysRevLett.101.146802

Quantum Anomalous Hall Effect in 2D Organic Topological Insulators
journal, May 2013

Wang, Z. F.; Liu, Zheng; Liu, Feng
Physical Review Letters, Vol. 110, Issue 19
DOI: 10.1103/PhysRevLett.110.196801

One-Parameter Scaling of Localization Length and Conductance in Disordered Systems
journal, November 1981

MacKinnon, A.; Kramer, B.
Physical Review Letters, Vol. 47, Issue 21
DOI: 10.1103/PhysRevLett.47.1546

Colloquium: Topological insulators
journal, November 2010

Hasan, M. Z.; Kane, C. L.
Reviews of Modern Physics, Vol. 82, Issue 4, p. 3045-3067
DOI: 10.1103/RevModPhys.82.3045

Orbital Analogue of the Quantum Anomalous Hall Effect in $p$ -Band Systems
journal, October 2008

Wu, Congjun
Physical Review Letters, Vol. 101, Issue 18
DOI: 10.1103/PhysRevLett.101.186807

Large-Chern-Number Quantum Anomalous Hall Effect in Thin-Film Topological Crystalline Insulators
journal, January 2014

Fang, Chen; Gilbert, Matthew J.; Bernevig, B. Andrei
Physical Review Letters, Vol. 112, Issue 4
DOI: 10.1103/PhysRevLett.112.046801

Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly"
journal, October 1988

Haldane, F. D. M.
Physical Review Letters, Vol. 61, Issue 18
DOI: 10.1103/PhysRevLett.61.2015

Quantum Anomalous Hall Effect with Higher Plateaus
journal, September 2013

Wang, Jing; Lian, Biao; Zhang, Haijun
Physical Review Letters, Vol. 111, Issue 13
DOI: 10.1103/PhysRevLett.111.136801

A unified field theory of mesons and baryons
journal, March 1962

Skyrme, T. H. R.
Nuclear Physics, Vol. 31
DOI: 10.1016/0029-5582(62)90775-7

Quantized Hall conductivity in two dimensions
journal, May 1981

Laughlin, R. B.
Physical Review B, Vol. 23, Issue 10
DOI: 10.1103/PhysRevB.23.5632

Global phase diagram in the quantum Hall effect
journal, July 1992

Kivelson, Steven; Lee, Dung-Hai; Zhang, Shou-Cheng
Physical Review B, Vol. 46, Issue 4
DOI: 10.1103/PhysRevB.46.2223

Quantized Anomalous Hall Effect in Magnetic Topological Insulators
journal, June 2010

Yu, R.; Zhang, W.; Zhang, H. -J.
Science, Vol. 329, Issue 5987
DOI: 10.1126/science.1187485

Berry phase effects on electronic properties
journal, July 2010

Xiao, Di; Chang, Ming-Che; Niu, Qian
Reviews of Modern Physics, Vol. 82, Issue 3
DOI: 10.1103/RevModPhys.82.1959

Similar Records in DOE PAGES and OSTI.GOV collections:

Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time-Reversal Invariant Materials

Journal Article Sodemann, Inti ; Fu, Liang - Physical Review Letters

It is well known that a nonvanishing Hall conductivity requires broken time-reversal symmetry. However, we demonstrate that Hall-like currents can occur in second-order response to external electric fields in a wide class of time-reversal invariant and inversion breaking materials, at both zero and twice the driving frequency. This nonlinear Hall effect has a quantum origin arising from the dipole moment of the Berry curvature in momentum space, which generates a net anomalous velocity when the system is in a current-carrying state. The nonlinear Hall coefficient is a rank-two pseudotensor, whose form is determined by point group symmetry. We discus optimalmore »« less
Cited by 23
https://doi.org/10.1103/physrevlett.115.216806

Full Text Available
Observation of the Quantum Anomalous Hall Insulator to Anderson Insulator Quantum Phase Transition and its Scaling Behavior

Journal Article Chang, Cui -Zu ; Zhao, Weiwei ; Li, Jian ; ... - Physical Review Letters

Fundamental insight into the nature of the quantum phase transition from a superconductor to an insulator in two dimensions, or from one plateau to the next or to an insulator in quantum Hall effect, has been revealed through the study of its scaling behavior. Here, we report on the experimental observation of a quantum phase transition from a quantum-anomalous-Hall (QAH) insulator to an Anderson insulator in a magnetic topological insulator by tuning the chemical potential. Our experiment demonstrates the existence of scaling behavior from which we extract the critical exponent for this quantum phase transition. Furthermore, we expect that ourmore »« less
Cited by 4
https://doi.org/10.1103/PhysRevLett.117.126802

Full Text Available
Theory of nonlinear Hall effects: Modified semiclassics from quantum kinetics

Journal Article Xiao, Cong ; Du, Z. Z. ; Niu, Qian - Physical Review B

We propose a modified Boltzmann nonlinear electric-transport framework which differs from the nonlinear generalization of the linear Boltzmann formalism by a contribution that has no counterpart in linear response. This contribution follows from the interband-coherence effect of dc electric fields during scattering and is related to the interband Berry connection. As an application, we demonstrate it in the second-order nonlinear Hall effect of the tilted massive Dirac model. The intuitive Boltzmann constructions are confirmed by a quantum kinetic theory, which shows that the arbitrary nth-order nonlinear dc response up to the first three leading contributions in the weak disorder potentialmore »« less
https://doi.org/10.1103/physrevb.100.165422

Full Text Available
Local Berry curvature signatures in dichroic angle-resolved photoelectron spectroscopy from two-dimensional materials

Journal Article Schüler, Michael ; De Giovannini, Umberto ; Hübener, Hannes ; ... - Science Advances

Topologically nontrivial two-dimensional materials hold great promise for next-generation optoelectronic applications. However, measuring the Hall or spin-Hall response is often a challenge and practically limited to the ground state. An experimental technique for tracing the topological character in a differential fashion would provide useful insights. In this work, we show that circular dichroism angle-resolved photoelectron spectroscopy provides a powerful tool that can resolve the topological and quantum-geometrical character in momentum space. In particular, we investigate how to map out the signatures of the momentum-resolved Berry curvature in two-dimensional materials by exploiting its intimate connection to the orbital polarization. A spin-resolvedmore »« less
Cited by 1
https://doi.org/10.1126/sciadv.aay2730

Full Text Available
Moiré commensurability and the quantum anomalous Hall effect in twisted bilayer graphene on hexagonal boron nitride

Journal Article Shi, Jingtian ; Zhu, Jihang ; MacDonald, A. H. - Physical Review B

The quantum anomalous Hall (QAH) effect is sometimes observed in twisted bilayer graphene (tBG) when it is nearly aligned with an encapsulating hexagonal boron nitride (hBN) layer. We propose that the appearance or absence of the QAH effect in individual devices could be related to commensurability between the graphene/graphene and graphene/hBN moiré patterns. We identify a series of points in the (θ_GG, θ_GBN) twist-angle space at which the two moiré patterns are commensurate, allowing moiré band theory to be applied, and we show that the band Chern numbers are in this case sensitive to a rigid in-plane hBN displacement. Givenmore »« less
https://doi.org/10.1103/physrevb.103.075122

Full Text Available

Similar Records

Title: Anderson Localization from the Berry-Curvature Interchange in Quantum Anomalous Hall Systems

Citation Formats

New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance journal, August 1980

Topological insulators and superconductors journal, October 2011

Metallic Phase in Quantum Hall Systems due to Inter-Landau-Band Mixing journal, November 2001

The Quantum Anomalous Hall Effect: Theory and Experiment journal, March 2016

Simple scheme for surface-band calculations. II. The Green's function journal, May 1981

Scale-Invariant Quantum Anomalous Hall Effect in Magnetic Topological Insulators beyond the Two-Dimensional Limit journal, September 2014

Absence of Diffusion in Certain Random Lattices journal, March 1958

Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells journal, December 2006

Disappearance of Integer Quantum Hall Effect journal, January 1997

Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential journal, February 1982

Quantum anomalous Hall effect and related topological electronic states journal, May 2015

Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors journal, August 2006

Quantized Hall effect and edge currents journal, February 1984

The electronic properties of graphene journal, January 2009

Quantum Anomalous Hall Effect in Graphene Proximity Coupled to an Antiferromagnetic Insulator journal, March 2014

Effects of spin-flip scattering on gapped Dirac fermions journal, August 2011

Quantized Anomalous Hall Effect in Two-Dimensional Ferromagnets: Quantum Hall Effect in Metals journal, May 2003

Real-space observation of a two-dimensional skyrmion crystal journal, June 2010

Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions journal, March 1979

Valley-Polarized Quantum Anomalous Hall Effect in Silicene journal, March 2014

Quick iterative scheme for the calculation of transfer matrices: application to Mo (100) journal, May 1984

The scaling theory of electrons in disordered solids: Additional numerical results journal, March 1983

Quantum anomalous Hall effect with tunable Chern number in magnetic topological insulator film journal, January 2012

High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator journal, March 2015

Topological phases in two-dimensional materials: a review journal, May 2016

Chern Insulators from Heavy Atoms on Magnetic Substrates journal, March 2013

Quantum anomalous Hall effect in graphene from Rashba and exchange effects journal, October 2010

Random-matrix theory of quantum transport journal, July 1997

Theory of Colossal Magnetoresistance in R 1 − x A x MnO 3 journal, September 1997

Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator journal, March 2013

Quantum Anomalous Hall Effect in Hg 1 − y Mn y Te Quantum Wells journal, October 2008

Quantum Anomalous Hall Effect in 2D Organic Topological Insulators journal, May 2013

One-Parameter Scaling of Localization Length and Conductance in Disordered Systems journal, November 1981

Colloquium: Topological insulators journal, November 2010

Orbital Analogue of the Quantum Anomalous Hall Effect in p -Band Systems journal, October 2008

Large-Chern-Number Quantum Anomalous Hall Effect in Thin-Film Topological Crystalline Insulators journal, January 2014

Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly" journal, October 1988

Quantum Anomalous Hall Effect with Higher Plateaus journal, September 2013

A unified field theory of mesons and baryons journal, March 1962

Quantized Hall conductivity in two dimensions journal, May 1981

Global phase diagram in the quantum Hall effect journal, July 1992

Quantized Anomalous Hall Effect in Magnetic Topological Insulators journal, June 2010

Berry phase effects on electronic properties journal, July 2010

New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance
journal, August 1980

Topological insulators and superconductors
journal, October 2011

Metallic Phase in Quantum Hall Systems due to Inter-Landau-Band Mixing
journal, November 2001

The Quantum Anomalous Hall Effect: Theory and Experiment
journal, March 2016

Simple scheme for surface-band calculations. II. The Green's function
journal, May 1981

Scale-Invariant Quantum Anomalous Hall Effect in Magnetic Topological Insulators beyond the Two-Dimensional Limit
journal, September 2014

Absence of Diffusion in Certain Random Lattices
journal, March 1958

Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
journal, December 2006

Disappearance of Integer Quantum Hall Effect
journal, January 1997

Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential
journal, February 1982

Quantum anomalous Hall effect and related topological electronic states
journal, May 2015

Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
journal, August 2006

Quantized Hall effect and edge currents
journal, February 1984

The electronic properties of graphene
journal, January 2009

Quantum Anomalous Hall Effect in Graphene Proximity Coupled to an Antiferromagnetic Insulator
journal, March 2014

Effects of spin-flip scattering on gapped Dirac fermions
journal, August 2011

Quantized Anomalous Hall Effect in Two-Dimensional Ferromagnets: Quantum Hall Effect in Metals
journal, May 2003

Real-space observation of a two-dimensional skyrmion crystal
journal, June 2010

Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions
journal, March 1979

Valley-Polarized Quantum Anomalous Hall Effect in Silicene
journal, March 2014

Quick iterative scheme for the calculation of transfer matrices: application to Mo (100)
journal, May 1984

The scaling theory of electrons in disordered solids: Additional numerical results
journal, March 1983

Quantum anomalous Hall effect with tunable Chern number in magnetic topological insulator film
journal, January 2012

High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator
journal, March 2015

Topological phases in two-dimensional materials: a review
journal, May 2016

Chern Insulators from Heavy Atoms on Magnetic Substrates
journal, March 2013

Quantum anomalous Hall effect in graphene from Rashba and exchange effects
journal, October 2010

Random-matrix theory of quantum transport
journal, July 1997

Theory of Colossal Magnetoresistance in $R_{1 - x} A_{x} {MnO}_{3}$
journal, September 1997

Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
journal, March 2013

Quantum Anomalous Hall Effect in ${Hg}_{1 - y} {Mn}_{y} Te$ Quantum Wells
journal, October 2008

Quantum Anomalous Hall Effect in 2D Organic Topological Insulators
journal, May 2013

One-Parameter Scaling of Localization Length and Conductance in Disordered Systems
journal, November 1981

Colloquium: Topological insulators
journal, November 2010

Orbital Analogue of the Quantum Anomalous Hall Effect in $p$ -Band Systems
journal, October 2008

Large-Chern-Number Quantum Anomalous Hall Effect in Thin-Film Topological Crystalline Insulators
journal, January 2014

Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly"
journal, October 1988

Quantum Anomalous Hall Effect with Higher Plateaus
journal, September 2013

A unified field theory of mesons and baryons
journal, March 1962

Quantized Hall conductivity in two dimensions
journal, May 1981

Global phase diagram in the quantum Hall effect
journal, July 1992

Quantized Anomalous Hall Effect in Magnetic Topological Insulators
journal, June 2010

Berry phase effects on electronic properties
journal, July 2010