Visualization of an axion insulating state at the transition between 2 chiral quantum anomalous Hall states
Abstract
Quantumrelativistic materials often host electronic phenomena with exotic spatial distributions. In particular, quantum anomalous Hall (QAH) insulators feature topological boundary currents whose chirality is determined by the magnetization orientation. However, understanding the microscopic nature of edge vs. bulk currents has remained a challenge due to the emergence of multidomain states at the phase transitions. Here we use microwave impedance microscopy (MIM) to directly image chiral edge currents and phase transitions in a magnetic topological insulator. Our images reveal a dramatic change in the edge state structure and an unexpected microwave response at the topological phase transition between the Chern number $N=1$ and $N=1$ states, consistent with the emergence of an insulating $N=0$ state. The magnetic transition width is independent of film thickness, but the transition pattern is distinct in differently initiated field sweeps. This behavior suggests that the $N=0$ state has 2 surface states with Hall conductivities of $\frac{1}{2}{e}^{2}/h$ but with opposite signs.
 Authors:

 Stanford Univ., CA (United States)
 Univ. of California, Riverside, CA (United States)
 Univ. of Tokyo (Japan)
 RIKEN Center for Emergent Matter Science, Saitama (Japan)
 Leibniz Inst. for Solid State and Materials Research (IFW), Dresden (Germany)
 Stanford Univ., CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States). Stanford Institute for Materials and Energy Science (SIMES)
 Univ. of Tokyo (Japan); RIKEN Center for Emergent Matter Science, Saitama (Japan)
 Publication Date:
 Research Org.:
 SLAC National Accelerator Lab., Menlo Park, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1546797
 Grant/Contract Number:
 AC0276SF00515; GBMF4546; DMR1305731
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Proceedings of the National Academy of Sciences of the United States of America
 Additional Journal Information:
 Journal Volume: 116; Journal Issue: 29; Journal ID: ISSN 00278424
 Publisher:
 National Academy of Sciences, Washington, DC (United States)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Allen, Monica, Cui, Yongtao, Yue Ma, Eric, Mogi, Masataka, Kawamura, Minoru, Fulga, Ion Cosma, GoldhaberGordon, David, Tokura, Yoshinori, and Shen, ZhiXun. Visualization of an axion insulating state at the transition between 2 chiral quantum anomalous Hall states. United States: N. p., 2019.
Web. doi:10.1073/pnas.1818255116.
Allen, Monica, Cui, Yongtao, Yue Ma, Eric, Mogi, Masataka, Kawamura, Minoru, Fulga, Ion Cosma, GoldhaberGordon, David, Tokura, Yoshinori, & Shen, ZhiXun. Visualization of an axion insulating state at the transition between 2 chiral quantum anomalous Hall states. United States. doi:10.1073/pnas.1818255116.
Allen, Monica, Cui, Yongtao, Yue Ma, Eric, Mogi, Masataka, Kawamura, Minoru, Fulga, Ion Cosma, GoldhaberGordon, David, Tokura, Yoshinori, and Shen, ZhiXun. Tue .
"Visualization of an axion insulating state at the transition between 2 chiral quantum anomalous Hall states". United States. doi:10.1073/pnas.1818255116. https://www.osti.gov/servlets/purl/1546797.
@article{osti_1546797,
title = {Visualization of an axion insulating state at the transition between 2 chiral quantum anomalous Hall states},
author = {Allen, Monica and Cui, Yongtao and Yue Ma, Eric and Mogi, Masataka and Kawamura, Minoru and Fulga, Ion Cosma and GoldhaberGordon, David and Tokura, Yoshinori and Shen, ZhiXun},
abstractNote = {Quantumrelativistic materials often host electronic phenomena with exotic spatial distributions. In particular, quantum anomalous Hall (QAH) insulators feature topological boundary currents whose chirality is determined by the magnetization orientation. However, understanding the microscopic nature of edge vs. bulk currents has remained a challenge due to the emergence of multidomain states at the phase transitions. Here we use microwave impedance microscopy (MIM) to directly image chiral edge currents and phase transitions in a magnetic topological insulator. Our images reveal a dramatic change in the edge state structure and an unexpected microwave response at the topological phase transition between the Chern number N=1 and N=1 states, consistent with the emergence of an insulating N=0 state. The magnetic transition width is independent of film thickness, but the transition pattern is distinct in differently initiated field sweeps. This behavior suggests that the N=0 state has 2 surface states with Hall conductivities of12e2/h but with opposite signs.},
doi = {10.1073/pnas.1818255116},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 29,
volume = 116,
place = {United States},
year = {2019},
month = {7}
}
Web of Science
Works referenced in this record:
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
Diracfermionmediated ferromagnetism in a topological insulator
journal, August 2012
 Checkelsky, Joseph G.; Ye, Jianting; Onose, Yoshinori
 Nature Physics, Vol. 8, Issue 10
Trajectory of the anomalous Hall effect towards the quantized state in a ferromagnetic topological insulator
journal, August 2014
 Checkelsky, J. G.; Yoshimi, R.; Tsukazaki, A.
 Nature Physics, Vol. 10, Issue 10
ScaleInvariant Quantum Anomalous Hall Effect in Magnetic Topological Insulators beyond the TwoDimensional Limit
journal, September 2014
 Kou, Xufeng; Guo, ShihTing; Fan, Yabin
 Physical Review Letters, Vol. 113, Issue 13
Highprecision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator
journal, March 2015
 Chang, CuiZu; Zhao, Weiwei; Kim, Duk Y.
 Nature Materials, Vol. 14, Issue 5
Precise Quantization of the Anomalous Hall Effect near Zero Magnetic Field
journal, May 2015
 Bestwick, A. J.; Fox, E. J.; Kou, Xufeng
 Physical Review Letters, Vol. 114, Issue 18
Large discrete jumps observed in the transition between Chern states in a ferromagnetic topological insulator
journal, July 2016
 Liu, Minhao; Wang, Wudi; Richardella, Anthony R.
 Science Advances, Vol. 2, Issue 7
Scaling of the Quantum Anomalous Hall Effect as an Indicator of Axion Electrodynamics
journal, June 2017
 Grauer, S.; Fijalkowski, K. M.; Schreyeck, S.
 Physical Review Letters, Vol. 118, Issue 24
Topological field theory of timereversal invariant insulators
journal, November 2008
 Qi, XiaoLiang; Hughes, Taylor L.; Zhang, ShouCheng
 Physical Review B, Vol. 78, Issue 19, Article No. 195424
Quantized Anomalous Hall Effect in Magnetic Topological Insulators
journal, June 2010
 Yu, R.; Zhang, W.; Zhang, H. J.
 Science, Vol. 329, Issue 5987
The Quantum Anomalous Hall Effect: Theory and Experiment
journal, March 2016
 Liu, ChaoXing; Zhang, ShouCheng; Qi, XiaoLiang
 Annual Review of Condensed Matter Physics, Vol. 7, Issue 1
Universal scaling of the quantum anomalous Hall plateau transition
journal, February 2014
 Wang, Jing; Lian, Biao; Zhang, ShouCheng
 Physical Review B, Vol. 89, Issue 8
Nobel Lecture: Topological quantum matter
journal, October 2017
 Haldane, F. Duncan M.
 Reviews of Modern Physics, Vol. 89, Issue 4
Massive Dirac Fermion on the Surface of a Magnetically Doped Topological Insulator
journal, August 2010
 Chen, Y. L.; Chu, J.  H.; Analytis, J. G.
 Science, Vol. 329, Issue 5992
Quantized topological magnetoelectric effect of the zeroplateau quantum anomalous Hall state
journal, August 2015
 Wang, Jing; Lian, Biao; Qi, XiaoLiang
 Physical Review B, Vol. 92, Issue 8
Topological magnetoelectric effects in thin films of topological insulators
journal, August 2015
 Morimoto, Takahiro; Furusaki, Akira; Nagaosa, Naoto
 Physical Review B, Vol. 92, Issue 8
A magnetic heterostructure of topological insulators as a candidate for an axion insulator
journal, February 2017
 Mogi, M.; Kawamura, M.; Yoshimi, R.
 Nature Materials, Vol. 16, Issue 5
Tailoring tricolor structure of magnetic topological insulator for robust axion insulator
journal, October 2017
 Mogi, Masataka; Kawamura, Minoru; Tsukazaki, Atsushi
 Science Advances, Vol. 3, Issue 10
Realization of the Axion Insulator State in Quantum Anomalous Hall Sandwich Heterostructures
journal, January 2018
 Xiao, Di; Jiang, Jue; Shin, JaeHo
 Physical Review Letters, Vol. 120, Issue 5
Visualization of superparamagnetic dynamics in magnetic topological insulators
journal, November 2015
 Lachman, Ella O.; Young, Andrea F.; Richardella, Anthony
 Science Advances, Vol. 1, Issue 10
Magnetic modulation doping in topological insulators toward highertemperature quantum anomalous Hall effect
journal, November 2015
 Mogi, M.; Yoshimi, R.; Tsukazaki, A.
 Applied Physics Letters, Vol. 107, Issue 18
Cryogenic microwave imaging of metal–insulator transition in doped silicon
journal, March 2011
 Kundhikanjana, Worasom; Lai, Keji; Kelly, Michael A.
 Review of Scientific Instruments, Vol. 82, Issue 3
Quartz tuning fork based microwave impedance microscopy
journal, June 2016
 Cui, YongTao; Ma, Eric Yue; Shen, ZhiXun
 Review of Scientific Instruments, Vol. 87, Issue 6
Imaging Diracmass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Cr _{x} (Bi _{0.1} Sb _{0.9} ) _{2x} Te _{3}
journal, January 2015
 Lee, Inhee; Kim, Chung Koo; Lee, Jinho
 Proceedings of the National Academy of Sciences, Vol. 112, Issue 5
Inducing a Magnetic Monopole with Topological Surface States
journal, February 2009
 Qi, X. L.; Li, R.; Zang, J.
 Science, Vol. 323, Issue 5918
Edge transport in the trivial phase of InAs/GaSb
journal, July 2016
 Nichele, Fabrizio; Suominen, Henri J.; Kjaergaard, Morten
 New Journal of Physics, Vol. 18, Issue 8
Chiral Majorana fermion modes in a quantum anomalous Hall insulator–superconductor structure
journal, July 2017
 He, Qing Lin; Pan, Lei; Stern, Alexander L.
 Science, Vol. 357, Issue 6348
Chiral topological superconductor and halfinteger conductance plateau from quantum anomalous Hall plateau transition
journal, August 2015
 Wang, Jing; Zhou, Quan; Lian, Biao
 Physical Review B, Vol. 92, Issue 6
Works referencing / citing this record:
Highprecision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator
journal, March 2015
 Chang, CuiZu; Zhao, Weiwei; Kim, Duk Y.
 Nature Materials, Vol. 14, Issue 5
A magnetic heterostructure of topological insulators as a candidate for an axion insulator
journal, February 2017
 Mogi, M.; Kawamura, M.; Yoshimi, R.
 Nature Materials, Vol. 16, Issue 5
Diracfermionmediated ferromagnetism in a topological insulator
journal, August 2012
 Checkelsky, Joseph G.; Ye, Jianting; Onose, Yoshinori
 Nature Physics, Vol. 8, Issue 10
Trajectory of the anomalous Hall effect towards the quantized state in a ferromagnetic topological insulator
journal, August 2014
 Checkelsky, J. G.; Yoshimi, R.; Tsukazaki, A.
 Nature Physics, Vol. 10, Issue 10
Cryogenic microwave imaging of metal–insulator transition in doped silicon
journal, March 2011
 Kundhikanjana, Worasom; Lai, Keji; Kelly, Michael A.
 Review of Scientific Instruments, Vol. 82, Issue 3
Magnetic modulation doping in topological insulators toward highertemperature quantum anomalous Hall effect
journal, November 2015
 Mogi, M.; Yoshimi, R.; Tsukazaki, A.
 Applied Physics Letters, Vol. 107, Issue 18
Quartz tuning fork based microwave impedance microscopy
journal, June 2016
 Cui, YongTao; Ma, Eric Yue; Shen, ZhiXun
 Review of Scientific Instruments, Vol. 87, Issue 6
Imaging Diracmass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Cr _{x} (Bi _{0.1} Sb _{0.9} ) _{2x} Te _{3}
journal, January 2015
 Lee, Inhee; Kim, Chung Koo; Lee, Jinho
 Proceedings of the National Academy of Sciences, Vol. 112, Issue 5
Edge transport in the trivial phase of InAs/GaSb
journal, July 2016
 Nichele, Fabrizio; Suominen, Henri J.; Kjaergaard, Morten
 New Journal of Physics, Vol. 18, Issue 8
Topological field theory of timereversal invariant insulators
journal, November 2008
 Qi, XiaoLiang; Hughes, Taylor L.; Zhang, ShouCheng
 Physical Review B, Vol. 78, Issue 19, Article No. 195424
Universal scaling of the quantum anomalous Hall plateau transition
journal, February 2014
 Wang, Jing; Lian, Biao; Zhang, ShouCheng
 Physical Review B, Vol. 89, Issue 8
Chiral topological superconductor and halfinteger conductance plateau from quantum anomalous Hall plateau transition
journal, August 2015
 Wang, Jing; Zhou, Quan; Lian, Biao
 Physical Review B, Vol. 92, Issue 6
Quantized topological magnetoelectric effect of the zeroplateau quantum anomalous Hall state
journal, August 2015
 Wang, Jing; Lian, Biao; Qi, XiaoLiang
 Physical Review B, Vol. 92, Issue 8
Topological magnetoelectric effects in thin films of topological insulators
journal, August 2015
 Morimoto, Takahiro; Furusaki, Akira; Nagaosa, Naoto
 Physical Review B, Vol. 92, Issue 8
ScaleInvariant Quantum Anomalous Hall Effect in Magnetic Topological Insulators beyond the TwoDimensional Limit
journal, September 2014
 Kou, Xufeng; Guo, ShihTing; Fan, Yabin
 Physical Review Letters, Vol. 113, Issue 13
Precise Quantization of the Anomalous Hall Effect near Zero Magnetic Field
journal, May 2015
 Bestwick, A. J.; Fox, E. J.; Kou, Xufeng
 Physical Review Letters, Vol. 114, Issue 18
Scaling of the Quantum Anomalous Hall Effect as an Indicator of Axion Electrodynamics
journal, June 2017
 Grauer, S.; Fijalkowski, K. M.; Schreyeck, S.
 Physical Review Letters, Vol. 118, Issue 24
Realization of the Axion Insulator State in Quantum Anomalous Hall Sandwich Heterostructures
journal, January 2018
 Xiao, Di; Jiang, Jue; Shin, JaeHo
 Physical Review Letters, Vol. 120, Issue 5
Nobel Lecture: Topological quantum matter
journal, October 2017
 Haldane, F. Duncan M.
 Reviews of Modern Physics, Vol. 89, Issue 4
Visualization of superparamagnetic dynamics in magnetic topological insulators
journal, November 2015
 Lachman, Ella O.; Young, Andrea F.; Richardella, Anthony
 Science Advances, Vol. 1, Issue 10
Large discrete jumps observed in the transition between Chern states in a ferromagnetic topological insulator
journal, July 2016
 Liu, Minhao; Wang, Wudi; Richardella, Anthony R.
 Science Advances, Vol. 2, Issue 7
Tailoring tricolor structure of magnetic topological insulator for robust axion insulator
journal, October 2017
 Mogi, Masataka; Kawamura, Minoru; Tsukazaki, Atsushi
 Science Advances, Vol. 3, Issue 10
Inducing a Magnetic Monopole with Topological Surface States
journal, February 2009
 Qi, X. L.; Li, R.; Zang, J.
 Science, Vol. 323, Issue 5918
Quantized Anomalous Hall Effect in Magnetic Topological Insulators
journal, June 2010
 Yu, R.; Zhang, W.; Zhang, H. J.
 Science, Vol. 329, Issue 5987
Massive Dirac Fermion on the Surface of a Magnetically Doped Topological Insulator
journal, August 2010
 Chen, Y. L.; Chu, J.  H.; Analytis, J. G.
 Science, Vol. 329, Issue 5992
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
Chiral Majorana fermion modes in a quantum anomalous Hall insulator–superconductor structure
journal, July 2017
 He, Qing Lin; Pan, Lei; Stern, Alexander L.
 Science, Vol. 357, Issue 6348
The Quantum Anomalous Hall Effect: Theory and Experiment
journal, March 2016
 Liu, ChaoXing; Zhang, ShouCheng; Qi, XiaoLiang
 Annual Review of Condensed Matter Physics, Vol. 7, Issue 1