Unexpected edge conduction in mercury telluride quantum wells under broken time-reversal symmetry

Ma, Eric Yue; Calvo, M. Reyes; Wang, Jing; Lian, Biao; Muhlbauer, Mathias; Brune, Christoph; Cui, Yong -Tao; Lai, Keji; Kundhikanjana, Worasom; Yang, Yongliang; Baenninger, Matthias; Konig, Markus; Ames, Christopher; Buhmann, Hartmut; Leubner, Philipp; Molenkamp, Laurens W.; Zhang, Shou -Cheng; Goldhaber-Gordon, David; Kelly, Michael A.; Shen, Zhi -Xun

doi:10.1038/ncomms8252

Title: Unexpected edge conduction in mercury telluride quantum wells under broken time-reversal symmetry

Abstract

The realization of quantum spin Hall effect in HgTe quantum wells is considered a milestone in the discovery of topological insulators. Quantum spin Hall states are predicted to allow current flow at the edges of an insulating bulk, as demonstrated in various experiments. A key prediction yet to be experimentally verified is the breakdown of the edge conduction under broken time-reversal symmetry. Here we first establish a systematic framework for the magnetic field dependence of electrostatically gated quantum spin Hall devices. We then study edge conduction of an inverted quantum well device under broken time-reversal symmetry using microwave impedance microscopy, and compare our findings to a non-inverted device. At zero magnetic field, only the inverted device shows clear edge conduction in its local conductivity profile, consistent with theory. Surprisingly, the edge conduction persists up to 9 T with little change. Finally, this indicates physics beyond simple quantum spin Hall model, including material-specific properties and possibly many-body effects.

Authors:

Ma, Eric Yue ^[1]; Calvo, M. Reyes ^[1];

^[1]; Lian, Biao ^[1]; Muhlbauer, Mathias ^[2]; Brune, Christoph ^[3]; Cui, Yong -Tao ^[1]; Lai, Keji ^[4]; Kundhikanjana, Worasom ^[1]; Yang, Yongliang ^[1]; Baenninger, Matthias ^[1]; Konig, Markus ^[1]; Ames, Christopher ^[3]; Buhmann, Hartmut ^[3]; Leubner, Philipp ^[3]; Molenkamp, Laurens W. ^[3]; Zhang, Shou -Cheng ^[1]; Goldhaber-Gordon, David ^[1]; Kelly, Michael A. ^[1]; Shen, Zhi -Xun ^[1]

Stanford Univ., Stanford, CA (United States)
Stanford Univ., Stanford, CA (United States); Univ. Wurzburg, Wurzburg (Germany)
Univ. Wurzburg, Wurzburg (Germany)
Stanford Univ., Stanford, CA (United States); Univ. of Texas, Austin, TX (United States)

Publication Date:: Tue May 26 00:00:00 EDT 2015

Research Org.:: Stanford Univ., CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1260964

Grant/Contract Number:: AC02-76SF00515; PHY-0830228; DMR1305731; FP7-PEOPLE-2010-274769

Resource Type:: Accepted Manuscript

Journal Name:: Nature Communications

Additional Journal Information:: Journal Volume: 6; Journal ID: ISSN 2041-1723

Publisher:: Nature Publishing Group

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats


                    Ma, Eric Yue, Calvo, M. Reyes, Wang, Jing, Lian, Biao, Muhlbauer, Mathias, Brune, Christoph, Cui, Yong -Tao, Lai, Keji, Kundhikanjana, Worasom, Yang, Yongliang, Baenninger, Matthias, Konig, Markus, Ames, Christopher, Buhmann, Hartmut, Leubner, Philipp, Molenkamp, Laurens W., Zhang, Shou -Cheng, Goldhaber-Gordon, David, Kelly, Michael A., and Shen, Zhi -Xun. Unexpected edge conduction in mercury telluride quantum wells under broken time-reversal symmetry.  United States: N. p., 2015. 
Web.  doi:10.1038/ncomms8252.

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                    Ma, Eric Yue, Calvo, M. Reyes, Wang, Jing, Lian, Biao, Muhlbauer, Mathias, Brune, Christoph, Cui, Yong -Tao, Lai, Keji, Kundhikanjana, Worasom, Yang, Yongliang, Baenninger, Matthias, Konig, Markus, Ames, Christopher, Buhmann, Hartmut, Leubner, Philipp, Molenkamp, Laurens W., Zhang, Shou -Cheng, Goldhaber-Gordon, David, Kelly, Michael A., & Shen, Zhi -Xun. Unexpected edge conduction in mercury telluride quantum wells under broken time-reversal symmetry.  United States.  https://doi.org/10.1038/ncomms8252

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                    Ma, Eric Yue, Calvo, M. Reyes, Wang, Jing, Lian, Biao, Muhlbauer, Mathias, Brune, Christoph, Cui, Yong -Tao, Lai, Keji, Kundhikanjana, Worasom, Yang, Yongliang, Baenninger, Matthias, Konig, Markus, Ames, Christopher, Buhmann, Hartmut, Leubner, Philipp, Molenkamp, Laurens W., Zhang, Shou -Cheng, Goldhaber-Gordon, David, Kelly, Michael A., and Shen, Zhi -Xun. Tue .  
"Unexpected edge conduction in mercury telluride quantum wells under broken time-reversal symmetry".  United States.  https://doi.org/10.1038/ncomms8252.  https://www.osti.gov/servlets/purl/1260964.

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@article{osti_1260964,

  title        = {Unexpected edge conduction in mercury telluride quantum wells under broken time-reversal symmetry},

  author       = {Ma, Eric Yue and Calvo, M. Reyes and Wang, Jing and Lian, Biao and Muhlbauer, Mathias and Brune, Christoph and Cui, Yong -Tao and Lai, Keji and Kundhikanjana, Worasom and Yang, Yongliang and Baenninger, Matthias and Konig, Markus and Ames, Christopher and Buhmann, Hartmut and Leubner, Philipp and Molenkamp, Laurens W. and Zhang, Shou -Cheng and Goldhaber-Gordon, David and Kelly, Michael A. and Shen, Zhi -Xun},

  abstractNote = {The realization of quantum spin Hall effect in HgTe quantum wells is considered a milestone in the discovery of topological insulators. Quantum spin Hall states are predicted to allow current flow at the edges of an insulating bulk, as demonstrated in various experiments. A key prediction yet to be experimentally verified is the breakdown of the edge conduction under broken time-reversal symmetry. Here we first establish a systematic framework for the magnetic field dependence of electrostatically gated quantum spin Hall devices. We then study edge conduction of an inverted quantum well device under broken time-reversal symmetry using microwave impedance microscopy, and compare our findings to a non-inverted device. At zero magnetic field, only the inverted device shows clear edge conduction in its local conductivity profile, consistent with theory. Surprisingly, the edge conduction persists up to 9 T with little change. Finally, this indicates physics beyond simple quantum spin Hall model, including material-specific properties and possibly many-body effects.},

  doi          = {10.1038/ncomms8252},

  journal      = {Nature Communications},

  number       = ,

  volume       = 6,

  place        = {United States},

  year         = {Tue May 26 00:00:00 EDT 2015},

  month        = {Tue May 26 00:00:00 EDT 2015}

}

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Here, we study the electronic transport across an electrostatically-gated lateral junction in a HgTe quantum well, a canonical 2D topological insulator, with and without applied magnetic field. We control carrier density inside and outside a junction region independently and hence tune the number and nature of 1D edge modes propagating in each of those regions. Outside the 2D gap, magnetic field drives the system to the quantum Hall regime, and chiral states propagate at the edge. In this regime, we observe fractional plateaus which reflect the equilibration between 1D chiral modes across the junction. As carrier density approaches zero inmore »« less
Cited by 12
https://doi.org/10.1103/PhysRevLett.119.226401

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Quantum Spin Hall Effect in Inverted Type II Semiconductors

Journal Article Liu, Chaoxing ; /Tsinghua U., Beijing /Stanford U., Phys. Dept. ; Hughes, Taylor L ; ... - Phys.Rev.Lett.100:236601,2008

The quantum spin Hall (QSH) state is a topologically non-trivial state of quantum matter which preserves time-reversal symmetry; it has an energy gap in the bulk, but topologically robust gapless states at the edge. Recently, this novel effect has been predicted and observed in HgTe quantum wells. In this work we predict a similar effect arising in Type-II semiconductor quantum wells made from InAs/GaSb/AlSb. Because of a rare band alignment the quantum well band structure exhibits an 'inverted' phase similar to CdTe/HgTe quantum wells, which is a QSH state when the Fermi level lies inside the gap. Due to themore »« less
Full Text Available
Observation of backscattering induced by magnetism in a topological edge state

Journal Article Jäck, Berthold ; Xie, Yonglong ; Andrei Bernevig, B. ; ... - Proceedings of the National Academy of Sciences of the United States of America

The boundary modes of topological insulators are protected by the symmetries of the nontrivial bulk electronic states. Unless these symmetries are broken, they can give rise to novel phenomena, such as the quantum spin Hall effect in one-dimensional (1D) topological edge states, where quasiparticle backscattering is suppressed by time-reversal symmetry (TRS). Here, we investigate the properties of the 1D topological edge state of bismuth in the absence of TRS, where backscattering is predicted to occur. Therefore, using spectroscopic imaging and spin-polarized measurements with a scanning tunneling microscope, we compared quasiparticle interference (QPI) occurring in the edge state of a pristinemore »« less
Cited by 7
https://doi.org/10.1073/pnas.2005071117
A high-temperature ferromagnetic topological insulating phase by proximity coupling

Journal Article Katmis, Ferhat ; Lauter, Valeria ; Nogueira, Flavio S. ; ... - Nature (London)

Topological insulators are insulating materials that display conducting surface states protected by time-reversal symmetry^1,2, wherein electron spins are locked to their momentum. This unique property opens up new opportunities for creating next-generation electronic, spintronic and quantum computation devices^3,4,5. Introducing ferromagnetic order into a topological insulator system without compromising its distinctive quantum coherent features could lead to the realization of several predicted physical phenomena^6,7. In particular, achieving robust long-range magnetic order at the surface of the topological insulator at specific locations without introducing spin-scattering centres could open up new possibilities for devices. Here we use spin-polarized neutron reflectivity experiments to demonstratemore »« less
Cited by 301
https://doi.org/10.1038/nature17635

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Title: Unexpected edge conduction in mercury telluride quantum wells under broken time-reversal symmetry

Abstract

Citation Formats

Z2 Topological Order and the Quantum Spin Hall Effect journal, September 2005

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

Quantum Spin Hall Insulator State in HgTe Quantum Wells journal, November 2007

Nonlocal Transport in the Quantum Spin Hall State journal, July 2009

Evidence for the ballistic intrinsic spin Hall effect in HgTe nanostructures journal, May 2010

Spin polarization of the quantum spin Hall edge states journal, May 2012

Induced superconductivity in the quantum spin Hall edge journal, August 2014

Imaging currents in HgTe quantum wells in the quantum spin Hall regime journal, June 2013

Colloquium: Topological insulators journal, November 2010

Topological insulators and superconductors journal, October 2011

Fine structure of zero-mode Landau levels in HgTe/Hg x Cd 1 − x Te quantum wells journal, March 2011

Magnetospectroscopy of two-dimensional HgTe-based topological insulators around the critical thickness journal, November 2012

Mesoscopic Percolating Resistance Network in a Strained Manganite Thin Film journal, July 2010

Cryogenic microwave imaging of metal–insulator transition in doped silicon journal, March 2011

Imaging of Coulomb-Driven Quantum Hall Edge States journal, October 2011

Finite Size Effects on Helical Edge States in a Quantum Spin-Hall System journal, December 2008

The Quantum Spin Hall Effect: Theory and Experiment journal, March 2008

Magnetic properties of HgTe quantum wells journal, August 2012

Quantum Hall transport as a probe of capacitance profile at graphene edges journal, January 2013

Band gap variation and lattice, surface, and interface ‘‘instabilities’’ in Hg 1− x Cd x Te and related compounds journal, July 1983

Surface-enhanced alloy effects in Hg 1 − x Cd x Te: (100) surface states and the site-dependent coherent-potential approximation journal, October 1985

Role of Spin in Quasiparticle Interference journal, November 2004

Kondo Effect in the Helical Edge Liquid of the Quantum Spin Hall State journal, June 2009

Effects of Interaction on Quantum Spin Hall Insulators journal, October 2011

Interplay of Exciton Condensation and the Quantum Spin Hall Effect in InAs / GaSb Bilayers journal, April 2014

Robust Helical Edge Transport in Gated InAs / GaSb Bilayers journal, March 2015

Bulk vacancies in Cd x Hg 1− x Te journal, May 1982

Effects of cation vacancies and diffusion on the surface states of Hg 1 − x Cd x Te journal, October 1987

Surface-enhanced alloy effects on Hg 1 − x Cd x Te(100) surface states and the site-dependent coherent-potential approximation journal, April 1987

Magnetic properties of HgTe quantum wells text, January 2012

Kondo effect in the helical edge liquid of the quantum spin Hall state text, January 2009

Imaging of the Coulomb driven quantum Hall edge states text, January 2011

Imaging currents in HgTe quantum wells in the quantum spin Hall regime text, January 2012

Induced Superconductivity in the Quantum Spin Hall Edge text, January 2013

Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells text, January 2006

Cryogenic microwave imaging of metal–insulator transition in doped silicon journal, March 2011

Electronic structures of HgTe and CdTe surfaces and HgTe/CdTe interfaces journal, October 1989

Mesoscopic Percolating Resistance Network in a Strained Manganite Thin Film journal, July 2010

Imaging of the Coulomb driven quantum Hall edge states text, January 2011

Quantum Hall transport as a probe of capacitance profile at graphene edges text, January 2011

Imaging currents in HgTe quantum wells in the quantum spin Hall regime text, January 2012

High-Frequency Nonlinear Transport and Photogalvanic Effects in 2D Topological Insulators: High-Frequency Nonlinear Transport and Photogalvanic Effects in 2D Topological Insulators journal, February 2019

Scanning Microwave Impedance Microscopy (sMIM) in Electronic and Quantum Materials book, August 2019

Quantum transport in topological semimetals under magnetic fields (II) journal, April 2019

Topological Insulator Superlattices journal, July 2018

Topological mosaics in moiré superlattices of van der Waals heterobilayers journal, November 2016

Edge conduction in monolayer WTe2 journal, April 2017

Quantum spin Hall state in monolayer 1T'-WTe2 journal, June 2017

Magneto-transport in inverted HgTe quantum wells journal, April 2019

Quartz tuning fork based microwave impedance microscopy journal, June 2016

Optically coupled methods for microwave impedance microscopy journal, April 2018

Quantitative measurements of nanoscale permittivity and conductivity using tuning-fork-based microwave impedance microscopy journal, April 2018

Research Update: Recent progress on 2D materials beyond graphene: From ripples, defects, intercalation, and valley dynamics to straintronics and power dissipation journal, August 2018

Uncovering edge states and electrical inhomogeneity in MoS 2 field-effect transistors journal, July 2016

A new mechanism of post-transfer editing by aminoacyl-tRNA synthetases: catalysis of hydrolytic reaction by bacterial-type prolyl-tRNA synthetase journal, March 2016

Optical properties of helical edge channels in zinc-blende-type topological insulators: selection rules, circular and linear dichroism, circular and linear photocurrents journal, December 2018

Electrical tuning of helical edge states in topological multilayers journal, September 2019

Edge transport in the trivial phase of InAs/GaSb journal, July 2016

Local Electrodynamics of a Disordered Conductor Model System Measured with a Microwave Impedance Microscope journal, January 2020

Josephson junction through a disordered topological insulator with helical magnetization journal, June 2016

Photogalvanic probing of helical edge channels in two-dimensional HgTe topological insulators journal, May 2017

Spontaneous supercurrent and φ 0 phase shift parallel to magnetized topological insulator interfaces journal, October 2017

Interaction-induced edge states in HgTe/CdTe quantum wells under a magnetic field journal, June 2019

Topological Protection Brought to Light by the Time-Reversal Symmetry Breaking journal, July 2019

Imaging quantum spin Hall edges in monolayer WTe 2 journal, February 2019

Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal journal, January 2018

Terahertz resistive response of a two-dimensional topological insulator in a quasiballistic transport regime journal, November 2016

A new mechanism of post-transfer editing by aminoacyl-tRNA synthetases: catalysis of hydrolytic reaction by bacterial-type prolyl-tRNA synthetase text, January 2016

Josephson junction through a disordered topological insulator with helical magnetization text, January 2016

A new mechanism of post-transfer editing by aminoacyl-tRNA synthetases: Catalysis of hydrolytic reaction by bacterial-type prolyl-tRNA synthetase text, January 2016

Photogalvanic probing of helical edge channels in two-dimensional HgTe topological insulators text, January 2017

Edge conduction in monolayer WTe2 text, January 2016

Interplay of chiral and helical states in a Quantum Spin Hall Insulator lateral junction text, January 2017

Optically Coupled Methods for Microwave Impedance Microscopy text, January 2017

Quantitative Measurements of Nanoscale Permittivity and Conductivity Using Tuning-fork-based Microwave Impedance Microscopy text, January 2018

Interaction induced edge states in HgTe/CdTe Quantum Well under magnetic field text, January 2018

Self-biased current, magnetic interference response, and superconducting vortices in tilted Weyl semimetals with disorder text, January 2018

$Z_{2}$ Topological Order and the Quantum Spin Hall Effect
journal, September 2005

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

Quantum Spin Hall Insulator State in HgTe Quantum Wells
journal, November 2007

Nonlocal Transport in the Quantum Spin Hall State
journal, July 2009

Evidence for the ballistic intrinsic spin Hall effect in HgTe nanostructures
journal, May 2010

Spin polarization of the quantum spin Hall edge states
journal, May 2012

Induced superconductivity in the quantum spin Hall edge
journal, August 2014

Imaging currents in HgTe quantum wells in the quantum spin Hall regime
journal, June 2013

Colloquium: Topological insulators
journal, November 2010

Topological insulators and superconductors
journal, October 2011

Fine structure of zero-mode Landau levels in HgTe/Hg $_{x}$ Cd $_{1 - x}$ Te quantum wells
journal, March 2011

Magnetospectroscopy of two-dimensional HgTe-based topological insulators around the critical thickness
journal, November 2012

Mesoscopic Percolating Resistance Network in a Strained Manganite Thin Film
journal, July 2010

Cryogenic microwave imaging of metal–insulator transition in doped silicon
journal, March 2011

Imaging of Coulomb-Driven Quantum Hall Edge States
journal, October 2011

Finite Size Effects on Helical Edge States in a Quantum Spin-Hall System
journal, December 2008

The Quantum Spin Hall Effect: Theory and Experiment
journal, March 2008

Magnetic properties of HgTe quantum wells
journal, August 2012

Quantum Hall transport as a probe of capacitance profile at graphene edges
journal, January 2013

Band gap variation and lattice, surface, and interface ‘‘instabilities’’ in Hg _{1− x} Cd _x Te and related compounds
journal, July 1983

Surface-enhanced alloy effects in ${Hg}_{1 - x}$ ${Cd}_{x}$ Te: (100) surface states and the site-dependent coherent-potential approximation
journal, October 1985

Role of Spin in Quasiparticle Interference
journal, November 2004

Kondo Effect in the Helical Edge Liquid of the Quantum Spin Hall State
journal, June 2009

Effects of Interaction on Quantum Spin Hall Insulators
journal, October 2011

Interplay of Exciton Condensation and the Quantum Spin Hall Effect in $InAs / GaSb$ Bilayers
journal, April 2014

Robust Helical Edge Transport in Gated $InAs / GaSb$ Bilayers
journal, March 2015

Bulk vacancies in Cd _x Hg _{1− x} Te
journal, May 1982

Effects of cation vacancies and diffusion on the surface states of ${Hg}_{1 - x}$ ${Cd}_{x}$ Te
journal, October 1987

Surface-enhanced alloy effects on ${Hg}_{1 - x}$ ${Cd}_{x}$ Te(100) surface states and the site-dependent coherent-potential approximation
journal, April 1987

Magnetic properties of HgTe quantum wells
text, January 2012

Kondo effect in the helical edge liquid of the quantum spin Hall state
text, January 2009

Imaging of the Coulomb driven quantum Hall edge states
text, January 2011

Imaging currents in HgTe quantum wells in the quantum spin Hall regime
text, January 2012

Induced Superconductivity in the Quantum Spin Hall Edge
text, January 2013

Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
text, January 2006

Cryogenic microwave imaging of metal–insulator transition in doped silicon
journal, March 2011

Electronic structures of HgTe and CdTe surfaces and HgTe/CdTe interfaces
journal, October 1989

Mesoscopic Percolating Resistance Network in a Strained Manganite Thin Film
journal, July 2010

Imaging of the Coulomb driven quantum Hall edge states
text, January 2011

Quantum Hall transport as a probe of capacitance profile at graphene edges
text, January 2011

Imaging currents in HgTe quantum wells in the quantum spin Hall regime
text, January 2012

High-Frequency Nonlinear Transport and Photogalvanic Effects in 2D Topological Insulators: High-Frequency Nonlinear Transport and Photogalvanic Effects in 2D Topological Insulators
journal, February 2019

Scanning Microwave Impedance Microscopy (sMIM) in Electronic and Quantum Materials
book, August 2019

Quantum transport in topological semimetals under magnetic fields (II)
journal, April 2019

Topological Insulator Superlattices
journal, July 2018

Topological mosaics in moiré superlattices of van der Waals heterobilayers
journal, November 2016

Edge conduction in monolayer WTe2
journal, April 2017

Quantum spin Hall state in monolayer 1T'-WTe2
journal, June 2017

Magneto-transport in inverted HgTe quantum wells
journal, April 2019

Quartz tuning fork based microwave impedance microscopy
journal, June 2016

Optically coupled methods for microwave impedance microscopy
journal, April 2018

Quantitative measurements of nanoscale permittivity and conductivity using tuning-fork-based microwave impedance microscopy
journal, April 2018

Research Update: Recent progress on 2D materials beyond graphene: From ripples, defects, intercalation, and valley dynamics to straintronics and power dissipation
journal, August 2018

Uncovering edge states and electrical inhomogeneity in MoS ₂ field-effect transistors
journal, July 2016

A new mechanism of post-transfer editing by aminoacyl-tRNA synthetases: catalysis of hydrolytic reaction by bacterial-type prolyl-tRNA synthetase
journal, March 2016

Optical properties of helical edge channels in zinc-blende-type topological insulators: selection rules, circular and linear dichroism, circular and linear photocurrents
journal, December 2018

Electrical tuning of helical edge states in topological multilayers
journal, September 2019

Edge transport in the trivial phase of InAs/GaSb
journal, July 2016

Local Electrodynamics of a Disordered Conductor Model System Measured with a Microwave Impedance Microscope
journal, January 2020

Josephson junction through a disordered topological insulator with helical magnetization
journal, June 2016

Photogalvanic probing of helical edge channels in two-dimensional HgTe topological insulators
journal, May 2017

Spontaneous supercurrent and $φ_{0}$ phase shift parallel to magnetized topological insulator interfaces
journal, October 2017

Interaction-induced edge states in HgTe/CdTe quantum wells under a magnetic field
journal, June 2019

Topological Protection Brought to Light by the Time-Reversal Symmetry Breaking
journal, July 2019

Imaging quantum spin Hall edges in monolayer WTe ₂
journal, February 2019

Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal
journal, January 2018

Terahertz resistive response of a two-dimensional topological insulator in a quasiballistic transport regime
journal, November 2016

A new mechanism of post-transfer editing by aminoacyl-tRNA synthetases: catalysis of hydrolytic reaction by bacterial-type prolyl-tRNA synthetase
text, January 2016

Josephson junction through a disordered topological insulator with helical magnetization
text, January 2016

A new mechanism of post-transfer editing by aminoacyl-tRNA synthetases: Catalysis of hydrolytic reaction by bacterial-type prolyl-tRNA synthetase
text, January 2016

Photogalvanic probing of helical edge channels in two-dimensional HgTe topological insulators
text, January 2017

Edge conduction in monolayer WTe2
text, January 2016

Interplay of chiral and helical states in a Quantum Spin Hall Insulator lateral junction
text, January 2017

Optically Coupled Methods for Microwave Impedance Microscopy
text, January 2017

Quantitative Measurements of Nanoscale Permittivity and Conductivity Using Tuning-fork-based Microwave Impedance Microscopy
text, January 2018

Interaction induced edge states in HgTe/CdTe Quantum Well under magnetic field
text, January 2018

Self-biased current, magnetic interference response, and superconducting vortices in tilted Weyl semimetals with disorder
text, January 2018

Topological protection brought to light by the time-reversal symmetry breaking
text, January 2019

Electrical tuning of helical edge states in topological multilayers
text, January 2019

Local electrodynamics of a disordered conductor model system measured with a microwave impedance microscope
text, January 2019