Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators

Zeljkovic, Ilija; Okada, Yoshinori; Serbyn, Maksym; Sankar, R.; Walkup, Daniel; Zhou, Wenwen; Liu, Junwei; Chang, Guoqing; Wang, Yung Jui; Hasan, M. Zahid; Chou, Fangcheng; Lin, Hsin; Bansil, Arun; Fu, Liang; Madhavan, Vidya

doi:10.1038/nmat4215

Title: Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators

Abstract

The tunability of topological surface states and controllable opening of the Dirac gap are of fundamental and practical interest in the field of topological materials. In the newly discovered topological crystalline insulators (TCIs), theory predicts that the Dirac node is protected by a crystalline symmetry and that the surface state electrons can acquire a mass if this symmetry is broken. Recent studies have detected signatures of a spontaneously generated Dirac gap in TCIs; however, the mechanism of mass formation remains elusive. In this work, we present scanning tunnelling microscopy (STM) measurements of the TCI Pb_1-xSn_xSe for a wide range of alloy compositions spanning the topological and non-topological regimes. The STM topographies reveal a symmetry-breaking distortion on the surface, which imparts mass to the otherwise massless Dirac electrons—a mechanism analogous to the long sought-after Higgs mechanism in particle physics. Interestingly, the measured Dirac gap decreases on approaching the trivial phase, whereas the magnitude of the distortion remains nearly constant. Our data and calculations reveal that the penetration depth of Dirac surface states controls the magnitude of the Dirac mass. At the limit of the critical composition, the penetration depth is predicted to go to infinity, resulting in zero mass, consistent withmore »« less

Authors:

Zeljkovic, Ilija ^[1]; Okada, Yoshinori ^[2]; Serbyn, Maksym ^[3]; Sankar, R. ^[4]; Walkup, Daniel ^[1]; Zhou, Wenwen ^[1]; Liu, Junwei ^[5]; Chang, Guoqing ^[6]; Wang, Yung Jui ^[7]; Hasan, M. Zahid ^[8]; Chou, Fangcheng ^[9]; Lin, Hsin ^[6]; Bansil, Arun ^[7]; Fu, Liang ^[5]; Madhavan, Vidya ^[10]

Boston College, Chestnut Hill, MA (United States)
Boston College, Chestnut Hill, MA (United States); Tohoku Univ., Sendai (Japan)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Univ. of California, Berkeley, CA (United States)
National Taiwan Univ., Taipei (Taiwan); Academia Sinica, Taipei (Taiwan)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
National Univ. of Singapore (Singapore)
Northeastern Univ., Boston, MA (United States)
Princeton Univ., Princeton, NJ (United States)
National Taiwan Univ., Taipei (Taiwan)
Boston College, Chestnut Hill, MA (United States); Univ. of Illinois Urbana-Champaign, Urbana, IL (United States)

Publication Date:: Mon Feb 16 00:00:00 EST 2015

Research Org.:: Boston College, Chestnut Hill, MA (United States)

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

OSTI Identifier:: 1349051

Grant/Contract Number:: SC0008615

Resource Type:: Accepted Manuscript

Journal Name:: Nature Materials

Additional Journal Information:: Journal Volume: 14; Journal Issue: 3; Journal ID: ISSN 1476-1122

Publisher:: Nature Publishing Group

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; topological insulators

Citation Formats


                    Zeljkovic, Ilija, Okada, Yoshinori, Serbyn, Maksym, Sankar, R., Walkup, Daniel, Zhou, Wenwen, Liu, Junwei, Chang, Guoqing, Wang, Yung Jui, Hasan, M. Zahid, Chou, Fangcheng, Lin, Hsin, Bansil, Arun, Fu, Liang, and Madhavan, Vidya. Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators.  United States: N. p., 2015. 
Web.  doi:10.1038/nmat4215.

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                    Zeljkovic, Ilija, Okada, Yoshinori, Serbyn, Maksym, Sankar, R., Walkup, Daniel, Zhou, Wenwen, Liu, Junwei, Chang, Guoqing, Wang, Yung Jui, Hasan, M. Zahid, Chou, Fangcheng, Lin, Hsin, Bansil, Arun, Fu, Liang, & Madhavan, Vidya. Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators.  United States.  https://doi.org/10.1038/nmat4215

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                    Zeljkovic, Ilija, Okada, Yoshinori, Serbyn, Maksym, Sankar, R., Walkup, Daniel, Zhou, Wenwen, Liu, Junwei, Chang, Guoqing, Wang, Yung Jui, Hasan, M. Zahid, Chou, Fangcheng, Lin, Hsin, Bansil, Arun, Fu, Liang, and Madhavan, Vidya. Mon .  
"Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators".  United States.  https://doi.org/10.1038/nmat4215.  https://www.osti.gov/servlets/purl/1349051.

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@article{osti_1349051,

  title        = {Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators},

  author       = {Zeljkovic, Ilija and Okada, Yoshinori and Serbyn, Maksym and Sankar, R. and Walkup, Daniel and Zhou, Wenwen and Liu, Junwei and Chang, Guoqing and Wang, Yung Jui and Hasan, M. Zahid and Chou, Fangcheng and Lin, Hsin and Bansil, Arun and Fu, Liang and Madhavan, Vidya},

  abstractNote = {The tunability of topological surface states and controllable opening of the Dirac gap are of fundamental and practical interest in the field of topological materials. In the newly discovered topological crystalline insulators (TCIs), theory predicts that the Dirac node is protected by a crystalline symmetry and that the surface state electrons can acquire a mass if this symmetry is broken. Recent studies have detected signatures of a spontaneously generated Dirac gap in TCIs; however, the mechanism of mass formation remains elusive. In this work, we present scanning tunnelling microscopy (STM) measurements of the TCI Pb1-xSnxSe for a wide range of alloy compositions spanning the topological and non-topological regimes. The STM topographies reveal a symmetry-breaking distortion on the surface, which imparts mass to the otherwise massless Dirac electrons—a mechanism analogous to the long sought-after Higgs mechanism in particle physics. Interestingly, the measured Dirac gap decreases on approaching the trivial phase, whereas the magnitude of the distortion remains nearly constant. Our data and calculations reveal that the penetration depth of Dirac surface states controls the magnitude of the Dirac mass. At the limit of the critical composition, the penetration depth is predicted to go to infinity, resulting in zero mass, consistent with our measurements. Lastly, we discover the existence of surface states in the non-topological regime, which have the characteristics of gapped, double-branched Dirac fermions and could be exploited in realizing superconductivity in these materials.},

  doi          = {10.1038/nmat4215},

  journal      = {Nature Materials},

  number       = 3,

  volume       = 14,

  place        = {United States},

  year         = {Mon Feb 16 00:00:00 EST 2015},

  month        = {Mon Feb 16 00:00:00 EST 2015}

}

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The recently discovered class of spin-orbit coupled materials with interesting topological character are fascinating both from fundamental as well as application point of view. Two striking examples are 3D topological insulators (TIs) and topological crystalline insulators (TCIs). These materials host linearly dispersing (Dirac like) surface states with an odd number of Dirac nodes and are predicted to carry a quantized half-integer value of the axion field. The non-trivial topological properties of TIs and TCIs arise from strong spin-orbit coupling leading to an inverted band structure; which also leads to the chiral spin texture in momentum space. In this project wemore »« less
https://doi.org/10.2172/1349055

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Topological crystalline insulator states in the Ca₂As family

Journal Article Zhou, Xiaoting ; Hsu, Chuang-Han ; Chang, Tay-Rong ; ... - Physical Review. B

Topological crystalline insulators (TCIs) are insulating electronic phases of matter with nontrivial topology originating from crystalline symmetries. Recent theoretical advances have proposed new TCI states protected by rotational symmetries and provided powerful guidelines to search for TCIs in real materials. Building upon recent theoretical works, we demonstrate a feasible method to identify new TCI states based on first-principles calculations. We systematically unveil the topological properties of the TCI states in Ca₂As. Here, on both top and side surfaces, we observe topological surface states protected independently by rotational and mirror symmetries. We show that a particular lattice distortion can single outmore »« less
Cited by 27
https://doi.org/10.1103/physrevb.98.241104

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Experimental Observation of Dirac-like Surface States and Topological Phase Transition in ${Pb}_{1 - x} {Sn}_{x} Te (111)$ Films

Journal Article Yan, Chenhui ; Liu, Junwei ; Zang, Yunyi ; ... - Physical Review Letters

The surface of a topological crystalline insulator (TCI) carries an even number of Dirac cones protected by crystalline symmetry. We epitaxially grew here high-qualitymore »« less
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https://doi.org/10.1103/physrevlett.112.186801

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Title: Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators

Abstract

Citation Formats

Topological Crystalline Insulators journal, March 2011

Topological crystalline insulators in the SnTe material class journal, January 2012

Observation of Dirac Node Formation and Mass Acquisition in a Topological Crystalline Insulator journal, August 2013

Mapping the unconventional orbital texture in topological crystalline insulators journal, July 2014

A topological Dirac insulator in a quantum spin Hall phase journal, April 2008

Observation of a large-gap topological-insulator class with a single Dirac cone on the surface journal, May 2009

Experimental Realization of a Three-Dimensional Topological Insulator, Bi2Te3 journal, June 2009

A tunable topological insulator in the spin helical Dirac transport regime journal, July 2009

Topological surface states protected from backscattering by chiral spin texture journal, August 2009

Topological Insulators in Three Dimensions journal, March 2007

Topological insulators and superconductors journal, October 2011

Colloquium: Topological insulators journal, November 2010

Symmetry breaking and Landau quantization in topological crystalline insulators journal, July 2014

Topological crystalline insulator states in Pb1−xSnxSe journal, September 2012

Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe journal, January 2012

Observation of Landau levels of Dirac fermions in graphite journal, July 2007

Momentum-resolved Landau-level spectroscopy of Dirac surface state in Bi 2 Se 3 journal, August 2010

X-ray investigations on Bridgeman-grown Pb1−xSnxTe single crystals journal, April 1979

Quasiparticle interference on the surface of the topological crystalline insulator Pb 1 − x Sn x Se journal, September 2013

STM measurements on the InAs(110) surface directly compared with surface electronic structure calculations journal, November 2003

Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states journal, July 2010

Scanning tunnelling microscopy imaging of symmetry-breaking structural distortion in the bismuth-based cuprate superconductors journal, May 2012

The domain structure of GeTe as observed by electron microscopy journal, August 1972

Anomalous finite size effects on surface states in the topological insulator Bi 2 Se 3 journal, November 2009

Experimental realization of a topological crystalline insulator in SnTe journal, September 2012

Tunability of the k -space location of the Dirac cones in the topological crystalline insulator Pb 1 − x Sn x Te journal, April 2013

Spin structure of the Shockley surface state on Au ( 111 ) journal, June 2004

Spin Splitting of an Au(111) Surface State Band Observed with Angle Resolved Photoelectron Spectroscopy journal, October 1996

Spin-polarized (001) surface states of the topological crystalline insulator Pb 0.73 Sn 0.27 Se journal, March 2013

Experimental Observation of Dirac-like Surface States and Topological Phase Transition in Pb 1 − x Sn x Te ( 111 ) Films journal, May 2014

Two types of surface states in topological crystalline insulators journal, December 2013

A tunable topological insulator in the spin helical Dirac transport regime text, January 2009

Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe text, January 2012

Observation of Landau levels of Dirac fermions in graphite text, January 2007

The Quantum Hall Transition in Real Space: From Localized to Extended States text, January 2008

Topological Surface States Protected From Backscattering by Chiral Spin Texture text, January 2009

Topological Crystalline Insulators text, January 2010

Topological crystalline insulator states in Pb(1-x)Sn(x)Se text, January 2012

Experimental realization of a topological crystalline insulator in SnTe text, January 2012

Topological Insulators in Three Dimensions text, January 2006

Giant Rashba Splitting in Pb 1- x Sn x Te (111) Topological Crystalline Insulator Films Controlled by Bi Doping in the Bulk journal, November 2016

Length Scale and Dimensionality of Defects in Epitaxial SnTe Topological Crystalline Insulator Films journal, January 2017

Tailoring of Electronic Structure and Thermoelectric Properties of a Topological Crystalline Insulator by Chemical Doping journal, October 2015

Zeeman splitting and dynamical mass generation in Dirac semimetal ZrTe5 journal, August 2016

Direct observation and temperature control of the surface Dirac gap in a topological crystalline insulator journal, October 2015

Interplay of orbital effects and nanoscale strain in topological crystalline insulators journal, April 2018

Massive and massless Dirac fermions in Pb1−xSnxTe topological crystalline insulator probed by magneto-optical absorption journal, February 2016

Enhancement of thermoelectric performance via weak disordering of topological crystalline insulators and band convergence by Se alloying in Pb 0.5 Sn 0.5 Te 1 − x Se x journal, January 2018

Enhanced thermoelectric performance in topological crystalline insulator n-type Pb 0.6 Sn 0.4 Te by simultaneous tuning of the band gap and chemical potential journal, January 2018

Enhancement of the anisotropic thermoelectric power factor of topological crystalline insulator SnTe and related alloys via external perturbations journal, January 2019

Unexpected superconductivity at nanoscale junctions made on the topological crystalline insulator Pb 0.6 Sn 0.4 Te journal, September 2016

Revealing surface-state transport in ultrathin topological crystalline insulator SnTe films journal, May 2019

Unusual diffusive effects on the ESR of Nd 3+ ions in the tunable topologically nontrivial semimetal YBiPt journal, February 2016

Topological phase transition and highly tunable topological transport in topological crystalline insulator Pb 1− x Sn x Te (111) thin films journal, April 2019

Quantum magnetotransport and de Haas–van Alphen measurements in the three-dimensional Dirac semimetal Pb 0.83 Sn 0.17 Se journal, March 2018

Landau quantization of nearly degenerate bands and full symmetry classification of Landau level crossings journal, July 2019

Proximity-induced superconductivity in a topological crystalline insulator journal, December 2019

Electrically tunable quantum spin Hall state in topological crystalline insulator thin films journal, February 2015

Topological phase diagram and saddle point singularity in a tunable topological crystalline insulator journal, August 2015

Surface electronic state of superconducting topological crystalline insulator journal, November 2015

Universal conductance fluctuations in Dirac semimetal C d 3 A s 2 nanowires journal, October 2016

Spin stiffness and domain walls in Dirac-electron mediated magnets journal, January 2019

Topological nature of step-edge states on the surface of the topological crystalline insulator Pb 0.7 Sn 0.3 Se journal, April 2019

Geometric Phase and Orbital Moment in Quantization Rules for Magnetic Breakdown journal, December 2017

Robust spin-polarized midgap states at step edges of topological crystalline insulators journal, December 2016

Robust spin-polarized midgap states at step edges of topological crystalline insulators text, January 2016

Electrically Tunable Quantum Spin Hall State in Topological Crystalline Insulator Thin films text, January 2015

Theory of interacting topological crystalline insulators text, January 2015

Surface electronic state of superconducting topological crystalline insulator text, January 2015

Topological phase diagram and saddle point singularity in a tunable topological crystalline insulator text, January 2015

Superconductivity in doped Dirac semimetals text, January 2016

Interplay of orbital effects and nanoscale strain in topological crystalline insulators text, January 2016

Weyl and Dirac Semimetals in Three Dimensional Solids text, January 2017

Spin Stiffness and Domain Walls in Dirac-Electron Mediated Magnets text, January 2018

Topological quantum phase transition from mirror to time reversal symmetry protected topological insulator journal, October 2017

Erratum: Observation of ultrahigh mobility surface states in a topological crystalline insulator by infrared spectroscopy journal, October 2017

Interplay of orbital effects and nanoscale strain in topological crystalline insulators text, January 2016

Topological Crystalline Insulators
journal, March 2011

Topological crystalline insulators in the SnTe material class
journal, January 2012

Observation of Dirac Node Formation and Mass Acquisition in a Topological Crystalline Insulator
journal, August 2013

Mapping the unconventional orbital texture in topological crystalline insulators
journal, July 2014

A topological Dirac insulator in a quantum spin Hall phase
journal, April 2008

Observation of a large-gap topological-insulator class with a single Dirac cone on the surface
journal, May 2009

Experimental Realization of a Three-Dimensional Topological Insulator, Bi₂Te₃
journal, June 2009

A tunable topological insulator in the spin helical Dirac transport regime
journal, July 2009

Topological surface states protected from backscattering by chiral spin texture
journal, August 2009

Topological Insulators in Three Dimensions
journal, March 2007

Topological insulators and superconductors
journal, October 2011

Colloquium: Topological insulators
journal, November 2010

Symmetry breaking and Landau quantization in topological crystalline insulators
journal, July 2014

Topological crystalline insulator states in Pb1−xSnxSe
journal, September 2012

Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe
journal, January 2012

Observation of Landau levels of Dirac fermions in graphite
journal, July 2007

Momentum-resolved Landau-level spectroscopy of Dirac surface state in ${Bi}_{2} {Se}_{3}$
journal, August 2010

X-ray investigations on Bridgeman-grown Pb1−xSnxTe single crystals
journal, April 1979

Quasiparticle interference on the surface of the topological crystalline insulator Pb $_{1 - x}$ Sn $_{x}$ Se
journal, September 2013

STM measurements on the InAs(110) surface directly compared with surface electronic structure calculations
journal, November 2003

Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states
journal, July 2010

Scanning tunnelling microscopy imaging of symmetry-breaking structural distortion in the bismuth-based cuprate superconductors
journal, May 2012

The domain structure of GeTe as observed by electron microscopy
journal, August 1972

Anomalous finite size effects on surface states in the topological insulator ${Bi}_{2} {Se}_{3}$
journal, November 2009

Experimental realization of a topological crystalline insulator in SnTe
journal, September 2012

Tunability of the $k$ -space location of the Dirac cones in the topological crystalline insulator Pb $_{1 - x}$ Sn $_{x}$ Te
journal, April 2013

Spin structure of the Shockley surface state on $Au (111)$
journal, June 2004

Spin Splitting of an Au(111) Surface State Band Observed with Angle Resolved Photoelectron Spectroscopy
journal, October 1996

Spin-polarized (001) surface states of the topological crystalline insulator Pb $_{0.73}$ Sn $_{0.27}$ Se
journal, March 2013

Experimental Observation of Dirac-like Surface States and Topological Phase Transition in ${Pb}_{1 - x} {Sn}_{x} Te (111)$ Films
journal, May 2014

Two types of surface states in topological crystalline insulators
journal, December 2013

A tunable topological insulator in the spin helical Dirac transport regime
text, January 2009

Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe
text, January 2012

Observation of Landau levels of Dirac fermions in graphite
text, January 2007

The Quantum Hall Transition in Real Space: From Localized to Extended States
text, January 2008

Topological Surface States Protected From Backscattering by Chiral Spin Texture
text, January 2009

Topological Crystalline Insulators
text, January 2010

Topological crystalline insulator states in Pb(1-x)Sn(x)Se
text, January 2012

Experimental realization of a topological crystalline insulator in SnTe
text, January 2012

Topological Insulators in Three Dimensions
text, January 2006

Giant Rashba Splitting in Pb _1- _x Sn _x Te (111) Topological Crystalline Insulator Films Controlled by Bi Doping in the Bulk
journal, November 2016

Length Scale and Dimensionality of Defects in Epitaxial SnTe Topological Crystalline Insulator Films
journal, January 2017

Tailoring of Electronic Structure and Thermoelectric Properties of a Topological Crystalline Insulator by Chemical Doping
journal, October 2015

Zeeman splitting and dynamical mass generation in Dirac semimetal ZrTe5
journal, August 2016

Direct observation and temperature control of the surface Dirac gap in a topological crystalline insulator
journal, October 2015

Interplay of orbital effects and nanoscale strain in topological crystalline insulators
journal, April 2018

Massive and massless Dirac fermions in Pb1−xSnxTe topological crystalline insulator probed by magneto-optical absorption
journal, February 2016

Enhancement of thermoelectric performance via weak disordering of topological crystalline insulators and band convergence by Se alloying in Pb _0.5 Sn _0.5 Te _{1 − x} Se _x
journal, January 2018

Enhanced thermoelectric performance in topological crystalline insulator n-type Pb _0.6 Sn _0.4 Te by simultaneous tuning of the band gap and chemical potential
journal, January 2018

Enhancement of the anisotropic thermoelectric power factor of topological crystalline insulator SnTe and related alloys via external perturbations
journal, January 2019

Unexpected superconductivity at nanoscale junctions made on the topological crystalline insulator Pb _0.6 Sn _0.4 Te
journal, September 2016

Revealing surface-state transport in ultrathin topological crystalline insulator SnTe films
journal, May 2019

Unusual diffusive effects on the ESR of Nd ³⁺ ions in the tunable topologically nontrivial semimetal YBiPt
journal, February 2016

Topological phase transition and highly tunable topological transport in topological crystalline insulator Pb _{1− x} Sn _x Te (111) thin films
journal, April 2019

Quantum magnetotransport and de Haas–van Alphen measurements in the three-dimensional Dirac semimetal Pb _0.83 Sn _0.17 Se
journal, March 2018

Landau quantization of nearly degenerate bands and full symmetry classification of Landau level crossings
journal, July 2019

Proximity-induced superconductivity in a topological crystalline insulator
journal, December 2019

Electrically tunable quantum spin Hall state in topological crystalline insulator thin films
journal, February 2015

Topological phase diagram and saddle point singularity in a tunable topological crystalline insulator
journal, August 2015

Surface electronic state of superconducting topological crystalline insulator
journal, November 2015

Universal conductance fluctuations in Dirac semimetal $C d_{3} A s_{2}$ nanowires
journal, October 2016

Spin stiffness and domain walls in Dirac-electron mediated magnets
journal, January 2019

Topological nature of step-edge states on the surface of the topological crystalline insulator Pb 0.7 Sn 0.3 Se
journal, April 2019

Geometric Phase and Orbital Moment in Quantization Rules for Magnetic Breakdown
journal, December 2017

Robust spin-polarized midgap states at step edges of topological crystalline insulators
journal, December 2016

Robust spin-polarized midgap states at step edges of topological crystalline insulators
text, January 2016

Electrically Tunable Quantum Spin Hall State in Topological Crystalline Insulator Thin films
text, January 2015

Theory of interacting topological crystalline insulators
text, January 2015

Surface electronic state of superconducting topological crystalline insulator
text, January 2015

Topological phase diagram and saddle point singularity in a tunable topological crystalline insulator
text, January 2015

Superconductivity in doped Dirac semimetals
text, January 2016

Interplay of orbital effects and nanoscale strain in topological crystalline insulators
text, January 2016

Weyl and Dirac Semimetals in Three Dimensional Solids
text, January 2017

Spin Stiffness and Domain Walls in Dirac-Electron Mediated Magnets
text, January 2018

Topological quantum phase transition from mirror to time reversal symmetry protected topological insulator
journal, October 2017

Erratum: Observation of ultrahigh mobility surface states in a topological crystalline insulator by infrared spectroscopy
journal, October 2017

Interplay of orbital effects and nanoscale strain in topological crystalline insulators
text, January 2016