skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

This content will become publicly available on March 26, 2020

Title: Three-dimensional superconductors with hybrid higher-order topology

Abstract

We consider three-dimensional superconductors in class DIII with a fourfold rotation axis and inversion symmetry. It is shown that such systems can exhibit higher-order topology with helical Majorana hinge modes. In the case of even-parity superconductors, we show that higher-order topological superconductors can be obtained by adding a small pairing with the appropriate C 4 symmetry implementation to a topological insulator. We also show that a hybrid case is possible, where Majorana surface cones resulting from nontrivial strong topology coexist with helical hinge modes. Here, we propose a bulk invariant detecting this hybrid scenario, and numerically analyze a tight binding model exhibiting both Majorana cones and hinge modes.

Authors:
 [1];  [2];  [3]
  1. Princeton Univ., Princeton, NJ (United States)
  2. Princeton Univ., Princeton, NJ (United States); Freie Univ. Berlin, Berlin (Germany); Max Planck Inst. of Microstructure Physics, Halle (Germany)
  3. Univ. of California, Berkeley, CA (United States); Princeton Univ., Princeton, NJ (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1571984
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 99; Journal Issue: 12; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Bultinck, Nick, Bernevig, B. Andrei, and Zaletel, Michael P. Three-dimensional superconductors with hybrid higher-order topology. United States: N. p., 2019. Web. doi:10.1103/physrevb.99.125149.
Bultinck, Nick, Bernevig, B. Andrei, & Zaletel, Michael P. Three-dimensional superconductors with hybrid higher-order topology. United States. doi:10.1103/physrevb.99.125149.
Bultinck, Nick, Bernevig, B. Andrei, and Zaletel, Michael P. Tue . "Three-dimensional superconductors with hybrid higher-order topology". United States. doi:10.1103/physrevb.99.125149.
@article{osti_1571984,
title = {Three-dimensional superconductors with hybrid higher-order topology},
author = {Bultinck, Nick and Bernevig, B. Andrei and Zaletel, Michael P.},
abstractNote = {We consider three-dimensional superconductors in class DIII with a fourfold rotation axis and inversion symmetry. It is shown that such systems can exhibit higher-order topology with helical Majorana hinge modes. In the case of even-parity superconductors, we show that higher-order topological superconductors can be obtained by adding a small pairing with the appropriate C4 symmetry implementation to a topological insulator. We also show that a hybrid case is possible, where Majorana surface cones resulting from nontrivial strong topology coexist with helical hinge modes. Here, we propose a bulk invariant detecting this hybrid scenario, and numerically analyze a tight binding model exhibiting both Majorana cones and hinge modes.},
doi = {10.1103/physrevb.99.125149},
journal = {Physical Review B},
number = 12,
volume = 99,
place = {United States},
year = {2019},
month = {3}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on March 26, 2020
Publisher's Version of Record

Citation Metrics:
Cited by: 6 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

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

  • Xu, Su-Yang; Liu, Chang; Alidoust, N.
  • Nature Communications, Vol. 3, Issue 1
  • DOI: 10.1038/ncomms2191

Observation of a phononic quadrupole topological insulator
journal, January 2018

  • Serra-Garcia, Marc; Peri, Valerio; Süsstrunk, Roman
  • Nature, Vol. 555, Issue 7696
  • DOI: 10.1038/nature25156

Bulk Band Gap and Surface State Conduction Observed in Voltage-Tuned Crystals of the Topological Insulator Bi 2 Se 3
journal, May 2011


Weak-pairing higher order topological superconductors
journal, October 2018


STM Imaging of Electronic Waves on the Surface of Bi2Te3: Topologically Protected Surface States and Hexagonal Warping Effects
journal, January 2010

  • Alpichshev, Zhanybek; Analytis, J. G.; Chu, J.-H.
  • Physical Review Letters, Vol. 104, Issue 1, Article No. 016401
  • DOI: 10.1103/PhysRevLett.104.016401

Hourglass fermions
journal, April 2016

  • Wang, Zhijun; Alexandradinata, A.; Cava, R. J.
  • Nature, Vol. 532, Issue 7598
  • DOI: 10.1038/nature17410

Symmetry Indicators and Anomalous Surface States of Topological Crystalline Insulators
journal, September 2018


Higher-order topological insulators
journal, June 2018

  • Schindler, Frank; Cook, Ashley M.; Vergniory, Maia G.
  • Science Advances, Vol. 4, Issue 6
  • DOI: 10.1126/sciadv.aat0346

Topological nonsymmorphic crystalline insulators
journal, August 2014


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


Odd-Parity Topological Superconductors: Theory and Application to Cu x Bi 2 Se 3
journal, August 2010


Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
journal, March 2015


Andreev Reflection of Helical Edge Modes in InAs / GaSb Quantum Spin Hall Insulator
journal, October 2012


Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures
journal, January 1997


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


Topological Phases Protected by Point Group Symmetry
journal, February 2017


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

Second-order topological insulators and superconductors with an order-two crystalline symmetry
journal, May 2018


High-Temperature Majorana Corner States
journal, October 2018


Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor
journal, December 2018


Topological Crystalline Insulators
journal, March 2011


Observation of quadrupole transitions and edge mode topology in an LC circuit network
journal, January 2019


Weyl Semimetal Phase in Noncentrosymmetric Transition-Metal Monophosphides
journal, March 2015


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

  • Roushan, Pedram; Seo, Jungpil; Parker, Colin V.
  • Nature, Vol. 460, Issue 7259, p. 1106-1109
  • DOI: 10.1038/nature08308

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

  • Dziawa, P.; Kowalski, B. J.; Dybko, K.
  • Nature Materials, Vol. 11, Issue 12
  • DOI: 10.1038/nmat3449

p-type Bi2Se3 for topological insulator and low-temperature thermoelectric applications
journal, May 2009

  • Hor, Y. S.; Richardella, A.; Roushan, P.
  • Physical Review B, Vol. 79, Issue 19, Article No. 195208
  • DOI: 10.1103/PhysRevB.79.195208

Higher-order topological insulators and superconductors protected by inversion symmetry
journal, May 2018


Symmetry-based indicators of band topology in the 230 space groups
journal, June 2017


Topological crystalline superconductivity and second-order topological superconductivity in nodal-loop materials
journal, March 2018


Building blocks of topological quantum chemistry: Elementary band representations
journal, January 2018


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

  • Hsieh, Timothy H.; Lin, Hsin; Liu, Junwei
  • Nature Communications, Vol. 3, Article No. 982
  • DOI: 10.1038/ncomms1969

New classes of three-dimensional topological crystalline insulators: Nonsymmorphic and magnetic
journal, April 2015


Evidence for Helical Edge Modes in Inverted InAs / GaSb Quantum Wells
journal, September 2011


Higher-order symmetry-protected topological states for interacting bosons and fermions
journal, December 2018


Translational Symmetry and Microscopic Constraints on Symmetry-Enriched Topological Phases: A View from the Surface
journal, December 2016


Direct Observation of Broken Time-Reversal Symmetry on the Surface of a Magnetically Doped Topological Insulator
journal, May 2011


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


Classification of two-dimensional topological crystalline superconductors and Majorana bound states at disclinations
journal, June 2014

  • Benalcazar, Wladimir A.; Teo, Jeffrey C. Y.; Hughes, Taylor L.
  • Physical Review B, Vol. 89, Issue 22
  • DOI: 10.1103/PhysRevB.89.224503

Quantized response and topology of magnetic insulators with inversion symmetry
journal, April 2012


Topological insulators and superconductors: tenfold way and dimensional hierarchy
journal, June 2010


Building crystalline topological phases from lower-dimensional states
journal, November 2017


Massive Dirac Fermion on the Surface of a Magnetically Doped Topological Insulator
journal, August 2010


Gauging Spatial Symmetries and the Classification of Topological Crystalline Phases
journal, March 2018


Observation of Unconventional Quantum Spin Textures in Topological Insulators
journal, February 2009


Graph theory data for topological quantum chemistry
journal, August 2017


Topological insulators with inversion symmetry
journal, July 2007


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


Quasiparticle scattering and the protected nature of the topological states in a parent topological insulator Bi 2 Se 3
journal, January 2010


Topology of crystalline insulators and superconductors
journal, October 2014


Quantum Spin Hall Effect in Graphene
journal, November 2005


Higher-order topology in bismuth
journal, July 2018


Structure and topology of band structures in the 1651 magnetic space groups
journal, August 2018

  • Watanabe, Haruki; Po, Hoi Chun; Vishwanath, Ashvin
  • Science Advances, Vol. 4, Issue 8
  • DOI: 10.1126/sciadv.aat8685

Inversion-symmetric topological insulators
journal, June 2011


Quantum Spin Hall Effect in Inverted Type-II Semiconductors
journal, June 2008


Observation of Time-Reversal-Protected Single-Dirac-Cone Topological-Insulator States in Bi 2 Te 3 and Sb 2 Te 3
journal, September 2009


Bulk topological invariants in noninteracting point group symmetric insulators
journal, September 2012


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

  • Xia, Y.; Qian, D.; Hsieh, D.
  • Nature Physics, Vol. 5, Issue 6, p. 398-402
  • DOI: 10.1038/nphys1274

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

  • Tanaka, Y.; Ren, Zhi; Sato, T.
  • Nature Physics, Vol. 8, Issue 11
  • DOI: 10.1038/nphys2442

Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators
journal, December 2017

  • Benalcazar, Wladimir A.; Bernevig, B. Andrei; Hughes, Taylor L.
  • Physical Review B, Vol. 96, Issue 24
  • DOI: 10.1103/PhysRevB.96.245115

Quantitative mappings between symmetry and topology in solids
journal, August 2018


New Class of Topological Superconductors Protected by Magnetic Group Symmetries
journal, March 2014


Experimental evidence of hourglass fermion in the candidate nonsymmorphic topological insulator KHgSb
journal, May 2017


Topological quantum chemistry
journal, July 2017

  • Bradlyn, Barry; Elcoro, L.; Cano, Jennifer
  • Nature, Vol. 547, Issue 7663
  • DOI: 10.1038/nature23268

Classification of topological insulators and superconductors in three spatial dimensions
journal, November 2008


Majorana Corner Modes in a High-Temperature Platform
journal, August 2018


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


Antiferromagnetic topological insulators
journal, June 2010


Reflection-Symmetric Second-Order Topological Insulators and Superconductors
journal, December 2017


Dislocation charges reveal two-dimensional topological crystalline invariants
journal, May 2018


( d 2 ) -Dimensional Edge States of Rotation Symmetry Protected Topological States
journal, December 2017


Topolectrical-circuit realization of topological corner modes
journal, September 2018


Quantum spin Hall effect in two-dimensional transition metal dichalcogenides
journal, November 2014


Spin-filtered edge states with an electrically tunable gap in a two-dimensional topological crystalline insulator
journal, December 2013

  • Liu, Junwei; Hsieh, Timothy H.; Wei, Peng
  • Nature Materials, Vol. 13, Issue 2
  • DOI: 10.1038/nmat3828

Quantized electric multipole insulators
journal, July 2017

  • Benalcazar, Wladimir A.; Bernevig, B. Andrei; Hughes, Taylor L.
  • Science, Vol. 357, Issue 6346
  • DOI: 10.1126/science.aah6442

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


Emergence of topological and topological crystalline phases in TlBiS2 and TlSbS2
journal, February 2015

  • Zhang, Qingyun; Cheng, Yingchun; Schwingenschlögl, Udo
  • Scientific Reports, Vol. 5, Issue 1
  • DOI: 10.1038/srep08379

The space group classification of topological band-insulators
journal, December 2012

  • Slager, Robert-Jan; Mesaros, Andrej; Juričić, Vladimir
  • Nature Physics, Vol. 9, Issue 2
  • DOI: 10.1038/nphys2513

Spin-Orbit-Free Topological Insulators without Time-Reversal Symmetry
journal, September 2014


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


A quantized microwave quadrupole insulator with topologically protected corner states
journal, March 2018

  • Peterson, Christopher W.; Benalcazar, Wladimir A.; Hughes, Taylor L.
  • Nature, Vol. 555, Issue 7696
  • DOI: 10.1038/nature25777

Transmission of topological surface states through surface barriers
journal, July 2010

  • Seo, Jungpil; Roushan, Pedram; Beidenkopf, Haim
  • Nature, Vol. 466, Issue 7304, p. 343-346
  • DOI: 10.1038/nature09189

Entanglement and inversion symmetry in topological insulators
journal, December 2010


One-dimensional topologically protected modes in topological insulators with lattice dislocations
journal, March 2009

  • Ran, Ying; Zhang, Yi; Vishwanath, Ashvin
  • Nature Physics, Vol. 5, Issue 4
  • DOI: 10.1038/nphys1220

Topological invariants for the Fermi surface of a time-reversal-invariant superconductor
journal, April 2010


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


A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class
journal, June 2015

  • Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya
  • Nature Communications, Vol. 6, Issue 1
  • DOI: 10.1038/ncomms8373