Odd-parity topological superconductor with nematic order: Application to CuxBi2Se3

Fu, Liang

doi:10.1103/physrevb.90.100509

Title: Odd-parity topological superconductor with nematic order: Application to ${Cu}_{x} {Bi}_{2} {Se}_{3}$

Abstract

Cu_xBi₂Se₃ was recently proposed as a promising candidate for time-reversal-invariant topological superconductors. In this work, we argue that the unusual anisotropy of the Knight shift observed by Zheng and co-workers (unpublished), taken together with specific heat measurements, provides strong support for an unconventional odd-parity pairing in the two-dimensional E_u representation of the D_3d crystal point group, which spontaneously breaks the threefold rotational symmetry of the crystal, leading to a subsidiary nematic order. We predict that the spin-orbit interaction associated with hexagonal warping plays a crucial role in pinning the two-component order parameter and makes the superconducting state generically fully gapped, leading to a topological superconductor. In conclusion, experimental signatures of the E_u pairing related to the nematic order are discussed.

Authors:

Fu, Liang ^[1]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Publication Date:: Fri Sep 26 00:00:00 EDT 2014

Research Org.:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

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

OSTI Identifier:: 1505788

Alternate Identifier(s):: OSTI ID: 1181411

Grant/Contract Number:: SC0010526

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review. B, Condensed Matter and Materials Physics

Additional Journal Information:: Journal Volume: 90; Journal Issue: 10; Journal ID: ISSN 1098-0121

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats


                    Fu, Liang. Odd-parity topological superconductor with nematic order: Application to CuxBi2Se3.  United States: N. p., 2014. 
Web.  doi:10.1103/physrevb.90.100509.

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                    Fu, Liang. Odd-parity topological superconductor with nematic order: Application to CuxBi2Se3.  United States.  https://doi.org/10.1103/physrevb.90.100509

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                    Fu, Liang. Fri .  
"Odd-parity topological superconductor with nematic order: Application to CuxBi2Se3".  United States.  https://doi.org/10.1103/physrevb.90.100509.  https://www.osti.gov/servlets/purl/1505788.

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@article{osti_1505788,

  title        = {Odd-parity topological superconductor with nematic order: Application to CuxBi2Se3},

  author       = {Fu, Liang},

  abstractNote = {CuxBi2Se3 was recently proposed as a promising candidate for time-reversal-invariant topological superconductors. In this work, we argue that the unusual anisotropy of the Knight shift observed by Zheng and co-workers (unpublished), taken together with specific heat measurements, provides strong support for an unconventional odd-parity pairing in the two-dimensional Eu representation of the D3d crystal point group, which spontaneously breaks the threefold rotational symmetry of the crystal, leading to a subsidiary nematic order. We predict that the spin-orbit interaction associated with hexagonal warping plays a crucial role in pinning the two-component order parameter and makes the superconducting state generically fully gapped, leading to a topological superconductor. In conclusion, experimental signatures of the Eu pairing related to the nematic order are discussed.},

  doi          = {10.1103/physrevb.90.100509},

  journal      = {Physical Review. B, Condensed Matter and Materials Physics},

  number       = 10,

  volume       = 90,

  place        = {United States},

  year         = {Fri Sep 26 00:00:00 EDT 2014},

  month        = {Fri Sep 26 00:00:00 EDT 2014}

}

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Figures / Tables:

FIG. 1: (a) Crystal structure of Cu_xBi₂Se₃ viewed from the c axis. Note that the x axis is normal to a mirror plane. (b) Hexagonal Fermi contour at k_z = 0 for the Hamiltonian. (c) and (d) show the angle dependence of the anisotropic superconducting gap over the k_z =more »

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We report comprehensive 77 Se NMR measurements on a single crystalline sample of the recently discovered FeSe-based high-temperature superconductor K x Fe 2 - y Se 2 ( T c = 33 K) in a broad temperature range up to 290 K. Despite deviations from the stoichiometric KFe 2 Se 2 composition, we observed 77 Se NMR line shapes as narrow as 4.5 kHz under a magnetic field applied along the crystal c axis, and found no evidence for co-existence of magnetic order with superconductivity. On the other hand, the 77 Se NMR line shape splits into two peaks withmore »« less
https://doi.org/10.1103/PhysRevB.83.104508
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Title: Odd-parity topological superconductor with nematic order: Application to Cu x Bi 2 Se 3

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The Transition Between Real and Complex Superconducting Order Parameter Phases in UPt3 journal, June 2010

Ising and spin orders in the iron-based superconductors journal, July 2008

Bulk Superconducting Phase with a Full Energy Gap in the Doped Topological Insulator Cu x Bi 2 Se 3 journal, March 2011

Striped superconductors: how spin, charge and superconducting orders intertwine in the cuprates journal, November 2009

Quantum Oscillations in the Topological Superconductor Candidate Cu 0.25 Bi 2 Se 3 journal, November 2012

Models of superconducting Cu:Bi 2 Se 3 : Single- versus two-band description journal, March 2013

Field-Angle-Dependent Low-Energy Excitations around a Vortex in the Superconducting Topological Insulator Cu x Bi 2 Se 3 journal, June 2014

Model Hamiltonian for topological insulators journal, July 2010

Time-Reversal-Invariant Topological Superconductors and Superfluids in Two and Three Dimensions journal, May 2009

Strong Increase of Tc of Sr2RuO4 Under Both Tensile and Compressive Strain journal, April 2014

Chiral superconductivity from repulsive interactions in doped graphene journal, January 2012

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

Topological Superconductivity in Cu x Bi 2 Se 3 journal, November 2011

Topological superconducting phase in the vicinity of ferromagnetic phases journal, July 2012

The order parameter for the superconducting phases of UPt 3 journal, February 1994

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

Phenomenological theory of unconventional superconductivity journal, April 1991

Topological odd-parity superconductors journal, June 2010

Topological Superconductivity in Bilayer Rashba System journal, April 2012

Evolution of the Fermi surface of a doped topological insulator with carrier concentration journal, November 2013

Two-dimensional time-reversal-invariant topological superconductivity in a doped quantum spin-Hall insulator journal, August 2014

Migdal's theorem and electron-phonon vertex corrections in Dirac materials journal, April 2014

Symmetry properties of triplet superconductors journal, September 1985

Time-reversal-invariant topological superconductivity in doped Weyl semimetals journal, July 2014

Hexagonal Warping Effects in the Surface States of the Topological Insulator Bi 2 Te 3 journal, December 2009

Superconductivity in Cu x Bi 2 Se 3 and its Implications for Pairing in the Undoped Topological Insulator journal, February 2010

Quasi-Classical Theory of Tunneling Spectroscopy in Superconducting Topological Insulator journal, June 2014

Superconductivity in the Doped Topological Insulator Cu x Bi 2 Se 3 under High Pressure journal, January 2012

Majorana Fermions and Exotic Surface Andreev Bound States in Topological Superconductors: Application to Cu x Bi 2 Se 3 journal, March 2012

Experimental Evidence for s -Wave Pairing Symmetry in Superconducting Cu x Bi 2 Se 3 Single Crystals Using a Scanning Tunneling Microscope journal, March 2013

Theory of electron nematic order in LaFeAsO journal, June 2008

Observation of topological order in a superconducting doped topological insulator journal, September 2010

Preemptive nematic order, pseudogap, and orbital order in the iron pnictides journal, January 2012

Point-contact spectroscopy of Cu 0.2 Bi 2 Se 3 single crystals journal, August 2012

Turning a band insulator into an exotic superconductor journal, July 2014

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

Topological Blount's theorem of odd-parity superconductors journal, July 2014

Classification of topological insulators and superconductors in three spatial dimensions text, January 2008

Preemptive nematic order, pseudogap, and orbital order in the iron pnictides text, January 2011

Superconductivity in the doped topological insulator Cu$_x$Bi$_2$Se$_3$ under high pressure text, January 2011

Turning a Band Insulator Into an Exotic Superconductor text, January 2013

Migdal's theorem and electron-phonon vertex corrections in Dirac materials text, January 2014

Two-dimensional time-reversal-invariant topological superconductivity in a doped quantum spin Hall insulator text, January 2014

Quasi-classical theory of tunneling spectroscopy in superconducting topological insulator text, January 2014

Field-angle-dependent low-energy excitations around a vortex in the superconducting topological insulator CuxBi2Se3 text, January 2014

Time-reversal invariant topological superconductivity in doped Weyl semimetals text, January 2014

Exploring Topological Superconductivity in Topological Materials journal, July 2019

Drive the Dirac electrons into Cooper pairs in SrxBi2Se3 journal, February 2017

Thermodynamic evidence for nematic superconductivity in CuxBi2Se3 journal, October 2016

Evidence for singular-phonon-induced nematic superconductivity in a topological superconductor candidate Sr0.1Bi2Se3 journal, June 2019

Direction and symmetry transition of the vector order parameter in topological superconductors CuxBi2Se3 journal, January 2020

Nematic topological superconducting phase in Nb-doped Bi2Se3 journal, October 2017

Superconductivity from valley fluctuations and approximate SO(4) symmetry in a weak coupling theory of twisted bilayer graphene journal, April 2019

Evidence of anisotropic Majorana bound states in 2M-WS2 journal, July 2019

Superconducting and normal-state anisotropy of the doped topological insulator Sr0.1Bi2Se3 journal, May 2018

Rotational symmetry breaking in the topological superconductor SrxBi2Se3 probed by upper-critical field experiments journal, June 2016

Visualizing pairing symmetry in nematic superconductors using spin-polarized spectroscopy of magnetic impurities journal, October 2019

Topological superconductors: a review journal, May 2017

Structural distortion behind the nematic superconductivity in Sr x Bi 2 Se 3 journal, October 2018

Effect of the electron-phonon interaction on the spin texture in Bi 2 − y Sb y Se 3 − x Te x journal, October 2019

Strain-driven nematicity of odd-parity superconductivity in Sr x Bi 2 Se 3 journal, December 2019

Microscopic characterization of the superconducting gap function in Sn 1 − x In x Te journal, January 2020

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

Identification of nematic superconductivity from the upper critical field journal, September 2016

Unusual upper critical field behavior in Nb-doped bismuth selenides journal, May 2017

Quantum oscillations and Dirac-Landau levels in Weyl superconductors journal, December 2017

Nanocalorimetric evidence for nematic superconductivity in the doped topological insulator Sr 0.1 Bi 2 Se 3 journal, November 2018

Nematic superconductivity in Cu 1.5 ( PbSe ) 5 ( Bi 2 Se 3 ) 6 journal, December 2018

Antichiral and nematicity-wave superconductivity journal, June 2019

Quasiparticle Evidence for the Nematic State above T c in Sr x Bi 2 Se 3 journal, July 2019

Possible structural origin of superconductivity in Sr-doped B i 2 S e 3 journal, January 2018

Direct Visualization of the Nematic Superconductivity in Cu x Bi 2 Se 3 journal, November 2018

Beyond triplet: Unconventional superconductivity in a spin-3/2 topological semimetal journal, April 2018

Superconductivity with twofold symmetry in Bi 2 Te 3 /FeTe 0.55 Se 0.45 heterostructures journal, June 2018

Generalized Anderson’s theorem for superconductors derived from topological insulators journal, February 2020

Nematic Superconductivity in Doped Bi2Se3 Topological Superconductors journal, December 2018

Title: Odd-parity topological superconductor with nematic order: Application to ${Cu}_{x} {Bi}_{2} {Se}_{3}$

The Transition Between Real and Complex Superconducting Order Parameter Phases in UPt3
journal, June 2010

Ising and spin orders in the iron-based superconductors
journal, July 2008

Bulk Superconducting Phase with a Full Energy Gap in the Doped Topological Insulator ${Cu}_{x} {Bi}_{2} {Se}_{3}$
journal, March 2011

Striped superconductors: how spin, charge and superconducting orders intertwine in the cuprates
journal, November 2009

Quantum Oscillations in the Topological Superconductor Candidate ${Cu}_{0.25} {Bi}_{2} {Se}_{3}$
journal, November 2012

Models of superconducting Cu:Bi $_{2}$ Se $_{3}$ : Single- versus two-band description
journal, March 2013

Field-Angle-Dependent Low-Energy Excitations around a Vortex in the Superconducting Topological Insulator Cu _x Bi ₂ Se ₃
journal, June 2014

Model Hamiltonian for topological insulators
journal, July 2010

Time-Reversal-Invariant Topological Superconductors and Superfluids in Two and Three Dimensions
journal, May 2009

Strong Increase of Tc of Sr2RuO4 Under Both Tensile and Compressive Strain
journal, April 2014

Chiral superconductivity from repulsive interactions in doped graphene
journal, January 2012

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

Topological Superconductivity in ${Cu}_{x} {Bi}_{2} {Se}_{3}$
journal, November 2011

Topological superconducting phase in the vicinity of ferromagnetic phases
journal, July 2012

The order parameter for the superconducting phases of UPt ₃
journal, February 1994

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

Phenomenological theory of unconventional superconductivity
journal, April 1991

Topological odd-parity superconductors
journal, June 2010

Topological Superconductivity in Bilayer Rashba System
journal, April 2012

Evolution of the Fermi surface of a doped topological insulator with carrier concentration
journal, November 2013

Two-dimensional time-reversal-invariant topological superconductivity in a doped quantum spin-Hall insulator
journal, August 2014

Migdal's theorem and electron-phonon vertex corrections in Dirac materials
journal, April 2014

Symmetry properties of triplet superconductors
journal, September 1985

Time-reversal-invariant topological superconductivity in doped Weyl semimetals
journal, July 2014

Hexagonal Warping Effects in the Surface States of the Topological Insulator ${Bi}_{2} {Te}_{3}$
journal, December 2009

Superconductivity in ${Cu}_{x} {Bi}_{2} {Se}_{3}$ and its Implications for Pairing in the Undoped Topological Insulator
journal, February 2010

Quasi-Classical Theory of Tunneling Spectroscopy in Superconducting Topological Insulator
journal, June 2014

Superconductivity in the Doped Topological Insulator ${Cu}_{x} {Bi}_{2} {Se}_{3}$ under High Pressure
journal, January 2012

Majorana Fermions and Exotic Surface Andreev Bound States in Topological Superconductors: Application to ${Cu}_{x} {Bi}_{2} {Se}_{3}$
journal, March 2012

Experimental Evidence for $s$ -Wave Pairing Symmetry in Superconducting ${Cu}_{x} {Bi}_{2} {Se}_{3}$ Single Crystals Using a Scanning Tunneling Microscope
journal, March 2013

Theory of electron nematic order in LaFeAsO
journal, June 2008

Observation of topological order in a superconducting doped topological insulator
journal, September 2010

Preemptive nematic order, pseudogap, and orbital order in the iron pnictides
journal, January 2012

Point-contact spectroscopy of Cu $_{0.2}$ Bi $_{2}$ Se $_{3}$ single crystals
journal, August 2012

Turning a band insulator into an exotic superconductor
journal, July 2014

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

Topological Blount's theorem of odd-parity superconductors
journal, July 2014

Classification of topological insulators and superconductors in three spatial dimensions
text, January 2008

Preemptive nematic order, pseudogap, and orbital order in the iron pnictides
text, January 2011

Superconductivity in the doped topological insulator Cu$_x$Bi$_2$Se$_3$ under high pressure
text, January 2011

Turning a Band Insulator Into an Exotic Superconductor
text, January 2013

Migdal's theorem and electron-phonon vertex corrections in Dirac materials
text, January 2014

Two-dimensional time-reversal-invariant topological superconductivity in a doped quantum spin Hall insulator
text, January 2014

Quasi-classical theory of tunneling spectroscopy in superconducting topological insulator
text, January 2014

Field-angle-dependent low-energy excitations around a vortex in the superconducting topological insulator CuxBi2Se3
text, January 2014

Time-reversal invariant topological superconductivity in doped Weyl semimetals
text, January 2014

Exploring Topological Superconductivity in Topological Materials
journal, July 2019

Drive the Dirac electrons into Cooper pairs in SrxBi2Se3
journal, February 2017

Thermodynamic evidence for nematic superconductivity in CuxBi2Se3
journal, October 2016

Evidence for singular-phonon-induced nematic superconductivity in a topological superconductor candidate Sr0.1Bi2Se3
journal, June 2019

Direction and symmetry transition of the vector order parameter in topological superconductors CuxBi2Se3
journal, January 2020

Nematic topological superconducting phase in Nb-doped Bi2Se3
journal, October 2017

Superconductivity from valley fluctuations and approximate SO(4) symmetry in a weak coupling theory of twisted bilayer graphene
journal, April 2019

Evidence of anisotropic Majorana bound states in 2M-WS2
journal, July 2019

Superconducting and normal-state anisotropy of the doped topological insulator Sr0.1Bi2Se3
journal, May 2018

Rotational symmetry breaking in the topological superconductor SrxBi2Se3 probed by upper-critical field experiments
journal, June 2016

Visualizing pairing symmetry in nematic superconductors using spin-polarized spectroscopy of magnetic impurities
journal, October 2019

Topological superconductors: a review
journal, May 2017

Structural distortion behind the nematic superconductivity in Sr _x Bi ₂ Se ₃
journal, October 2018

Effect of the electron-phonon interaction on the spin texture in ${Bi}_{2 - y} {Sb}_{y} {Se}_{3 - x} {Te}_{x}$
journal, October 2019

Strain-driven nematicity of odd-parity superconductivity in ${Sr}_{x} {Bi}_{2} {Se}_{3}$
journal, December 2019

Microscopic characterization of the superconducting gap function in ${Sn}_{1 - x} {In}_{x} Te$
journal, January 2020

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

Identification of nematic superconductivity from the upper critical field
journal, September 2016

Unusual upper critical field behavior in Nb-doped bismuth selenides
journal, May 2017

Quantum oscillations and Dirac-Landau levels in Weyl superconductors
journal, December 2017

Nanocalorimetric evidence for nematic superconductivity in the doped topological insulator ${Sr}_{0.1} {Bi}_{2} {Se}_{3}$
journal, November 2018

Nematic superconductivity in ${Cu}_{1.5} {(PbSe)}_{5} {({Bi}_{2} {Se}_{3})}_{6}$
journal, December 2018

Antichiral and nematicity-wave superconductivity
journal, June 2019

Quasiparticle Evidence for the Nematic State above $T_{c}$ in ${Sr}_{x} {Bi}_{2} {Se}_{3}$
journal, July 2019

Possible structural origin of superconductivity in Sr-doped $B i_{2} S e_{3}$
journal, January 2018

Direct Visualization of the Nematic Superconductivity in ${Cu}_{x} {Bi}_{2} {Se}_{3}$
journal, November 2018

Beyond triplet: Unconventional superconductivity in a spin-3/2 topological semimetal
journal, April 2018

Superconductivity with twofold symmetry in Bi 2 Te 3 /FeTe 0.55 Se 0.45 heterostructures
journal, June 2018

Generalized Anderson’s theorem for superconductors derived from topological insulators
journal, February 2020

Nematic Superconductivity in Doped Bi2Se3 Topological Superconductors
journal, December 2018

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

Odd-parity superconductivity in the vicinity of inversion symmetry breaking in spin-orbit-coupled systems
text, January 2015

Beyond Triplet: Unconventional Superconductivity in a Spin-3/2 Topological Semimetal
text, January 2016