Three-dimensional Majorana fermions in chiral superconductors

Kozii, Vladyslav; Venderbos, Jorn W.  F.; Fu, Liang

doi:10.1126/sciadv.1601835

Title: Three-dimensional Majorana fermions in chiral superconductors

Abstract

Using a systematic symmetry and topology analysis, we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are spin-nondegenerate and realize Majorana fermions in three dimensions. By examining all types of chiral Cooper pairs with total angular momentum J formed by Bloch electrons with angular momentum j in crystals, we obtain a comprehensive classification of gapless Majorana quasiparticles in terms of energy-momentum relation and location on the Fermi surface. We show that the existence of bulk Majorana fermions in the vicinity of spin-selective point nodes is rooted in the nonunitary nature of chiral pairing in spin-orbit–coupled superconductors. We address experimental signatures of Majorana fermions and find that the nuclear magnetic resonance spin relaxation rate is significantly suppressed for nuclear spins polarized along the nodal direction as a consequence of the spin-selective Majorana nature of nodal quasiparticles. Furthermore, Majorana nodes in the bulk have nontrivial topology and imply the presence of Majorana bound states on the surface, which form arcs in momentum space. We conclude by proposing the heavy fermion superconductor PrOs₄Sb₁₂ and related materials as promising candidates for nonunitary chiral superconductors hosting three-dimensional Majorana fermions.

Authors:

Kozii, Vladyslav ^[1]; Venderbos, Jorn W. F. ^[1]; Fu, Liang ^[1]

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

Publication Date:: Wed Dec 07 00:00:00 EST 2016

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

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division

OSTI Identifier:: 1424930

Grant/Contract Number:: SC0010526

Resource Type:: Accepted Manuscript

Journal Name:: Science Advances

Additional Journal Information:: Journal Volume: 2; Journal Issue: 12; Journal ID: ISSN 2375-2548

Publisher:: AAAS

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Spin-orbit coupling; unconventional superconductivity; topological nodal superconductors; Majorana fermions; heavy fermion skutterudites; NMR spin relaxation; Majorana arcs

Citation Formats


                    Kozii, Vladyslav, Venderbos, Jorn W.  F., and Fu, Liang. Three-dimensional Majorana fermions in chiral superconductors.  United States: N. p., 2016. 
Web.  doi:10.1126/sciadv.1601835.

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                    Kozii, Vladyslav, Venderbos, Jorn W.  F., & Fu, Liang. Three-dimensional Majorana fermions in chiral superconductors.  United States.  https://doi.org/10.1126/sciadv.1601835

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                    Kozii, Vladyslav, Venderbos, Jorn W.  F., and Fu, Liang. Wed .  
"Three-dimensional Majorana fermions in chiral superconductors".  United States.  https://doi.org/10.1126/sciadv.1601835.  https://www.osti.gov/servlets/purl/1424930.

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@article{osti_1424930,

  title        = {Three-dimensional Majorana fermions in chiral superconductors},

  author       = {Kozii, Vladyslav and Venderbos, Jorn W.  F. and Fu, Liang},

  abstractNote = {Using a systematic symmetry and topology analysis, we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are spin-nondegenerate and realize Majorana fermions in three dimensions. By examining all types of chiral Cooper pairs with total angular momentum J formed by Bloch electrons with angular momentum j in crystals, we obtain a comprehensive classification of gapless Majorana quasiparticles in terms of energy-momentum relation and location on the Fermi surface. We show that the existence of bulk Majorana fermions in the vicinity of spin-selective point nodes is rooted in the nonunitary nature of chiral pairing in spin-orbit–coupled superconductors. We address experimental signatures of Majorana fermions and find that the nuclear magnetic resonance spin relaxation rate is significantly suppressed for nuclear spins polarized along the nodal direction as a consequence of the spin-selective Majorana nature of nodal quasiparticles. Furthermore, Majorana nodes in the bulk have nontrivial topology and imply the presence of Majorana bound states on the surface, which form arcs in momentum space. We conclude by proposing the heavy fermion superconductor PrOs4Sb12 and related materials as promising candidates for nonunitary chiral superconductors hosting three-dimensional Majorana fermions.},

  doi          = {10.1126/sciadv.1601835},

  journal      = {Science Advances},

  number       = 12,

  volume       = 2,

  place        = {United States},

  year         = {Wed Dec 07 00:00:00 EST 2016},

  month        = {Wed Dec 07 00:00:00 EST 2016}

}

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DOI: 10.48550/arxiv.1102.1322

Weyl Semimetal in a Topological Insulator Multilayer
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DOI: 10.48550/arxiv.1105.5138

Types of topological surface states in nodal noncentrosymmetric superconductors
text, January 2011

Schnyder, Andreas P.; Brydon, P. M. R.; Timm, Carsten
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Friedel oscillations due to Fermi arcs in Weyl semimetals
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Hosur, Pavan
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DOI: 10.48550/arxiv.cond-mat/0206193

Works referencing / citing this record:

Chiral superconductivity in heavy-fermion metal UTe2
journal, March 2020

Jiao, Lin; Howard, Sean; Ran, Sheng
Nature, Vol. 579, Issue 7800
DOI: 10.1038/s41586-020-2122-2

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Klotz, J.; Götze, K.; Lorenz, V.
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Physical Review X, Vol. 8, Issue 1
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DOI: 10.48550/arxiv.1710.07403

Non-Abelian Charge Transport in Three-Flavor Gauge Semimetal Model with Braiding Majoranas
preprint, January 2017

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DOI: 10.48550/arxiv.1712.05144

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Title: Three-dimensional Majorana fermions in chiral superconductors

Abstract

Citation Formats

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A theoretical description of the new phases of liquid He 3 journal, April 1975

Weyl electrons kiss journal, May 2011

Majorana returns journal, September 2009

Search for Majorana Fermions in Superconductors journal, April 2013

Phenomenological theory of unconventional superconductivity journal, April 1991

Possible Pairing Mechanism and Double Transitions in UPt 3 journal, November 1996

Nonunitary Spin-Triplet Superconductivity in UPt 3 : Evidence from P 195 t Knight Shift Study journal, April 1998

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

Pairing Symmetry of the Superconductor Sr 2 RuO 4 journal, November 1996

Odd-Parity Pairing Superconductivity under Tetragonal Symmetry -Possible Application to Sr 2 RuO 4 - journal, December 1996

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Relativistic analysis of the pairing symmetry of the noncentrosymmetric superconductor LaNiC 2 journal, November 2010

Thermal Anomalies of He 3 : Pairing in a Magnetic Field journal, January 1973

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Pairing of j = 3 / 2 Fermions in Half-Heusler Superconductors journal, April 2016

Exotic Multigap Structure in UPt 3 Unveiled by a First-Principles Analysis journal, November 2016

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Topological relation between bulk gap nodes and surface bound states: Application to iron-based superconductors journal, September 2012

Nodal structure of superconductors with time-reversal invariance and Z 2 topological number journal, June 2006

Topologically stable gapless phases of time-reversal-invariant superconductors journal, April 2010

Topological phases and surface flat bands in superconductors without inversion symmetry journal, August 2011

Topologically protected flat zero-energy surface bands in noncentrosymmetric superconductors journal, July 2011

Types of topological surface states in nodal noncentrosymmetric superconductors journal, January 2012

Topology of Andreev bound states with flat dispersion journal, June 2011

Surface density of states and topological edge states in noncentrosymmetric superconductors journal, February 2011

Anomalous Andreev Bound State in Noncentrosymmetric Superconductors journal, August 2010

Superconductivity of doped Weyl semimetals: Finite-momentum pairing and electronic analog of the 3 He- A phase journal, December 2012

Weyl phases in point-group symmetric superconductors journal, October 2013

Odd-parity superconductivity in Weyl semimetals journal, January 2014

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Topological Superconductivity in Dirac Semimetals journal, October 2015

Crossed Surface Flat Bands of Weyl Semimetal Superconductors journal, March 2015

Superconductivity in Weyl metals journal, July 2015

Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates journal, May 2011

Multi-Weyl Topological Semimetals Stabilized by Point Group Symmetry journal, June 2012

Nodal structure of unconventional superconductors probed by angle resolved thermal transport measurements journal, October 2006

Nuclear Spin Relaxation in Normal and Superconducting Aluminum journal, March 1959

Detecting the Majorana Fermion Surface State of He 3 − B through Spin Relaxation journal, December 2009

Protected boundary states in gapless topological phases journal, June 2013

Majorana surface states of superfluid He 3 A and B phases in a slab journal, March 2011

Topological Weyl superconductor to diffusive thermal Hall metal crossover in the B phase of UPt 3 journal, December 2015

Weyl Semimetal in a Topological Insulator Multilayer journal, September 2011

Topological nodal semimetals journal, December 2011

Friedel oscillations due to Fermi arcs in Weyl semimetals journal, November 2012

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Discovery of a Weyl fermion semimetal and topological Fermi arcs journal, July 2015

Experimental Discovery of Weyl Semimetal TaAs journal, July 2015

Observation of Weyl nodes in TaAs journal, August 2015

Weyl semimetal phase in the non-centrosymmetric compound TaAs journal, August 2015

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Experimental observation of Weyl points journal, July 2015

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Multiple Superconducting Phases in New Heavy Fermion Superconductor P r O s 4 S b 12 journal, March 2003

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Time-Reversal Symmetry-Breaking Superconductivity in Heavy-Fermion P r O s 4 S b 12 Detected by Muon-Spin Relaxation journal, August 2003

Spin-triplet superconductivity in Pr Os 4 Sb 12 probed by muon Knight shift journal, January 2007

Superconducting states in the tetrahedral compound PrOs 4 Sb 12 journal, October 2004

Symmetry properties of the nodal superconductor Pr Os 4 Sb 12 journal, August 2007

Chiral p-wave order in Sr ₂ RuO ₄
journal, March 2012

The superconductivity of ${Sr}_{2} {RuO}_{4}$ and the physics of spin-triplet pairing
journal, May 2003

A theoretical description of the new phases of liquid ${}^{3}{He}$
journal, April 1975

Weyl electrons kiss
journal, May 2011

Majorana returns
journal, September 2009

Search for Majorana Fermions in Superconductors
journal, April 2013

Phenomenological theory of unconventional superconductivity
journal, April 1991

Possible Pairing Mechanism and Double Transitions in UPt ₃
journal, November 1996

Nonunitary Spin-Triplet Superconductivity in ${UPt}_{3}$ : Evidence from ${}^{195}P t$ Knight Shift Study
journal, April 1998

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

Pairing Symmetry of the Superconductor Sr ₂ RuO ₄
journal, November 1996

Odd-Parity Pairing Superconductivity under Tetragonal Symmetry -Possible Application to Sr ₂ RuO ₄ -
journal, December 1996

Two-Gap Superconductivity in ${LaNiGa}_{2}$ with Nonunitary Triplet Pairing and Even Parity Gap Symmetry
journal, July 2016

Relativistic analysis of the pairing symmetry of the noncentrosymmetric superconductor ${LaNiC}_{2}$
journal, November 2010

Thermal Anomalies of ${He}^{3}$ : Pairing in a Magnetic Field
journal, January 1973

Superconducting states of reduced symmetry: General order parameters and physical implications
journal, August 1993

Pairing of $j = 3 / 2$ Fermions in Half-Heusler Superconductors
journal, April 2016

Exotic Multigap Structure in ${UPt}_{3}$ Unveiled by a First-Principles Analysis
journal, November 2016

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to ³ He—
journal, February 2016

Weyl superconductors
journal, August 2012

Topologically protected surface Majorana arcs and bulk Weyl fermions in ferromagnetic superconductors
journal, September 2012

Chiral $d$ -wave superconductivity in SrPtAs
journal, January 2014

Topological relation between bulk gap nodes and surface bound states: Application to iron-based superconductors
journal, September 2012

Nodal structure of superconductors with time-reversal invariance and $Z_{2}$ topological number
journal, June 2006

Topologically stable gapless phases of time-reversal-invariant superconductors
journal, April 2010

Topological phases and surface flat bands in superconductors without inversion symmetry
journal, August 2011

Topologically protected flat zero-energy surface bands in noncentrosymmetric superconductors
journal, July 2011

Types of topological surface states in nodal noncentrosymmetric superconductors
journal, January 2012

Topology of Andreev bound states with flat dispersion
journal, June 2011

Surface density of states and topological edge states in noncentrosymmetric superconductors
journal, February 2011

Anomalous Andreev Bound State in Noncentrosymmetric Superconductors
journal, August 2010

Superconductivity of doped Weyl semimetals: Finite-momentum pairing and electronic analog of the $^{3}$ He- $A$ phase
journal, December 2012

Weyl phases in point-group symmetric superconductors
journal, October 2013

Odd-parity superconductivity in Weyl semimetals
journal, January 2014

Dirac and Weyl Superconductors in Three Dimensions
journal, July 2014

Topological Superconductivity in Dirac Semimetals
journal, October 2015

Crossed Surface Flat Bands of Weyl Semimetal Superconductors
journal, March 2015

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journal, July 2015

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journal, May 2011

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journal, June 2012

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journal, October 2006

Nuclear Spin Relaxation in Normal and Superconducting Aluminum
journal, March 1959

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journal, December 2009

Protected boundary states in gapless topological phases
journal, June 2013

Majorana surface states of superfluid ${}^{3}{He}$ $A$ and $B$ phases in a slab
journal, March 2011

Topological Weyl superconductor to diffusive thermal Hall metal crossover in the $B$ phase of ${UPt}_{3}$
journal, December 2015

Weyl Semimetal in a Topological Insulator Multilayer
journal, September 2011

Topological nodal semimetals
journal, December 2011

Friedel oscillations due to Fermi arcs in Weyl semimetals
journal, November 2012

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

Discovery of a Weyl fermion semimetal and topological Fermi arcs
journal, July 2015

Experimental Discovery of Weyl Semimetal TaAs
journal, July 2015

Observation of Weyl nodes in TaAs
journal, August 2015

Weyl semimetal phase in the non-centrosymmetric compound TaAs
journal, August 2015

It's been a Weyl coming
journal, August 2015

Weyl points and line nodes in gyroid photonic crystals
journal, March 2013

Topological photonics
journal, October 2014

Experimental observation of Weyl points
journal, July 2015

Dirac Semimetal in Three Dimensions
journal, April 2012

Chern Semimetal and the Quantized Anomalous Hall Effect in ${HgCr}_{2} {Se}_{4}$
journal, October 2011

Quantum Hall effects in a Weyl semimetal: Possible application in pyrochlore iridates
journal, August 2011

Topological and magnetic phases of interacting electrons in the pyrochlore iridates
journal, January 2012

Dirac versus Weyl Fermions in Topological Insulators: Adler-Bell-Jackiw Anomaly in Transport Phenomena
journal, December 2013

Prediction of a Weyl semimetal in ${Hg}_{1 - x - y}$ ${Cd}_{x}$ ${Mn}_{y}$ Te
journal, February 2014

Room-temperature magnetic topological Weyl fermion and nodal line semimetal states in half-metallic Heusler Co2TiX (X=Si, Ge, or Sn)
journal, December 2016

Surface Majorana fermions and bulk collective modes in superfluid ${}^{3}{He} - B$
journal, February 2015

Superconductivity and heavy fermion behavior in ${PrOs}_{4} {Sb}_{12}$
journal, February 2002

Thermodynamical Study on the Heavy-Fermion Superconductor PrOs ₄ Sb ₁₂ : Evidence for Field-Induced Phase Transition
journal, September 2002

Superconductivity in the Platinum Germanides ${MPt}_{4} {Ge}_{12}$ ( $M = Rare − Earth$ or Alkaline-Earth Metal) with Filled Skutterudite Structure
journal, January 2008

Multiple Superconducting Phases in New Heavy Fermion Superconductor ${P r O s}_{4} {S b}_{12}$
journal, March 2003

Evolution of crystalline electric field effects, superconductivity, and heavy-fermion behavior in the specific heat of $\Pr {({Os}_{1 - x} {Ru}_{x})}_{4} {Sb}_{12}$
journal, February 2005

Probing the Superconducting Gap Symmetry of ${P r O s}_{4} {S b}_{12}$ : A Penetration Depth Study
journal, December 2003

Evidence for Point Nodes in the Superconducting Gap Function in the Filled Skutterudite Heavy-Fermion Compound PrOs ₄ Sb ₁₂ : ¹²³ Sb-NQR Study under Pressure
journal, February 2007

Time-Reversal Symmetry-Breaking Superconductivity in Heavy-Fermion ${P r O s}_{4} {S b}_{12}$ Detected by Muon-Spin Relaxation
journal, August 2003

Spin-triplet superconductivity in $\Pr {Os}_{4} {Sb}_{12}$ probed by muon Knight shift
journal, January 2007

Superconducting states in the tetrahedral compound ${PrOs}_{4} {Sb}_{12}$
journal, October 2004

Symmetry properties of the nodal superconductor $\Pr {Os}_{4} {Sb}_{12}$
journal, August 2007

Probing the superconductivity of ${PrPt}_{4} {Ge}_{12}$ through Ce substitution
journal, January 2014

Evidence for time-reversal symmetry breaking in superconducting ${PrPt}_{4} {Ge}_{12}$
journal, July 2010

Superconducting Characteristics of Filled Skutterudites LaPt ₄ Ge ₁₂ and PrPt ₄ Ge ₁₂ : ⁷³ Ge-NQR/NMR Studies
journal, June 2010