Three-dimensional Majorana fermions in chiral superconductors

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

doi:10.1126/sciadv.1601835

Three-dimensional Majorana fermions in chiral superconductors

Journal Article · Wed Dec 07 00:00:00 EST 2016 · Science Advances

DOI:https://doi.org/10.1126/sciadv.1601835· OSTI ID:1424930

Kozii, Vladyslav ^[1]; Venderbos, Jorn W. F. ^[2]; Fu, Liang ^[2]

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

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.

View Accepted Manuscript (DOE)

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

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

Grant/Contract Number:: SC0010526

OSTI ID:: 1424930

Journal Information:: Science Advances, Journal Name: Science Advances Journal Issue: 12 Vol. 2; ISSN 2375-2548

Publisher:: AAASCopyright Statement

Country of Publication:: United States

Language:: English

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Odd-Parity Pairing Superconductivity under Tetragonal Symmetry -Possible Application to Sr ₂ RuO ₄ - Machida, Kazushige; Ozaki, Masa-aki; Ohmi, Tetsuo Journal of the Physical Society of Japan, Vol. 65, Issue 12 https://doi.org/10.1143/JPSJ.65.3720	journal	December 1996
Thermodynamical Study on the Heavy-Fermion Superconductor PrOs ₄ Sb ₁₂ : Evidence for Field-Induced Phase Transition Aoki, Yuji; Namiki, Takahiro; Ohsaki, Shuji Journal of the Physical Society of Japan, Vol. 71, Issue 9 https://doi.org/10.1143/JPSJ.71.2098	journal	September 2002
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 Katayama, Kouta; Kawasaki, Shinji; Nishiyama, Masahide Journal of the Physical Society of Japan, Vol. 76, Issue 2 https://doi.org/10.1143/JPSJ.76.023701	journal	February 2007
Strong Anisotropy in Spin Susceptibility of Superfluid ³ He-B Film Caused by Surface Bound States Nagato, Yasushi; Higashitani, Seiji; Nagai, Katsuhiko Journal of the Physical Society of Japan, Vol. 78, Issue 12 https://doi.org/10.1143/JPSJ.78.123603	journal	December 2009
Superconducting Characteristics of Filled Skutterudites LaPt ₄ Ge ₁₂ and PrPt ₄ Ge ₁₂ : ⁷³ Ge-NQR/NMR Studies Kanetake, Fumiya; Mukuda, Hidekazu; Kitaoka, Yoshio Journal of the Physical Society of Japan, Vol. 79, Issue 6 https://doi.org/10.1143/JPSJ.79.063702	journal	June 2010
Search for Majorana Fermions in Superconductors Beenakker, C. W. J. Annual Review of Condensed Matter Physics, Vol. 4, Issue 1 https://doi.org/10.1146/annurev-conmatphys-030212-184337	journal	April 2013
Penetration depth, multiband superconductivity, and absence of muon-induced perturbation in superconducting PrOs$_{4}$Sb$_{12}$ Shu, Lei; MacLaughlin, D. E.; Beyermann, W. P. arXiv https://doi.org/10.48550/arxiv.0806.2386	text	January 2008
Superfluid Density and Energy Gap-Function of Superconducting PrPt4Ge12 Maisuradze, A.; Nicklas, M.; Gumeniuk, R. arXiv https://doi.org/10.48550/arxiv.0902.1083	text	January 2009
Topologically stable gapless phases of time-reversal invariant superconductors Béri, B. arXiv https://doi.org/10.48550/arxiv.0909.5680	text	January 2009
Strong Anisotropy in Spin Suceptibility of Superfluid 3He-B Film Caused by Surface Bound States Nagato, Yasushi; Higashitani, Seiji; Nagai, Katsuhiko arXiv https://doi.org/10.48550/arxiv.0910.2816	text	January 2009
Surface density of states and topological edge states in non-centrosymmetric superconductors Yada, Keiji; Sato, Masatoshi; Tanaka, Yukio arXiv https://doi.org/10.48550/arxiv.1011.2002	text	January 2010
Topology of Andreev Bound States with Flat Dispersion Sato, Masatoshi; Tanaka, Yukio; Yada, Keiji arXiv https://doi.org/10.48550/arxiv.1102.1322	text	January 2011
Weyl Semimetal in a Topological Insulator Multilayer Burkov, A. A.; Balents, Leon arXiv https://doi.org/10.48550/arxiv.1105.5138	text	January 2011
Types of topological surface states in nodal noncentrosymmetric superconductors Schnyder, Andreas P.; Brydon, P. M. R.; Timm, Carsten arXiv https://doi.org/10.48550/arxiv.1111.1207	text	January 2011
Search for Majorana fermions in superconductors Beenakker, C. W. J. arXiv https://doi.org/10.48550/arxiv.1112.1950	text	January 2011
Friedel oscillations due to Fermi arcs in Weyl semimetals Hosur, Pavan arXiv https://doi.org/10.48550/arxiv.1208.0027	text	January 2012
Topological Fermi arcs in superfluid $^3$He Silaev, M. A.; Volovik, G. E. arXiv https://doi.org/10.48550/arxiv.1209.3368	text	January 2012
Chiral $d$-wave Superconductivity in SrPtAs Fischer, Mark H.; Neupert, Titus; Platt, Christian arXiv https://doi.org/10.48550/arxiv.1311.4909	text	January 2013
Weyl points in three-dimensional optical lattices: synthetic magnetic monopoles in momentum space Dubček, Tena; Kennedy, Colin J.; Lu, Ling arXiv https://doi.org/10.48550/arxiv.1412.7615	text	January 2014
Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs Xu, Su-Yang; Belopolski, Ilya; Alidoust, Nasser arXiv https://doi.org/10.48550/arxiv.1502.03807	text	January 2015
Experimental discovery of Weyl semimetal TaAs Lv, B. Q.; Weng, H. M.; Fu, B. B. arXiv https://doi.org/10.48550/arxiv.1502.04684	text	January 2015
Observation of Weyl nodes in TaAs Lv, B. Q.; Xu, N.; Weng, H. M. arXiv https://doi.org/10.48550/arxiv.1503.09188	text	January 2015
It has been a Weyl coming Bernevig, B. Andrei arXiv https://doi.org/10.48550/arxiv.1508.04170	text	January 2015
Landau level degeneracy and quantum Hall effect in a graphite bilayer McCann, Edward; Fal'ko, Vladimir I. arXiv https://doi.org/10.48550/arxiv.cond-mat/0510237	text	January 2005
Nodal Structure of Unconventional Superconductors Probed by the Angle Resolved Thermal Transport Measurements Matsuda, Y.; Izawa, K.; Vekhter, I. arXiv https://doi.org/10.48550/arxiv.cond-mat/0611371	text	January 2006
Evidence for Point Nodes in the Superconducting Gap Function in the Filled Skutterudite Heavy-Fermion Compound PrOs4Sb12: 123Sb-NQR Study under Pressure Katayama, Kouta; Kawasaki, Shinji; Nishiyama, Masahide arXiv https://doi.org/10.48550/arxiv.cond-mat/0701613	text	January 2007
Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to ³ He— Mizushima, Takeshi; Tsutsumi, Yasumasa; Kawakami, Takuto Journal of the Physical Society of Japan, Vol. 85, Issue 2 https://doi.org/10.7566/JPSJ.85.022001	journal	February 2016

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Generalized Spin Fluctuation Feedback In Correlated Fermion Superconductors Amin, Adil; Agterberg, D. F. arXiv https://doi.org/10.48550/arxiv.1910.10780	text	January 2019
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Chiral superconductivity in heavy-fermion metal UTe2 Jiao, Lin; Howard, Sean; Ran, Sheng Nature, Vol. 579, Issue 7800 https://doi.org/10.1038/s41586-020-2122-2	journal	March 2020
Broken time-reversal symmetry in superconducting Pr 1 − x La x Pt 4 Ge 12 Zhang, J.; Ding, Z. F.; Huang, K. Physical Review B, Vol. 100, Issue 2 https://doi.org/10.1103/physrevb.100.024508	journal	July 2019
Fermi surface investigation of the filled skutterudite LaRu 4 As 12 Klotz, J.; Götze, K.; Lorenz, V. Physical Review B, Vol. 100, Issue 20 https://doi.org/10.1103/physrevb.100.205106	journal	November 2019
P 2 3 superfluids are topological Mizushima, Takeshi; Masuda, Kota; Nitta, Muneto Physical Review B, Vol. 95, Issue 14 https://doi.org/10.1103/physrevb.95.140503	journal	April 2017
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Weak-pairing higher order topological superconductors Wang, Yuxuan; Lin, Mao; Hughes, Taylor L. Physical Review B, Vol. 98, Issue 16 https://doi.org/10.1103/physrevb.98.165144	journal	October 2018
Polar Kerr Effect from Time-Reversal Symmetry Breaking in the Heavy-Fermion Superconductor PrOs 4 Sb 12 Levenson-Falk, E. M.; Schemm, E. R.; Aoki, Y. Physical Review Letters, Vol. 120, Issue 18 https://doi.org/10.1103/physrevlett.120.187004	journal	May 2018
Quasi-Two-Dimensional Fermi Surfaces and Unitary Spin-Triplet Pairing in the Heavy Fermion Superconductor UTe 2 Xu, Yuanji; Sheng, Yutao; Yang, Yi-feng Physical Review Letters, Vol. 123, Issue 21 https://doi.org/10.1103/physrevlett.123.217002	journal	November 2019
Symmetry of Order Parameters in Multiband Superconductors LaRu 4 As 12 and PrOs 4 Sb 12 Probed by Local Magnetization Measurements Juraszek, J.; Wawryk, R.; Henkie, Z. Physical Review Letters, Vol. 124, Issue 2 https://doi.org/10.1103/physrevlett.124.027001	journal	January 2020
Pairing States of Spin- 3 2 Fermions: Symmetry-Enforced Topological Gap Functions Venderbos, Jörn W. F.; Savary, Lucile; Ruhman, Jonathan Physical Review X, Vol. 8, Issue 1 https://doi.org/10.1103/physrevx.8.011029	journal	February 2018
Weak-Pairing Higher Order Topological Superconductors Wang, Yuxuan; Lin, Mao; Hughes, Taylor L. arXiv https://doi.org/10.48550/arxiv.1804.01531	text	January 2018

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