Fermi arc criterion for surface Majorana modes in superconducting time-reversal symmetric Weyl semimetals

Abstract

Many clever routes to Majorana fermions have been discovered by exploiting the interplay between superconductivity and band topology in metals and insulators. However, realizations in semimetals remain less explored. We ask, ``under what conditions do superconductor vortices in time-reversal symmetric Weyl semimetals -- three-dimensional semimetals with only time-reversal symmetry -- trap Majorana fermions on the surface?'' If each constant-$k_z$ plane, where $z$ is the vortex axis, contains equal numbers of Weyl nodes of each chirality, we predict a generically gapped vortex and derive a topological invariant $\nu =\pm 1$ in terms of the Fermi arc structure that signals the presence or absence of surface Majorana fermions. In contrast, if certain constant-$k_z$ planes contain a net chirality of Weyl nodes, the vortex is gapless. We analytically calculate $\nu$ within a perturbative scheme and provide numerical support with a lattice model. The criteria survive the presence of other bulk and surface bands and yield phase transitions between trivial, gapless and topological vortices upon tilting the vortex. We propose Li(Fe${}_{0.91}$Co${}_{0.09}$)As and Fe${}_{1+y}$Se${}_{0.45}$Te${}_{0.55}$ with broken inversion symmetry as candidates for realizing our proposals.

arXiv comment5+6 pages, 4+2 figures Generality of result clarified; materials predictions updated; continuum limit calculation added to Appendix

References in corpus (58)

• Topological insulators and superconductors
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Topological Insulators in Three Dimensions
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• New directions in the pursuit of Majorana fermions in solid state systems
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Weyl Semimetal in a Topological Insulator Multilayer
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Search for Majorana fermions in superconductors
• Topological superconductors: a review
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Chiral Anomaly and Classical Negative Magnetoresistance of Weyl Metals
• Observation of the fractional ac Josephson effect: the signature of Majorana particles
• Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal NbP
• Topological response in Weyl semimetals and the chiral anomaly
• Quantum Hall effects in a Weyl Semi-Metal: possible application in pyrochlore Iridates
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Introduction to topological superconductivity and Majorana fermions
• Evidence for Majorana bound state in an iron-based superconductor
• Recent developments in transport phenomena in Weyl semimetals
• Observation of topological superconductivity on the surface of an iron-based superconductor
• Quantized circular photogalvanic effect in Weyl semimetals
• Electromagnetic Response of Weyl Semimetals
• Anomalous Hall Effect in Weyl Metals
• Chiral anomaly and transport in Weyl metals
• Chiral gauge field and axial anomaly in a Weyl semi-metal
• Weyl Metals
• Classification of Topological Insulators and Superconductors
• Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te)
• Topological superconductivity on the surface of Fe-based superconductors
• Search for Majorana fermions in multiband semiconducting nanowires
• Multiple topological states in iron-based superconductors
• Electronic Transport and quantum oscillation of Topological Semimetals
• Weyl semimetals from noncentrosymmetric topological insulators
• Proximity effect at the superconductor - topological insulator interface
• Robust and clean Majorana zero mode in the vortex core of high-temperature superconductor (Li0.84Fe0.16)OHFeSe
• Anomaly related transport of Weyl fermions for Weyl semi-metals
• Axion response in Weyl semimetals
• Observation of half-integer level shift of vortex bound states in an iron-based superconductor
• Majorana Fermions in Nodal Superconductors: Gapless Topological Phase
• Anomaly/Transport in an Ideal Weyl gas
• Tunable circular dichroism due to the chiral anomaly in Weyl semimetals
• Optical gyrotropy as a test for dynamic chiral magnetic effect of Weyl semimetals
• 3D Quantum Hall Effect Manipulated by Chiral Landau Levels in Weyl Semimetals
• Giant optical activity and Kerr effect in type-I and type-II Weyl semimetals
• Quasi 1D topological nodal vortex line phase in doped superconducting 3D Dirac Semimetals
• Crystalline symmetry protected helical Majorana modes in the iron pnictides
• Vortex end Majorana zero modes in superconducting Dirac and Weyl semimetals
• Spin-Fluctuation-Induced Non-Fermi-Liquid Behavior with suppressed superconductivity in LiFe${}_{1-x}$Co${}_x$As
• Topological superconductivity and Majorana bound states at the LaAlO${}_3$/SrTiO${}_3$ interface
• Electron Transport in Dirac and Weyl Semimetals
• A direct road to Majorana fields
• Negative thermal magnetoresistivity as a signature of chiral anomaly in Weyl superconductors
• Characterizations of topological superconductors: Chern numbers, edge states and Majorana zero modes