Vortex end Majorana zero modes in superconducting Dirac and Weyl semimetals

Abstract

Time-reversal invariant (TRI) Dirac and Weyl semimetals in three dimensions (3D) can host open Fermi arcs and spin-momentum locking Fermi loops on the surfaces. We find that when they become superconducting with $s$-wave pairing and the doping is lower than a critical level, straight $\pi$-flux vortex lines terminating at surfaces with Fermi arcs or spin-momentum locking Fermi loops can realize 1D topological superconductivity and harbor Majorana zero modes at their ends. Remarkably, we find that the vortex-generation-associated Zeeman field can open (when the surfaces have only Fermi arcs) or enhance the topological gap protecting Majorana zero modes, which is contrary to the situation in superconducting topological insulators. By studying the tilting effect of bulk Dirac and Weyl cones, we further find that type-I Dirac and Weyl semimetals in general have a much broader topological regime than type-II ones. Our findings build up a connection between TRI Dirac and Weyl semimetals and Majorana zero modes in vortices.

7 pages, 4 figures, published version without including the very long supplementary

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• Prediction of Spin Polarized Fermi Arcs in Quasiparticle Interference of CeBi
• Unveiling spin-orbital angular momentum locking in photonic Dirac vortex cavities
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• Chiral Meissner effect in time-reversal invariant Weyl superconductors
• Surface-dependent Majorana vortex phases in topological crystalline insulators
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• Chiral Majorana Edge Modes and Vortex Majorana Zero Modes in Superconducting Antiferromagnetic Topological Insulator
• Anomalous Linear and Quadratic Nodeless Surface Dirac Cones in Three-Dimensional Dirac Semimetals
• Fermi arc criterion for surface Majorana modes in superconducting time-reversal symmetric Weyl semimetals
• Higher-order topological superconductivity in type-II time-reversal-symmetric Weyl semimetals with a hybrid pairing
• Majorana Flat Bands in the Vortex Line of Superconducting Weyl Semimetals
• Majorana vortex phases in time-reversal invariant higher-order topological insulators and topologically trivial insulators
• Altermagnetism Induced Bogoliubov Fermi Surfaces Form Topological Superconductivity