Majorana vortex-bound states in three-dimensional nodal noncentrosymmetric superconductors

TL;DR

This paper investigates the existence and properties of Majorana vortex-bound states in three-dimensional noncentrosymmetric superconductors, revealing how crystal symmetries influence zero-energy modes and their potential experimental signatures.

Contribution

It provides a comprehensive analysis of how different crystal point-group symmetries affect Majorana vortex-bound states in 3D NCSs, combining analytical and numerical methods.

Findings

Nodal NCSs with $C_{4v}$ symmetry host dispersionless Majorana flat bands.

$D_4$ symmetry NCSs exhibit helical Majorana states with linear dispersion.

Monoclinic $C_2$ NCSs do not support zero-energy vortex-bound states.

Abstract

Noncentrosymmetric superconductors (NCSs), characterized by antisymmetric spin-orbit coupling and a mixture of spin-singlet and spin-triplet pairing components, are promising candidate materials for topological superconductivity. An important hallmark of topological superconductors is the existence of protected zero-energy states at surfaces or in vortex cores. Here we investigate Majorana vortex-bound states in three-dimensional nodal and fully gapped NCSs by combining analytical solutions of Bogoliubov-de Gennes (BdG) equations in the continuum with exact diagonalization of BdG Hamiltonians. We show that depending on the crystal point-group symmetries and the topological properties of the bulk Bogoliubov-quasiparticle wave functions, different types of zero-energy Majorana modes can appear inside the vortex core. We find that for nodal NCSs with tetragonal point group $C_{4v}$ the vortex states are dispersionless along the vortex line, forming one-dimensional Majorana flat bands, while for NCSs with $D_{4}$ point-group symmetry the vortex modes are helical Majorana states with a linear dispersion along the vortex line. NCSs with monoclinic point group $C_2$, on the other hand, do not exhibit any zero-energy vortex-bound states. We show that in the case of the $C_{4v}$ ($D_4$) point group the stability of these Majorana zero modes is guaranteed by a combination of reflection ($\pi$ rotation), time-reversal, and particle-hole symmetry. Considering continuous deformations of the quasiparticle spectrum in the presence of vortices, we show that the flat-band vortex-bound states of $C_{4v}$ point-group NCSs can be adiabatically connected to the dispersionless vortex-bound states of time-reversal symmetric Weyl superconductors. Experimental implications of our results for thermal transport and tunneling measurements are discussed.