Majorana Flat Bands in the Vortex Line of Superconducting Weyl Semimetals

TL;DR

This paper demonstrates the emergence of Majorana flat bands in the vortex lines of superconducting Weyl semimetals, revealing their topological nature and tunability through chemical potential and pairing strength.

Contribution

It introduces a topological framework for understanding Majorana flat bands in SC Weyl semimetals using a $k_z$-resolved Chern number approach.

Findings

Majorana flat bands appear along the entire $k_z$ axis under certain conditions.

A $k_z$-resolved $Z_2$ Chern-Simons invariant characterizes the topological phase.

Tuning chemical potential or pairing strength affects the presence of MFBs.

Abstract

We report the emergence of Majorana flat bands (MFBs) in the vortex line of superconducting (SC) time-reversal-symmetry-breaking Weyl semimetals. By considering a Weyl semimetal as a stack of Chern insulators with varying Chern numbers along one ($z$) direction, we decompose the vortex bound states of SC Weyl semimetals into those of $k_{z}$-resolved SC Chern insulators. Through analytical and numerical calculations of the topological phase diagram of the SC Chern insulators, we explain the appearance of MFBs and determine the exact boundaries of them. Notably, the tuning of chemical potential or pairing strength results in the MFBs along the entire $k_{z}$ axis. To characterize the MFBs, we propose a $k_{z}$-resolved $Z_{2}$ Chern-Simons invariant as the topological indicator. Finally, we take an attractive Hubbard interaction into consideration, and the aforementioned SC Weyl semimetal with BCS pairing can be realized under appropriate parameters.