Majorana bound states in two-channel time-reversal-symmetric nanowire systems

TL;DR

This paper investigates the conditions under which two-channel time-reversal-symmetric nanowire systems can host Majorana bound states, highlighting the importance of pairing matrix sign, inversion symmetry breaking, and differing spin-orbit couplings.

Contribution

It provides a comprehensive analysis of the topological criteria for Majorana states in two-channel nanowires, including explicit zero mode solutions and topological invariant expressions.

Findings

Necessary conditions for topological phase identified

Explicit zero mode solutions derived

Topological invariant expression obtained

Abstract

We consider time-reversal-symmetric two-channel semiconducting quantum wires proximity coupled to an s-wave superconductor. We analyze the requirements for a nontrivial topological phase and find that necessary conditions are 1) the determinant of the pairing matrix in channel space must be negative, 2) inversion symmetry must be broken, and 3) the two channels must have different spin-orbit couplings. The first condition can be implemented in semiconducting nanowire systems where interactions suppress intra-channel pairing, while the inversion symmetry can be broken by tuning the chemical potentials of the channels. For the case of collinear spin-orbit directions, we find a general expression for the topological invariant by block diagonalization into two blocks with chiral symmetry only. By projection to the low-energy sector, we solve for the zero modes explicitly and study the details of the gap closing, which in the general case happens at finite momenta.