Boundary Green's function approach for spinful single-channel and multichannel Majorana nanowires

TL;DR

This paper develops a versatile boundary Green's function method for analyzing spinful multi-channel Majorana nanowires, enabling efficient computation of topological and spectral properties relevant for quantum device applications.

Contribution

It introduces a general analytical and numerical approach to compute boundary Green's functions for complex Majorana nanowire models, linking root behavior to physical observables.

Findings

Analytical expressions for roots of secular polynomial in complex momentum space.

Efficient numerical evaluation of boundary Green's functions.

Application to single- and two-channel nanowires and multi-terminal Josephson junctions.

Abstract

The boundary Green's function (bGF) approach has been established as a powerful theoretical technique for computing the transport properties of tunnel-coupled hybrid nanowire devices. Such nanowires may exhibit topologically nontrivial superconducting phases with Majorana bound states at their boundaries. We introduce a general method for computing the bGF of spinful multi-channel lattice models for such Majorana nanowires, where the bGF is expressed in terms of the roots of a secular polynomial evaluated in complex momentum space. In many cases, those roots, and thus the bGF, can be accurately described by simple analytical expressions, while otherwise our approach allows for the numerically efficient evaluation of bGFs. We show that from the behavior of the roots, many physical quantities of key interest can be inferred, e.g., the value of bulk topological invariants, the energy dependence of the local density of states, or the spatial decay of subgap excitations. We apply the method to single- and two-channel nanowires of symmetry class D or DIII. In addition, we study the spectral properties of multi-terminal Josephson junctions made out of such Majorana nanowires.