Low-energy theory of transport in Majorana wire junctions

TL;DR

This paper develops a comprehensive low-energy transport theory for hybrid devices with topological superconductor wires, capturing Majorana states and quasiparticles, and provides analytical results for various junction configurations.

Contribution

It introduces a unified Green's function approach for TS wires, enabling systematic analysis of transport properties and inclusion of many-body interactions in hybrid junctions.

Findings

Exact $I$-$V$ characteristics for N-TS junctions at arbitrary transparency

Analytical thermal noise spectrum for TS-TS junctions in high-transparency regime

Conditions for finite Josephson current in S-TS junctions

Abstract

We formulate and apply a low-energy transport theory for hybrid quantum devices containing junctions of topological superconductor (TS) wires and conventional normal (N) or superconducting (S) leads. We model TS wires as spinless $p$-wave superconductors and derive their boundary Keldysh Green's function, capturing both the Majorana end state and continuum quasiparticle excitations in a unified manner. We also specify this Green's function for a finite-length TS wire. Junctions connecting different parts of the device are described by the standard tunneling Hamiltonian. Using this Hamiltonian approach, one also has the option to include many-body interactions in a systematic manner. For N-TS junctions, we provide the current-voltage ($I$-$V$) characteristics at arbitrary junction transparency and give exact results for the shot noise power and the excess current. For TS-TS junctions, analytical results for the thermal noise spectrum and for the $I$-$V$ curve in the high-transparency low-bias regime are presented. For S-TS junctions, we compute the entire $I$-$V$ curve and clarify the conditions for having a finite Josephson current.