Transport in a long-range Kitaev ladder: role of Majorana and subgap Andreev states

TL;DR

This paper investigates how long-range pairing and Majorana fermions influence local and nonlocal electron transport in a Kitaev ladder, revealing conditions that enhance crossed Andreev reflection and nonlocal conductance.

Contribution

It demonstrates how long-range pairing and phase differences modify Majorana and Andreev states, affecting local and nonlocal transport in a Kitaev ladder system.

Findings

Long-range pairing lifts Majorana degeneracy and reduces localization.

Subgap Andreev states significantly enhance nonlocal conductance.

Phase difference and long-range pairing together promote crossed Andreev reflection.

Abstract

We study local and non-local transport across a two-leg long-range Kitaev ladder connected to two normal metal leads. We focus on the role of the constituent Majorana fermions and the subgap Andreev states. The double degeneracy of Majorana fermions of the individual legs of the ladder gets lifted by a coupling between the two leading to the formation of Andreev bound states. The coupling can be induced by a superconducting phase difference between the two legs of the ladder accompanied by a finite inter-leg hopping. Andreev bound states formed strongly enhance local Andreev reflection. When the ladder and normal metal are weakly coupled, the Andreev bound states, which are the controlling factor, result in weak nonlocal scattering. In sharp contrast, when the ladder - normal metal interface is transparent to electron flow, we find that the subgap Andreev states enhance nonlocal conductance strongly. The features in the local and nonlocal conductances resemble the spectrum of the isolated ladder. Long-range pairing helps lift the degeneracy of the Majorana modes, makes them less localized, and thus inhibits local transport, while aiding non-local transport. In particular, long-range pairing alone (without a superconducting phase difference) can enhance crossed Andreev reflection.