Conductance of a Finite Kitaev Chain

TL;DR

This paper develops a stochastic Keldysh approach to analyze conductance in finite Kitaev chains, revealing universal conductance behavior in topological regimes and detailed current decay properties.

Contribution

It introduces a stochastic formulation of Keldysh theory for finite Kitaev chains and provides analytical and numerical insights into conductance and current decay.

Findings

Conductance approaches 2e^2/h in long topological chains.

Exponential decay of current inside the chain.

Nonmonotonic maximal current as a function of reservoir coupling.

Abstract

We present a stochastic formulation of the Keldysh theory to calculate the conductance of a finite Kitaev chain coupled to two electron reservoirs. We study the dependence of the conductance on the number of sites in the chain and find that only for sufficiently long chains and in the regime that the chain is a topological superconducter the conductance at both ends tends to the universal value $2e^2/h$, as expected on the basis of the contact resistance of a single conducting channel provided by the Majorana zero mode. In this topologically nontrivial case we find an exponential decay of the current inside the chain and a simple analytical expression for the decay length. Finally, we also study the differential conductance at nonzero bias and the full current-voltage curves. We find a nonmonotonic behavior of the maximal current through the Kitaev chain as a function of the coupling strength with the reservoirs.