Measuring coherence factors of states in superconductors through local current

TL;DR

This paper introduces a method to measure local coherence factors in superconductors using local transport measurements, enabling the assessment of Majorana states in quantum dot chains.

Contribution

The authors propose a novel local current measurement technique to infer coherence factors and Majorana polarization in superconducting systems, validated through analytical and numerical analysis.

Findings

The method accurately estimates local coherence factors in superconductors.

It allows quantification of Majorana polarization in Kitaev chains.

The approach is validated with numerical simulations including interactions and magnetic fields.

Abstract

The coherence factors of quasiparticles in a superconductor determine their properties, including transport and susceptibility to electric fields. In this work, we propose a way to infer the local coherence factors using local transport to normal leads. Our method is based on measuring the local current through a lead as the coupling to a second one is varied: the shape of the current is determined by the ratio between the local coherence factors, becoming independent of the coupling to the second lead in the presence of local electron-hole symmetry, {\it i.e.} coherence factors $|u|=|v|$. We apply our method to minimal Kitaev chains: arrays of quantum dots coupled via narrow superconducting segments. These chains feature Majorana-like quasiparticles (zero-energy states with $|u|=|v|$) at discrete points in parameter space. We demonstrate that the local current allows us to estimate the local Majorana polarization (MP) -- a measurement of the local Majorana properties of the state. We derive an analytical expression for the MP in terms of local currents and benchmark it against numerical calculations for 2- and 3-sites chains that include a finite Zeeman field and electron-electron interactions. These results provide a way to quantitatively assess the quality of Majorana states in short Kitaev chains.