Full counting statistics of Majorana interferometers

TL;DR

This paper analyzes the full counting statistics of chiral Majorana fermion interferometers, revealing a factorization property of charge transfer processes linked to the scattering matrix structure.

Contribution

It provides explicit formulas for current correlations and demonstrates a universal factorization property for a broad class of interferometer geometries.

Findings

Cumulant-generating function shows charge transfer as two half-charge processes.

Factorization property verified for general $SO(4)$ scattering matrices.

Analytical and numerical methods confirm the universality of the results.

Abstract

We study the full counting statistics of interferometers for chiral Majorana fermions with two incoming and two outgoing Dirac fermion channels. In the absence of interactions, the FCS can be obtained from the $4\times4$ scattering matrix $S$ that relates the outgoing Dirac fermions to the incoming Dirac fermions. After presenting explicit expressions for the higher-order current correlations for a modified Hanbury Brown-Twiss interferometer, we note that the cumulant-generating function can be interpreted such that unit-charge transfer processes correspond to two independent half-charge transfer processes, or alternatively, to two independent electron-hole conversion processes. By a combination of analytical and numerical approaches, we verify that this factorization property holds for a general $SO(4)$ scattering matrix, i.e. for a general interferometer geometry.