Detecting Majoranas in 1D wires by charge sensing

TL;DR

This paper proposes using charge sensing to detect Majorana modes in 1D semiconductor wires, offering a non-contact method that complements existing tunneling techniques and helps confirm topological superconductivity.

Contribution

It introduces a theoretical framework for charge density jumps associated with Majorana parity changes and suggests charge sensing as a novel experimental approach.

Findings

Charge density jumps are spatially uniform along the wire.

Charge sensing can detect parity changes without direct contact.

The method distinguishes Majorana states from other phenomena.

Abstract

The electron number-parity of the ground state of a semiconductor narowire proximity-coupled to a bulk superconductor can alternate between the quantised values $\pm 1$ if parameters such as the wire length $L$, the chemical potential $\mu$ or the magnetic field $B$ are varied inside the topological superconductor phase. % The parity jumps, which may be interpreted as changes in the occupancy of the fermion state formed from the pair of Majorana modes at opposite ends of the wire, are accompanied by jumps $\delta N$ in the charge of the nanowire, whose values decrease exponentially with the wire length. % We study theoretically the dependence of $\delta N$ on system parameters, and compare the locations in the $\mu$-$B$ plane of parity jumps when the nanowire is or is not proximity-coupled to a bulk superconductor. % We show that, despite the fact that the wave functions of the Majorana modes are localised near the two ends of the wire, the charge-density jumps have spatial distributions that are essentially uniform along the wire length, being proportional to the product of the two Majorana wave functions. % We explain how charge measurements, say by an external single-electron transistor, could reveal these effects. % Whereas existing experimental methods require direct contact to the wire for tunneling measurements, charge sensing avoids this issue and provides an orthogonal measurement to confirm recent experimental developments. % Furthermore, by comparing density of states measurements which show Majorana features at the wire ends with the uniformly-distributed charge measurements, one can rule out alternative explanations for earlier results. % We shed light on a new parameter regime for these wire-superconductor hybrid systems, and propose a related experiment to measure spin density.