Non-Abelian holonomy of Majorana zero modes coupled to a chaotic quantum dot

TL;DR

This paper investigates the non-Abelian holonomy arising from Majorana zero modes coupled to a quantum dot with chaotic dynamics, revealing measurable signatures of non-Abelian time evolution using random matrix theory.

Contribution

It introduces a novel analysis of non-Abelian holonomy in Majorana modes coupled to a chaotic quantum dot, expanding understanding of topological quantum systems.

Findings

Non-Abelian holonomy can be characterized in chaotic quantum dots.

Ground state degeneracy persists for five or more Majorana modes.

Measurable signatures of non-Abelian evolution are identified.

Abstract

If a quantum dot is coupled to a topological superconductor via tunneling contacts, each contact hosts a Majorana zero mode in the limit of zero transmission. Close to a resonance and at a finite contact transparency, the resonant level in the quantum dot couples the Majorana modes, but a ground state degeneracy per fermion parity subspace remains if the number of Majorana modes coupled to the dot is five or larger. Upon varying shape-defining gate voltages while remaining close to resonance, a nontrivial evolution within the degenerate ground-state manifold is achieved. We characterize the corresponding non-Abelian holonomy for a quantum dot with chaotic classical dynamics using random matrix theory and discuss measurable signatures of the non-Abelian time-evolution.