Quantum dots as parafermion detectors

TL;DR

This paper demonstrates how quantum dots can be used to detect parafermionic zero modes in strongly correlated topological systems, providing a practical method to identify non-trivial phases.

Contribution

It introduces a novel approach combining numerical and analytical methods to identify parafermionic zero modes via quantum dot properties.

Findings

Quantum dot spectral function reveals zero modes.

Occupation numbers distinguish topological phases.

Method applicable to strongly correlated systems.

Abstract

Parafermionic zero modes, $\mathbb{Z}_n$-symmetric generalizations of the well-known $\mathbb{Z}_2$ Majorana zero modes, can emerge as edge states in topologically nontrivial strongly correlated systems displaying fractionalized excitations. In this paper, we investigate how signatures of parafermionic zero modes can be detected by its effects on the properties of a quantum dot tunnel-coupled to a system hosting such states. Concretely, we consider a strongly-correlated 1D fermionic model supporting $\mathbb{Z}_4$ parafermionic zero modes coupled to an interacting quantum dot at one of its ends. By using a combination of density matrix renormalization group calculations and analytical approaches, we show that the dot's zero-energy spectral function and average occupation numbers can be used to distinguish between trivial, $\mathbb{Z}_4$ and $2\times \mathbb{Z}_2$ phases of the system. The present work opens the prospect of using quantum dots as detection tools to probe non-trivial topological phases in strongly correlated systems.