Interaction-induced strong zero modes in short quantum dot chains with time-reversal symmetry

TL;DR

This paper theoretically demonstrates the emergence of strong zero modes in a short quantum dot chain with time-reversal symmetry, revealing a protected three-fold ground-state degeneracy linked to Majorana and parafermion operators.

Contribution

It introduces a model showing how strong zero modes arise in a two-site quantum dot chain with Coulomb interactions, protected by time-reversal symmetry, and constructs corresponding Majorana and parafermion operators.

Findings

Ground-state degeneracy is protected and tunable via inter-dot couplings.

Strong interactions lead to maximal protection and triply degenerate spectrum.

Zero-bias conductance peaks are stable, but finite-bias spectroscopy distinguishes these modes.

Abstract

We theoretically explore the emergence of strong zero modes in a two-site chain consisting of two quantum dots coupled due to a central dot that mediates electron hopping and singlet superconducting pairing. In the presence of time-reversal symmetry, the on-site Coulomb interaction leads to a three-fold ground-state degeneracy when tuning the system to a sweet spot as a function of the inter-dot couplings. This degeneracy is protected against changes of the dot energies in the same way as "poor man's'' Majorana bound states in short Kitaev chains. In the limit of strong interactions, this protection is maximal and the entire spectrum becomes triply degenerate, indicating the emergence of a ''poor man's'' version of a strong zero mode. We explain the degeneracy and protection by constructing corresponding Majorana Kramers-pair operators and $\mathbb{Z}_3$-parafermion operators. The strong zero modes share many properties of Majorana bound states in short Kitaev chains, including the stability of zero-bias peaks in the conductance and the behavior upon coupling to an additional quantum dot. However, they can be distinguished through finite-bias spectroscopy and the exhibit a different behavior when scaling to longer chains.