Zero-dimensional topologically nontrivial state in a superconducting quantum dot

TL;DR

This paper demonstrates that a quantum dot coupled with superconducting leads can host a zero-dimensional topologically nontrivial superconducting state, revealing unique fermion parity transitions and zero-energy modes.

Contribution

It introduces a model for realizing a zero-dimensional topological superconductor in a quantum dot system with broken time-reversal symmetry.

Findings

Fermion parity changes at topological phase transitions.

Zero-energy modes appear at the transition points.

Discontinuities in the current-phase relation indicate topological states.

Abstract

The classification of topological states of matter in terms of unitary symmetries and dimensionality predicts the existence of nontrivial topological states even in zero-dimensional systems, i.e., a system with a discrete energy spectrum. Here, we show that a quantum dot coupled with two superconducting leads can realize a nontrivial zero-dimensional topological superconductor with broken time-reversal symmetry, which corresponds to the finite size limit of the one-dimensional topological superconductor. Topological phase transitions corresponds to a change of the fermion parity, and to the presence of zero-energy modes and discontinuities in the current-phase relation at zero temperature. These fermion parity transitions therefore can be revealed by the current discontinuities or by a measure of the critical current at low temperatures.