In-gap states of the quantum dot coupled between a normal and superconducting lead

TL;DR

This paper investigates the in-gap states in a quantum dot system coupled to normal and superconducting leads, revealing how Andreev scattering and Coulomb interactions influence bound state formation and tunneling conductance.

Contribution

It provides a detailed analysis of the emergence and properties of in-gap states in hybrid quantum dot systems, highlighting the role of Coulomb repulsion and Andreev processes.

Findings

Multiple in-gap bound states depend on Coulomb and pairing competition.

In-gap states manifest as signatures in tunneling conductance.

Even number of bound states can appear in the quantum dot spectrum.

Abstract

We study the in-gap states of the quantum dot hybridized to a conducting and superconducting electrode. The usual proximity effect suppresses electronic states over the entire subgap regime $|\omega| < \Delta$, where $\Delta$ denotes the energy gap of superconductor. Owing to the Andreev scattering there can, however, emerge additional in-gap states whose line-broadening (inverse life-time) depends on the coupling to a normal electrode. We show that even number of such bound states appears in the quantum dot spectrum, depending on a competition between the Coulomb repulsion and the induced on-dot pairing. We discuss signatures of these in-gap states showing up in the tunneling conductance, especially in a low-bias regime dominated by the Andreev channel.