X-shaped and Y-shaped Andreev resonance profiles in a superconducting quantum dot

TL;DR

This paper investigates the behavior of Andreev resonances in superconducting quantum dots, revealing distinct X-shaped and Y-shaped conductance profiles linked to different symmetry classes and their impact on zero-bias peaks.

Contribution

It introduces a random-matrix model to analyze how symmetry classes affect Andreev resonance profiles and zero-bias conductance peaks in superconducting quantum dots.

Findings

Y-shaped conductance profile with pinned zero-bias peak in class D.

X-shaped profile with splitting of conductance peaks in class C.

Poles of the scattering matrix behave differently depending on symmetry class.

Abstract

The quasi-bound states of a superconducting quantum dot that is weakly coupled to a normal metal appear as resonances in the Andreev reflection probability, measured via the differential conductance. We study the evolution of these Andreev resonances when an external parameter (such as magnetic field or gate voltage) is varied, using a random-matrix model for the $N\times N$ scattering matrix. We contrast the two ensembles with broken time-reversal symmetry, in the presence or absence of spin-rotation symmetry (class C or D). The poles of the scattering matrix in the complex plane, encoding the center and width of the resonance, are repelled from the imaginary axis in class C. In class D, in contrast, a number $\propto\sqrt{N}$ of the poles has zero real part. The corresponding Andreev resonances are pinned to the middle of the gap and produce a zero-bias conductance peak that does not split over a range of parameter values (Y-shaped profile), unlike the usual conductance peaks that merge and then immediately split (X-shaped profile).