Normal and superconducting currents through the Sachdev-Ye-Kitaev model

TL;DR

This paper investigates the time-dependent current behavior through the Sachdev-Ye-Kitaev model with normal and superconducting reservoirs, revealing distinct dynamics and oscillations influenced by coupling strength and lead type.

Contribution

It provides a detailed analysis of current dynamics in the SYK model with both normal and superconducting leads, highlighting differences from quadratic interaction models.

Findings

Normal leads: current reaches stationarity monotonically in strong coupling.

Superconducting leads: currents exhibit oscillations determined by gap and voltage.

A peak appears before stationarity in superconducting case due to different short time scales.

Abstract

We study the current driven by an applied voltage as a function of time through the Sachdev-Ye-Kitaev model when coupled to two normal or superconducting reservoirs. For normal leads, in the strong coupling limit and for small bias, the current through the Sachdev-Ye-Kitaev model, described by a quartic interaction term, reaches monotonically the stationarity, in contrast to the case of a disordered quadratic interaction where the current has a peak before reaching the stationary phase. For superconducting leads the currents have oscillations whose frequencies are determined by the gap and the voltage, and are suppressed in the strong coupling limit. Moreover, due to different short time scales between the normal and the oscillating part of the superconducting current, a peak appears before reaching the stationarity.