On universality and non-universality for a quantum dot in the Kondo regime

TL;DR

This paper investigates the transient conductance response of a quantum dot in the Kondo regime using the time-dependent non-crossing approximation, revealing both universal and non-universal behaviors across different timescales.

Contribution

It introduces a new numerical scheme to study the slow universal timescale and demonstrates that universality is maintained as a function of T/T_K in the Kondo regime.

Findings

Rapid oscillations occur at the dot level frequency in the non-universal timescale.

The new scheme accurately computes conductance down to fractions of T_K.

Universality is confirmed for the conductance as a function of T/T_K.

Abstract

The time-dependent non-crossing approximation is employed for the single-electron transistor to calculate the transient response of the conductance for a variety of temperatures and biases. We consider the case when the dot-lead tunneling constant is suddenly changed such that the Kondo effect is present in the final state. In the fast non-universal timescale, which was previously identified, we see rapid oscillations. The frequency of these oscillations is equal to the dot level and their amplitude is modulated by the initial and final tunneling constants. To study the slow universal timescale, we develop a new numerical scheme. We compute the conductance for two systems which have different Kondo temperatures down to a fraction of $T_{K}$ in infinitesimal bias with this scheme. We conclude that universality is preserved as a function of $T/ T_{K}$. We also investigate the decay rate of recently identified SKP oscillations down to zero temperature and compare it with the previous analytical results obtained with the perturbative renormalization group.