Transient currents and universal timescales for a fully time-dependent quantum dot in the Kondo regime

TL;DR

This paper investigates the transient current response in a quantum dot within the Kondo regime, revealing universal timescales and dynamics of Kondo resonance formation using the time-dependent non-crossing approximation.

Contribution

It introduces a detailed analysis of the universal transient response and identifies two key timescales for Kondo resonance development in quantum dots.

Findings

Two distinct timescales for Kondo resonance formation identified

Universal function of conductance in terms of temperature, bias, and time

Method to experimentally access the decay rate of split Kondo peaks

Abstract

Using the time-dependent non-crossing approximation, we calculate the transient response of the current through a quantum dot subject to a finite bias when the dot level is moved suddenly into a regime where the Kondo effect is present. After an initial small but rapid response, the time-dependent conductance is a universal function of the temperature, bias, and inverse time, all expressed in units of the Kondo temperature. Two timescales emerge: the first is the time to reach a quasi-metastable point where the Kondo resonance is formed as a broad structure of half-width of the order of the bias; the second is the longer time required for the narrower split peak structure to emerge from the previous structure and to become fully formed. The first time can be measured by the gross rise time of the conductance, which does not substantially change later while the split peaks are forming. The second time characterizes the decay rate of the small split Kondo peak (SKP) oscillations in the conductance, which may provide a method of experimental access to it. This latter timescale is accessible via linear response from the steady stateand appears to be related to the scale identified in that manner [A. Rosch, J. Kroha, and P. Wolfle, Phys. Rev. Lett. 87, 156802 (2001)].