How long does it take for the Kondo effect to develop?

TL;DR

This paper investigates the dynamic formation of the Kondo effect in quantum dots after a sudden voltage change, revealing how the Kondo resonance develops over time and affects transport properties.

Contribution

It introduces a theoretical framework using time-dependent Anderson and Kondo Hamiltonians to describe the Kondo resonance buildup after a voltage quench.

Findings

Kondo resonance forms over time following a voltage shift

Effective temperature describes the resonance development

Transport current is influenced by the Kondo buildup

Abstract

The time-development of the Kondo effect is theoretically investigated by studying a quantum dot suddenly shifted into the Kondo regime by a change of voltage on a nearby gate. Using time-dependent versions of both the Anderson and Kondo Hamiltonians, it is shown that after a time $t$ following the voltage shift, the form of the Kondo resonance matches the {\it time-independent} resonance at an effective temperature $T_{eff} = T/\tanh(\pi T t/2)$. Relevance of the buildup of the Kondo resonance to the transport current through a quantum dot is demonstrated.