Universality of the Kondo effect in a quantum dot out of equilibrium

Abstract

We study the Kondo effect in a quantum dot subject to an external ac field. The Kondo effect can be probed by measuring the dc current induced by an auxiliary dc bias $V_{\mathrm{dc}}$ applied across the dot. In the absence of ac perturbation, the corresponding differential conductance ${G(V}_{\mathrm{dc}})$ is known to exhibit a sharp peak at $V_{\mathrm{dc}}=0,$ which is the manifestation of the Kondo effect. There exists only one energy scale, the Kondo temperature $T_K,$ which controls all the low-energy physics of the system; G is some universal function of ${\mathrm{eV}}_{\mathrm{dc}}{/T}_K.$ We demonstrate that the dot driven out of equilibrium by an ac field is also characterized by a universal behavior: the conductance G depends on the ac field only through two dimensionless parameters, which are the frequency $\omega$ and the amplitude of the ac perturbation, both divided by $T_K.$ We analytically find the large- and small-frequency asymptotes of the universal dependence of G on these parameters. The obtained results allow us to predict the behavior of the conductance in the crossover regime $ħ\omega \sim T_K.$