Universality of the Kondo Effect in a Quantum Dot out of Equilibrium
Abstract
We study the Kondo effect in a quantum dot driven out of equilibrium by an external ac field. The Kondo effect can be probed by measuring the dc current induced by an auxiliary dc bias
V
dc
applied across the dot. In the absence of ac perturbation, the corresponding differential conductance
G(
V
dc
)
is known to exhibit a sharp peak at
V
dc
=0
, which is the manifestation of the Kondo effect. In the equilibrium, 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
e
V
dc
/
T
K
. We demonstrate that the dot out of equilibrium is also characterized by a universal behavior: conductance
G
depends on the ac field only through two dimensionless parameters, which are the frequency
ω
and the amplitude of the ac perturbation, both divided by
T
K
. We find analytically 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
ℏω∼
T
K
.