Anderson Model out of equilibrium: decoherence effects in transport through a quantum dot

TL;DR

This paper studies how nonequilibrium conditions affect decoherence and transport in a quantum dot modeled by the Anderson model, revealing universal scaling behaviors and the impact of bias voltage on the Kondo effect.

Contribution

It introduces a generalized out-of-equilibrium self-consistent method to calculate decoherence rates, elucidating their role in transport and the Kondo regime in quantum dots.

Findings

Decoherence rate $oldsymbol{ ext{}\gamma^{(4)} ext{}}$ cuts off infrared divergences.

Low-bias conductance is a universal function of $oldsymbol{V/T_K}$.

Voltage dependence causes splitting of the Kondo peak and affects conductance behavior.

Abstract

The paper deals with the nonequilibrium two-lead Anderson model, considered as an adequate description for transport through a d-c biased quantum dot. Using a self-consistent equation-of-motion method generalized out of equilibrium, we calculate a fourth-order decoherence rate $\gamma^{(4)}$ induced by a bias voltage $V$. This decoherence rate provides a cut-off to the infrared divergences of the self-energy showing up in the Kondo regime. At low temperature, the Kondo peak in the density of states is split into two peaks pinned at the chemical potential of the two leads. The height of these peaks is controlled by $\gamma^{(4)}$. The voltage dependence of the differential conductance exhibits a zero-bias peak followed by a broad Coulomb peak at large $V$, reflecting charge fluctuations inside the dot. The low-bias differential conductance is found to be a universal function of the normalized bias voltage $V/T_K$, where $T_K$ is the Kondo temperature. The universal scaling with a single energy scale $T_K$ at low bias voltages is also observed for the renormalized decoherence rate $\gamma^{(4)}/T_K$. We discuss the effect of $\gamma^{(4)}$ on the crossover from strong to weak coupling regime when either the temperature or the bias voltage is increased.