Kondo model in nonequilibrium: Interplay between voltage, temperature, and crossover from weak to strong coupling

TL;DR

This paper develops a real-time renormalization group approach to study the nonequilibrium Kondo model, revealing how voltage and temperature influence the crossover from weak to strong coupling and matching experimental observations.

Contribution

It introduces a universal, divergence-free RG formalism for nonequilibrium quantum impurity systems and applies it to analyze the Kondo crossover under finite bias and temperature.

Findings

Conductance exhibits non-monotonic temperature dependence with a peak.

Peak position and width scale linearly with applied voltage.

Universal ratios of low-energy scales agree with known results.

Abstract

We consider an open quantum system in contact with fermionic metallic reservoirs in a nonequilibrium setup. For the case of spin, orbital or potential fluctuations, we present a systematic formulation of real-time renormalization group at finite temperature, where the complex Fourier variable of an effective Liouvillian is used as flow parameter. We derive a universal set of differential equations free of divergencies written as a systematic power series in terms of the frequency-independent two-point vertex only, and solve it in different truncation orders by using a universal set of boundary conditions. We apply the formalism to the description of the weak to strong coupling crossover of the isotropic spin-1/2 nonequilibrium Kondo model at zero magnetic field. From the temperature and voltage dependence of the conductance in different energy regimes we determine various characteristic low-energy scales and compare their universal ratio to known results. For a fixed finite bias voltage larger than the Kondo temperature, we find that the temperature-dependence of the differential conductance exhibits non-monotonic behavior in the form of a peak structure. We show that the peak position and peak width scale linearly with the applied voltage over many orders of magnitude in units of the Kondo temperature. Finally, we compare our calculations with recent experiments.