Out of equilibrium transport through an Anderson impurity: Probing scaling laws within the equation of motion approach

TL;DR

This paper investigates non-equilibrium electron transport through a quantum impurity using the equation of motion method, revealing universal scaling laws and effects of magnetic fields consistent with experimental quantum dot data.

Contribution

It introduces a detailed analysis of out-of-equilibrium transport and scaling laws in Anderson impurities, including new configurations mimicking recent experiments.

Findings

G_2(T,V)/G_2(T,0) is a universal function of eV/T_K and T/T_K

Differential conductance peak splitting depends only on elta/T_K

Double peak structure observed in modified configurations with amplitude decreasing as V/T_K

Abstract

We study non-equilibrium electron transport through a quantum impurity coupled to metallic leads using the equation of motion technique at finite temperature T. Assuming that the interactions are taking place solely in the impurity and focusing in the infinite Hubbard limit, we compute the out of equilibrium density of states and the differential conductance G_2(T,V) to test several scaling laws. We find that G_2(T,V)/G_2(T,0) is a universal function of both eV/T_K and T/T_K, being T_K the Kondo temperature. The effect of an in plane magnetic field on the splitting of the zero bias anomaly in the differential conductance is also analyzed. For a Zeeman splitting \Delta, the computed differential conductance peak splitting depends only on \Delta/T_K, and for large fields approaches the value of 2\Delta . Besides the traditional two leads setup, we also consider other configurations that mimics recent experiments, namely, an impurity embedded in a mesoscopic wire and the presence of a third weakly coupled lead. In these cases, a double peak structure of the Kondo resonance is clearly obtained in the differential conductance while the amplitude of the highest peak is shown to decrease as \ln(eV/T_K). Several features of these results are in qualitative agreement with recent experimental observations reported on quantum dots.