Non-equilibrium Transport in the Anderson model of a biased Quantum Dot: Scattering Bethe Ansatz Phenomenology

TL;DR

This paper develops an exact theoretical framework using the Scattering Bethe Ansatz to analyze non-equilibrium transport in a quantum dot described by the Anderson model, revealing detailed conductance behavior under bias.

Contribution

It introduces a generalized Bethe Ansatz approach for out-of-equilibrium quantum dot transport, providing exact results for occupation and conductance in the Anderson model.

Findings

Exact differential conductance for large U/Γ derived

Transition from mixed valence to Kondo regime studied

Numerical results for current and occupation as functions of voltage

Abstract

We derive the transport properties of a quantum dot subject to a source-drain bias voltage at zero temperature and magnetic field. Using the Scattering Bethe Anstaz, a generalization of the traditional Thermodynamic Bethe Ansatz to open systems out of equilibrium, we derive exact results for the quantum dot occupation out of equilibrium and, by introducing phenomenological spin- and charge-fluctuation distribution functions in the computation of the current, obtain the differential conductance for large U/\Gamma. The Hamiltonian to describe the quantum dot system is the Anderson impurity Hamiltonian and the current and dot occupation as a function of voltage are obtained numerically. We also vary the gate voltage and study the transition from the mixed valence to the Kondo regime in the presence of a non-equilibrium current. We conclude with the difficulty we encounter in this model and possible way to solve them without resorting to a phenomenological method.