Nonlinear Fermi-liquid transport through a quantum dot in asymmetric tunnel junctions

TL;DR

This paper develops an exact Fermi-liquid theory for nonlinear conductance through a quantum dot with asymmetric tunnel couplings and bias voltages, validated by NRG calculations across various regimes.

Contribution

It extends the microscopic Fermi-liquid theory to include asymmetries and provides exact formulas for nonlinear conductance up to third order in bias voltage.

Findings

Order V^2 nonlinear current is enhanced in the valence fluctuation regime.

Order V^3 nonlinear current shows a shoulder structure influenced by three-body correlations.

NRG calculations confirm the theoretical predictions across different impurity fillings.

Abstract

We study the nonlinear conductance through a quantum dot, specifically its dependence on the asymmetries in the tunnel couplings and bias voltages $V$, at low energies. Extending the microscopic Fermi-liquid theory for the Anderson impurity model, we obtain an exact formula for the steady current $I$ up to terms of order $V^3$ in the presence of these asymmetries. The coefficients for the nonlinear terms are described in terms of a set of the Fermi-liquid parameters: the phase shift, static susceptibilities, and three-body correlation functions of electrons in the quantum dots, defined with respect to the equilibrium ground state. We calculate these correlation functions, using the numerical renormalization group approach (NRG), over a wide range of impurity-electron filling that can be controlled by a gate voltage in real systems. The NRG results show that the order $V^2$ nonlinear current is enhanced significantly in the valence fluctuation regime. It is caused by the order $V$ energy shift of the impurity level, induced in the presence of the tunneling or bias asymmetry. Furthermore, in the valence fluctuation regime, we also find that the order $V^3$ nonlinear current exhibits a shoulder structure, for which the three-body correlations that evolve for large asymmetries play an essential role.