AC-Conductance through an Interacting Quantum Dot

TL;DR

This paper derives a general formula for the linear ac-conductance through an interacting quantum dot under finite dc bias, expressed via local correlations, and demonstrates its application to specific models.

Contribution

We present a novel, general formula for ac-conductance in interacting quantum dots, extending the Meir-Wingreen approach to finite ac frequencies and biases.

Findings

Derived a general ac-conductance formula in terms of local correlations

Applied the formula to the noninteracting resonant level model

Reproduced known results in specific limits

Abstract

We investigate the linear ac-conductance for tunneling through an arbitrary interacting quantum dot in the presence of a finite dc-bias. In analogy to the well-known Meir-Wingreen formula for the dc case, we are able to derive a general formula for the ac-conductance. It can be expressed entirely in terms of local correlations on the quantum dot, in the form of a Keldysh block diagram with four external legs. We illustrate the use of this formula as a starting point for diagrammatic calculations by considering the ac-conductance of the noninteracting resonant level model and deriving the result for the lowest order of electron-phonon coupling. We show how known results are recovered in the appropriate limits.