Admittance of planar two-terminal quantum systems

TL;DR

This paper presents a microscopic approach to calculating the quantum admittance of one-dimensional open quantum systems, incorporating Coulomb interactions and charge correlations, with explicit formulas and experimental testability.

Contribution

It introduces a new RPA-based method for quantum admittance calculation that accounts for Coulomb interactions and provides explicit expressions for practical systems.

Findings

Quantum admittance can be derived microscopically using RPA.

Classical equivalent circuits are insufficient at higher frequencies.

The theory is testable through small-frequency expansions in quantum capacitors.

Abstract

We develop an approach to calculate the admittance of effectively one-dimensional open quantum systems in random phase approximation. The stationary, unperturbed system is described within the Landauer-B\"uttiker formalism taking into account the Coulomb interaction in the Hartree approximation. The dynamic changes in the effective potential are calculated microscopically from the charge-charge correlation function resulting from the stationary scattering states. We provide explicit RPA-expressions for the quantum admittance. As a first example the case of a quantum capacitor is considered where we can derive a small-frequency expansion for the admittance which lends itself to an experimental testing of the theory. A comparison of the low-frequency expansion with the complete RPA-expression shows that for a quantum capacitor a simple classical equivalent circuit with frequency-independent elements does not describe satisfactorily the quantum-admittance with increasing the frequency.