Delayed currents and interaction effects in mesoscopic capacitors

TL;DR

This paper derives the dynamic admittance of a quantum dot, showing current lag due to delay times, and analyzes Coulomb-blockade oscillations, revealing their disappearance in open dots, thus clarifying previous conflicting results.

Contribution

It provides an alternative derivation of the quantum dot's admittance, including interaction effects, and clarifies the behavior of Coulomb-blockade oscillations in different regimes.

Findings

Current lags after entering by the Wigner-Smith delay time.

Coulomb-blockade oscillations disappear when the dot is fully open.

Reconciliation of previous conflicting results on oscillations.

Abstract

We propose an alternative derivation for the dynamic admittance of a gated quantum dot connected by a single-channel lead to an electron reservoir. Our derivation, which reproduces the result of Pr\^{e}tre, Thomas, and B\"{u}ttiker for the universal charge-relaxation resistance, shows that at low frequencies, the current leaving the dot lags after the entering one by the Wigner-Smith delay time. We compute the capacitance when interactions are taken into account only on the dot within the Hartree-Fock approximation and study the Coulomb-blockade oscillations as a function of the Fermi energy in the reservoir. In particular we find that those oscillations disappear when the dot is fully `open', thus we reconcile apparently conflicting previous results.