Alternating-current response of one-dimensional quantum dotarrays

Abstract

A general approach is presented for calculating the dynamicconductance of coupled quantum dot systems. To consider thelong-range Coulomb interaction, we introduce the capacitancesbetween the leads and dots, gate electrodes and dots, and dots anddots. The displacement currents are also taken into account. Ourresults fulfil charge and current conservation requirements, as wellas current and charge response invariance under an overall potentialshift. We apply our approach to a one-dimensional quantum dot arrayby use of the non-equilibrium Green function techniques. Thenumerical results are presented for a three-quantum-dot system.Three-peak resonant structure of the alternating-current conductanceis observed at low temperature. The effect of the capacitance onthe frequency-dependent conductance is obvious, but less so at lowfrequency. The low-frequency conductance shows either capacitive orinductive behaviour depending on the chemical potential of theelectron reservoirs, but sufficiently large capacitances may changethis situation.