Coulomb-blockade effect in nonlinear mesoscopic capacitors

TL;DR

This paper analyzes the Coulomb blockade effects in a nonlinear mesoscopic capacitor, revealing how electron interactions influence quantized charge emission, resonance splitting, and dynamic capacitance in a quantum dot system under ac driving.

Contribution

It extends previous models by deriving the time-dependent current in the Coulomb blockade regime using Keldysh-Green functions, accounting for strong electron interactions in nonlinear response.

Findings

Resonance splitting occurs when charging energy exceeds tunnel broadening.

Charge quantization is reduced and additional plateaus appear due to Coulomb repulsion.

Current can be approximated as a sum of shifted noninteracting currents at leading order.

Abstract

We consider an interacting quantum dot working as a coherent source of single electrons. The dot is tunnel coupled to a reservoir and capacitively coupled to a gate terminal with an applied ac potential. At low frequencies, this is the quantum analog of the RC circuit with a purely dynamical response. We investigate the quantized dynamics as a consequence of ac pulses with large amplitude. Within a Keldysh-Green function formalism we derive the time-dependent current in the Coulomb blockade regime. Our theory thus extends previous models that considered either noninteracting electrons in nonlinear response or interacting electrons in the linear regime. We prove that the electron emission and absorption resonances undergo a splitting when the charging energy is larger than the tunnel broadening. For very large charging energies, the additional peaks collapse and the original resonances are recovered, though with a reduced amplitude. Quantization of the charge emitted by the capacitor is reduced due to Coulomb repulsion and additional plateaus arise. Additionally, we discuss the differential capacitance and resistance as a function of time. We find that to leading order in driving frequency the current can be expressed as a weighted sum of noninteracting currents shifted by the charging energy.