Wigner Function Description of the A.C.-Transport Through a Two-Dimensional Quantum Point Contact

TL;DR

This paper introduces a quantum kinetic approach using a Wigner distribution function to analyze the admittance of a 2D quantum point contact, revealing stepwise behavior and geometry-dependent emittance influenced by propagating and nonpropagating electron modes.

Contribution

It presents a novel Wigner function-based formalism for quantum transport, capturing both propagating and nonpropagating modes and their effects on admittance and emittance in QPCs.

Findings

Admittance exhibits stepwise behavior linked to propagating modes.

Emittance is sensitive to QPC geometry and gate voltage.

Quantum inductance and capacitance contributions are identified.

Abstract

We have calculated the admittance of a two-dimensional quantum point contact (QPC) using a novel variant of the Wigner distribution function (WDF) formalism. In the semiclassical approximation, a Boltzman-like equation is derived for the partial WDF describing both propagating and nonpropagating electron modes in an effective potential generated by the adiabatic QPC. We show that this quantum kinetic approach leads to the well-known stepwise behavior of the real part of the admittance (the conductance), and of the imaginary part of the admittance (the emittance), in agreement with the latest results, which is determined by the number of propagating electron modes. It is shown, that the emittance is sensitive to the geometry of the QPC, and can be controlled by the gate voltage. We established that the emittance has contributions corresponding to both quantum inductance and quantum capacitance. Stepwise oscillations in the quantum inductance are determined by the harmonic mean of the velocities for the propagating modes, whereas the quantum capacitance is a significant mesoscopic manifestation of the non-propagating (reflecting) modes.