Low frequency admittance of a quantum point contact

TL;DR

This paper develops a theory for the low frequency admittance of quantum point contacts, linking electrochemical capacitance and emittance, and describing their behavior during conductance channel opening.

Contribution

It introduces a current and charge conserving framework that relates capacitance and emittance, providing new insights into their step-like changes with conductance.

Findings

Capacitance and emittance decrease stepwise with channel opening.

Emittance becomes negative when reflection vanishes.

Capacitance approaches zero in the limit of no reflection.

Abstract

We present a current and charge conserving theory for the low frequency admittance of a quantum point contact. We derive expressions for the electrochemical capacitance and the displacement current. The latter is determined by the {\em emittance} which equals the capacitance only in the limit of vanishing transmission. With the opening of channels the capacitance and the emittance decrease in a step-like manner in synchronism with the conductance steps. For vanishing reflection, the capacitance vanishes and the emittance is negative.