Electrochemical Capacitance and Transit Time in Quantum Hall Conductors

Abstract

In a two dimensional electron gas, low energy transport in presence of a magnetic field occurs in chiral 1D channels located on the edge of the sample. In the AC description of quantum transport, the emittance determines the amplitude of the imaginary part of the admittance, whose sign and physical meaning are determined by the sample topology: a Hall bar is inductive while a Corbino ring is capacitive. In this article, the perfect capacitive character of Corbino samples in the quantum Hall effect regime is shown. A vanishing conductance and an electrochemical capacitance which depends on the density of states of 1D channels are measured. Our samples have no gate, neither on the side nor on the top, and the inner capacitances are measured. The transit time of electrons across the device is obtained and the drift velocity of carriers is deduced.

Coulomb interactions and effective quantum inertia of charge carriers in a macroscopic conductor

“…On the contrary, in a Corbino sample, the injected charge returns to the contact it comes from, as does the image charge. It was experimentally shown by Delgard et al [59] that Corbino emittances will exhibit this predicted capacitive behavior. Here, we will highlight the inductive behavior of quantum Hall bars in a multi-contact geometry that ensures vanishing longitudinal resistance.…”

“…where l is the length of the Hall bar [see Fig. 1(b)], C q (ν) = νe 2 l/hv d (ν) is the quantum capacitance of ν edge channels recently measured in Corbino geometries [56], and the geometric capacitance C H (ν) describes the effect of Coulomb interactions between counterpropagating edge channels. This is different from the quantum RL circuit where, because of the gating, the capacitance C H has to be replaced by the capacitance C g with the nearby gates leading to a renormalization of v d by 1 + C q /C g for right and left moving charge density waves [24].…”