Inductances cinétiques et capacités quantiques en régime d'effet Hall dans les conducteurs de Hall

Abstract : In a two dimensional electron gas, low energy transport in presence of a magnetic field occurs in chiral 1D channels located on the edges of the sample. In the Buttiker’s description of a.c. quantum transport, the “emittance” determines the amplitude of the imaginary part of the admittance, whose sign and physical meaning are determined by the topology: in the case of an Hall bar the emittance is an inductance, while it is a capacitance in the case of a corbino sample.Emittance is related to the density of states and to the drift velocity of carriers. So quantum capacitances and inductances give access to the velocity of the charge carriers through the transit time/dwell time of charges in the quantum circuit.We performed systematic studies on samples with different topologies : Hall bars and Corbino disks. Our samples have no gate, which makes us able to observe the inner properties of the quantum states. We have measured the ac admittance of quantum Hall samples using standard electrical techniques in the [0.1-100] kHz frequency range, at low temperature under high magnetic field.We measured kinetic inductances of Hall bars with three contacts and showed the perfect inductive nature of edge states. We measured quantum capacitances of Corbino disks as well. In both topologies we observed the close relation between the emittance and the density of states. We show also the proportionality between the emittance and the length of the circuit. We obtain the transit time of electrons through the device, and finally the drift velocity on edge states.At high temperature we still observe an inductive behavior of Hall bars, induced by increase of energy relaxation time with magnetic field.
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Adrien Delgard. Inductances cinétiques et capacités quantiques en régime d'effet Hall dans les conducteurs de Hall. Physique Quantique [quant-ph]. Université Montpellier, 2018. Français. ⟨NNT : 2018MONTS063⟩. ⟨tel-02136205⟩

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