Equilibration of quantum Hall edge states by an Ohmic contact

TL;DR

This paper models Ohmic contacts in quantum Hall systems as finite-capacitance metal pieces attached to edge states, revealing limitations in their ability to equilibrate edge states at low temperatures due to weak coupling to neutral excitations.

Contribution

It provides a theoretical model of Ohmic contacts as finite-capacitance metals attached to quantum Hall edges, explaining their limited equilibration capabilities at low temperatures.

Findings

Weak coupling of charged edge states to neutral excitations in Ohmic contacts.

Equilibration is ineffective if contact temperature is below hbar\u03a9_c.

Energy scale for equilibration can reach the single-electron charging energy.

Abstract

Ohmic contacts are crucial elements of electron optics that have not received a clear theoretical description yet. We propose a model of an Ohmic contact as a piece of metal of the finite capacitance $C$ attached to a quantum Hall edge. It is shown that charged quantum Hall edge states may have weak coupling to neutral excitations in an Ohmic contact. Consequently, despite being a reservoir of neutral excitations, an Ohmic contact is not able to efficiently equilibrate edge states if its temperature is smaller than $\hbar\Omega_c$, where $\Omega_c$ is the inverse RC time of the contact. This energy scale for a floating contact may become as large as the single-electron charging energy $e^2/ C$.