Equilibration of quantum Hall edge states by an Ohmic contact

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 $\hbarΩ_c$, where $Ω_c$ 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 $e^2/ C$.

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