Nonlinear current-voltage characteristics at quantum Hall resistance minima

Abstract

The longitudinal resistivity ${\mathrm{\ensuremath{\rho}}}_{\mathit{x}\mathit{x}}$ at the quantum Hall midplateau of a low-mobility two-dimensional electron gas in a GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterostructure has been studied for different sample widths and different sample currents. The critical current for breakdown of the quantum Hall effect was found to be proportional to the width of the samples. A subcritical rise of ${\mathrm{\ensuremath{\rho}}}_{\mathit{x}\mathit{x}}$ with current density was found to be exponential, a relation which to the best of our knowledge has not previously been reported. The power dissipation thus increases exponentially with current, leading to a critical current determined by a thermal runaway.