Electron-phonon scattering in strong magnetic fields and the temperature scaling between quantum Hall plateaus

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Abstract
The electron-phonon scattering rate is calculated in a strong magnetic field for a two-dimensional electron gas moving in a smooth random potential within the framework of semiclassical approximation. This inelastic scattering rate is strongly influenced by the strong magnetic field and is found to be linear in temperature for a wide range of temperatures, corresponding to an effective reduction of the Debye temperature. Applying this result to the temperature scaling exponent κ for the width of the transition region between quantum Hall effect plateaus, we argue that κ=3/7 is dictated by the inelastic scattering rate and the percolation length, instead of the localization length.