Isotopic disorder in integer and fractional quantum Hall effects

Abstract

The energy of the activation gaps in the quantum Hall effect has been thought to be reduced by the broadening of the Landau levels due to disorder. The isotopic mass can affect the electron-phonon interactions and the 0 K renormalization of the conduction and valence bands, leading to appreciable energy offsets between lattice sites with different nuclear masses. The isotopic disorder originating from the natural occurrence of nuclear masses could be the dominant broadening mechanism remaining, leading to the experimentally observed quantum Hall effect gaps in high-mobility devices. The Landau level broadening due to the isotopic disorder has been calculated microscopically without fitting parameters.