Quantum Hall effect induced by electron-electron interaction in disordered GaAs layers with a three-dimensional spectrum

It is shown that the observed quantum Hall effect in epitaxial layers of heavily doped n-type GaAs with thickness $(50\ensuremath{-}140\mathrm{nm})$ larger the mean free path of the conduction electrons $(15--30 \mathrm{nm})$ and, therefore, with a three-dimensional single-particle spectrum is induced by the electron-electron interaction. The Hall resistance ${R}_{\mathrm{xy}}$ of the thinnest sample reveals a wide plateau at small activation energy ${E}_{a}=0.4 \mathrm{K}$ found in the temperature dependence of the transverse resistance ${R}_{\mathrm{xx}}.$ The different minima in the transverse conductance ${G}_{\mathrm{xx}}$ of the different samples show a universal temperature dependence (logarithmic in a large range of rescaled temperatures ${T/T}_{0})$ that is reminiscent of electron-electron-interaction effects in coherent diffusive transport.