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Abstract

We investigate the magnetoresistance of epitaxially grown,
heavily doped n-type GaAs layers with thickness (40-50 nm)
larger than the electronic mean free path (23 nm). The
temperature dependence of the dissipative resistance R-xx in
the quantum Hall effect regime can be well described by a
hopping law (R-xx proportional to exp{-(T-0/T)(p)}) with p
approximate to0.6. We discuss this result in terms of variable
range hopping in a Coulomb gap together with a dependence of
the electron localization length on the energy in the gap. The
value of the exponent p greater than or equal to0.5 shows that
electron-electron interactions have to be taken into account in
order to explain the occurrence of the quantum Hall effect in
these samples, which have a three-dimensional single electron
density of states.