Abstract
The Hall conductivity of extended states in disordered materials is reinvestigated using the standard linear response Kubo formalism. Our aim is to find an answer to the question: what replaces the concept of ‘effective mass’ in a disordered system? We attempt this in two ways: (1) using the usual tight-binding formalism and (2) using a more general representation. The latter approach is normally avoided because it is more difficult. In both cases we find that the derivative of the density of states of the Fermi energy (for metals) comes close to giving us a universal sign rule for the Hall constant RH. In the weak scattering limit the sign of RH is given by (-) the sign of the derivative of the density of states of the Fermi energy. In the tight-binding basis this has to be combined with knowledge of the topological structure of the system. In fact near the band edge we recover Emin’s topological rule derived for hopping conduction of polarons.
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© 1985 Plenum Press , New York
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Movaghar, B. (1985). The Sign of the Hall Effect in Disordered Materials. In: Adler, D., Fritzsche, H., Ovshinsky, S.R. (eds) Physics of Disordered Materials. Institute for Amorphous Studies Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2513-0_32
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DOI: https://doi.org/10.1007/978-1-4613-2513-0_32
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