Quantum theory of Ohmic galvano- and thermomagnetic effects in semiconductors

Abstract

A density-matrix formalism developed earlier for the evaluation of Ohmic magnetoconductivity is further elaborated and applied to other magnetotransport effects in nonpolar semiconductors in the presence of a magnetic field of arbitrary strength. The difference from earlier transport theories lies in a natural extension of the scattering dynamics beyond the strict Born approximation. The well-known divergence difficulties of older theories, usually removed by any of a number of ad hoc cutoff procedures, do not appear here. The transverse-conductivity expression turns out to be equivalent to that of some earlier theories of cyclotron resonance extrapolated to zero frequency, but derived in a different way. When applied to elastic scattering of electrons in a simple model of a semiconductor, the theory gives galvanomagnetic and thermomagnetic coefficients within the range of values usually seen experimentally, showing the basic correctness of the theory. It is then applied to the magnetophonon effect, where the resonance peaks are shown to be finite. An interesting inversion of one of the peaks in the Ettingshausen-Nernst coefficient is found. Landau-level broadening and phonon drag are not included in the present paper, although they can be incorporated when deemed important.