Quantum transport theory in magnetic fields and the electron-hole-droplet magnetoresonance in Germanium
This thesis develops a general procedure for the calculation of longitudinal magnetoconductivities in the high field quantum regime, assuming a transport equation of Boltzmann form. Earlier work has been extended, both in the treatment of the scattering problem, and in the generality of the solution to the Boltzmann equation. Potential scattering in a magnetic field is treated via a quasi one-dimensional Schrodinger equation, giving a simple physical picture of the scattering process. The 0 function scatterer is briefly mentioned, while scattering by a cylindrical square well is treated in detail. Green's Function methods for the solution of the scattering equations are developed, and general features of the theory, in particular resonant bound states, are noted. Transport theory is developed from the Kubo formula by resolvent methods, to derive the Boltzmann equation with transition rates given either by the Born approximation or the t-matrix element. A general solution of the Boltzmann equation valid for elastic scattering is derived, involving multiple 'relaxation times' obtained by the inversion of a relaxation matrix. Time dependent relaxation is also treated and shown to involve multiple decay constants related to, but not identical with, the above 'relaxation times'. Regimes in which simple or approximate inversions of the relaxation matrix apply are investigated, in particular ihe quantum limit and isotropic scattering. The above theory is applied to an analysis of the electron-holedroplet (EHD) magnetoresonance of germanium. The practicability of the relaxation matrix method is shown, and accurate analytical approximations to the solution obtained. The experimentally observed features are explained by the analysis, which shows how accurate estimates of the droplet radius· may be obtained from the data. Further resonances are predicted which, if observed, will reinforce these estimates. Certain features of the analysis also suggest that the strength of EHO's as scattering potentials is less than has been previously assumed.