LINEAR RESPONSE THEORY FOR A DEGENERATE ELECTRON GAS IN A STRONG MAGNETIC FIELD

The complete quantum-mechanical response of an electron gas in the presence of a strong dc magnetic field is discussed. The effect of collisions of the electrons with impurities and lattice imperfections is accounted for by means of a single relaxation time. In addition to the conduction current, a diffusion current associated with spatial variations in the electron density and a collision drag current for the case of acoustic propagation are evaluated. The results are expressed in a form quite analogous to the semiclassical result and convenient for studying quantum effects in the case of small-wavelength disturbances. A formal application of the results to the problem of acoustic propagation and to the diamagnetic interaction among the conduction electrons is presented. A number of useful sum rules and mathematical results are derived in appendices. © 1969 The American Physical Society.