Parallel transport in a quasi-two-dimensional electron gas subjected to an in-plane magnetic field

The transport coefficients R xx and S xx are calculated for electrons confined to a parabolic potential well V c (z)=a 2 z 2 and subjected to an in-plane magnetic field B=(B,0,0). A Boltzmann transport formalism is used to develop general formulae for all the transport coefficients in the presence of delta -function scatterers. The anisotropic scattering lifetime when B not=0 is evaluated. It allows an immediate calculation of R xx and S xx , which show the structure expected with increasing B as successive sub-band minima pass through the Fermi level. In particular S xx exhibits a sign change and the behaviour of R xx is consistent with recent experimental data. The formulae for R yy and S yy requires the numerical iterative calculation of a renormalised velocity in the y direction for their evaluation.