Two-dimensional electron gas in a linearly varying magnetic field: Quantization of the electron and current density

We have developed methods to calculate dispersion curves (analytically, in the simpler cases) from which we are able to derive the spatial distribution of electron and current densities. We investigate the case where the magnetic field varies linearly with position and the results provide useful insights into the properties of this and other field distributions. We consider a spin as well as a confining electrostatic potential. We show that the electron and the current density exhibit a very rich structure related to the quantization of the energy. Moreover, there is a direct contribution to the current density due to the spin, which could be of interest in relation to the spin-polarized current.