Linear and nonlinear electrical conduction in quasi-two-dimensional quantum wells

The dc electrical transport parallel to the walls of a quasi-two-dimensional quantum well, with a magnetic field B=Bz applied normal to its barriers, is considered. The influence of scattering by optical phonons on the dc current is investigated at high temperatures and strong electric fields (nonlinear transport). Certain values of the electric field induce transitions of the carriers between neighboring Landau levels and the usual magnetophonon maxima, reported previously, convert into minima and vice versa. This behavior of the magnetophonon extrema has been recently observed in $n^{+}$-$n^{\mathrm{-}}$-$n^{+}$ structures. For scattering by impurities at very low temperatures and weak electric fields (linear transport) the dc conductivity ${\sigma }_{\mathrm{xx}}$ oscillates with period (${\varepsilon }_F$-${\varepsilon }_0$ $n^2$)/ħ${\omega }_0$, where ${\varepsilon }_F$ is the Fermi level, n denotes energy-level quantization in the z direction, and ${\varepsilon }_0$ is the energy of the lowest level. For strong electric fields, transitions between neighboring Landau levels can occur, leading to an additional oscillatory structure. The Hall conductivity ${\sigma }_{\mathrm{yx}}$ is evaluated. The possibility of transitions between the levels n in wide wells is also investigated. The dependence of the conductivities (or currents), inverse scattering rates, and level widths on the magnetic field, the thickness of the well, and the temperature is shown explicitly.