Quantum Effects in the Conductivity of a Quasi 2D Electron Gas

We consider the role of the third dimension in the conductivity of a quasi 2D electron gas. It is demonstrated that, if the transverse correlation radius of the scattering potential is smaller than the width of the channel, i.e. the width of the transverse electron density distribution, then scattering to higher levels of the confinement potential becomes important and the current flow profile becomes broader than the electron density profile. The resulting conductivity is larger than that obtained from a 2D Boltzmann equation. A magnetic field, parallel to the driving electric field, effectively narrows the current flow profile, which may result in a strong positive longitudinal magnetoresistivity of the quasi 2D electron gas. Impurity-limited conductivity of a quasi-two-dimensional electron gas (quasi-2DEG) is usually calculated by means of a quasi-classical 2D Boltzmann equation (see, e.g. [1–6]) and references therein). Quantum corrections to the 2D conductivity are assumed to be only due to the weak localization or interaction mechanisms. The starting point of the quasi-classical approach is the Hamiltonian