F. Quantum size effectsQuantum size

F. Quantum size effectsQuantum size effects on the resistivity result from modifications of the 2D density of states in a 2DEG channel of width comparable to the Fermi wavelength. The electrostatic lateral confinement in such a narrow channel leads to the formation of 1D subbands in the conduction band of the 2DEG (see Section I.D.1). The number N ≈ kFW/π of occupied 1D subbands is reduced by decreasing the Fermi energy or the channel width. This depopulation of individual subbands can be detected via the resistivity. An alternative method to depopulate the subbands is by means of a magnetic field perpendicular to the 2DEG. The magnetic field B has a negligible effect on the density of states at the Fermi level if the cyclotron diameter 2lcycl ≫ W (i.e., for B ≪ Bcrit ≡ 2¯hkF/eW). If B ≫ Bcrit, the electrostatic confinement can be neglected for the density of states, which is then described by Landau levels [Eq. (1.7)]. The number of occupied Landau levels N ≈ BF/¯hωc ≈ kFlcycl/2 decreases linearly with B for B ≫ Bcrit. In the intermediate field range where B and Bcrit are comparable, the electrostatic confinement and the magnetic field together determine the density of states. The corresponding magnetoelectric subbands are depopulated more slowly by a magnetic field than are the Landau levels, which results in an increased spacing of the Shubnikov-De Haas oscillations in the magnetoresistivity (cf. Section I.D.3).