Fractional magnetic breakdown frequencies in semiconductor lattices with one-dimensional modulation

Four-terminal devices with semiconductor lattices based on a two-dimensional electron gas have been simulated within single-particle quantum mechanics at different Fermi energies and amplitudes of one-dimensional modulation of the electrostatic potential in the presence or absence of disorder. The four-terminal resistances have been determined by the transmission coefficients in the Landauer–Buttiker formalism. The Fourier analysis of the density of states or the resistance $R_{xx}$ as a function of the inverse magnetic field $1/B$ gives the frequencies of magnetic oscillations caused by the magnetic breakdown. It has been shown that the frequencies of commensurability oscillations observed in the experiments are absent in the Fourier transform of the density of states but are present for the resistance $R_{xx}(1/B)$. With an increase in the modulation amplitude, oscillations with fractional combinations of the magnetic breakdown frequencies appear in the resistance, but they are absent in the density of states.