On the theory of magnetotransport in a periodically modulated two-dimensional electron gas

Abstract

A semiclassical theory based on the Boltzmann transport equation for a two-dimensional electron gas modulated along one direction with weak electrostatic or magnetic modulations is proposed. It is shown that oscillations of the magnetoresistivity ρ || corresponding to the current driven along the modulation lines observed at moderately low magnetic fields, can be explained as classical geometric resonances reflecting the commensurability of the period of spatial modulations and the cyclotron radius of electrons.PACS numbers: 73.21 Cd; 73.40. -C Theoretical studies of magnetotransport properties of a two-dimensional electron gas (2DEG) spatially modulated along a certain direction due to periodic electrostatic or magnetostatic fields are lasting more than a decade. At present the theory of magnetotransport in modulated 2DEG is well developed and the most of effects observed in such systems at low magnetic fields have been explained both by quantum mechanical (in a semiclassical limit) [1,2,3,4,5,6,7] and classical [8,9,10,11,12] transport calculations, giving consistent results. One of a few exceptions is an effect of oscillations of the resistivity component ρ || which corresponds to the current driven in parallel with the lines of modulation. These oscillations were observed along with the commensurability oscillations of another resistivity component ρ ⊥ corresponding to the current driven across the modulation lines, and have the same period and a phase opposite to those of ρ ⊥ .The oscillations of ρ || had been immediately explained as an effect of a pure quantum nature which originates from the quantum oscillations of the electron density of states (DOS) in the applied magnetic field B [1, 3]. However, actual results obtained in these works [1,3] are not consistent with these conclusions. This can be easily demonstrated, basing on the results of Ref.[3] which are reproduced here (Fig.1). It is clearly seen in Fig.1 that both ρ ⊥ and ρ || exhibit oscillations of the same period at low (unquantizing) magnetic fields where quantum oscillations of DOS are not resolved, and only effects controlled with classical mechanisms could survive.It is very well known that periods of quantum oscillations and semiclassical commensurability oscillations (geometric resonance) are different. Their ratio equals 2π/λk F where λ is the space period of modulations, and k F is the Fermi wave vector of electrons [13]. Therefore, the observed coincidence on periods of the low-field Weiss oscillations of the resistivity component ρ ⊥ and the weaker anti-phase oscillations of ρ || gives an evidence that for both resistivity components these oscillations are geometric oscillations. Such oscillations arise in modulated 2DEG due to the periodic reproduction of commensura- bility between the diameters of electron cyclotron orbits and the period of applied modulations λ. Consequently, we can treat the low-field oscillations of ρ || as an effect basically following from classical mechanisms, and develop a theory of this effect based on Bolt...