Commensurability resonances in two-dimensional magnetoelectric lateral superlattices

Abstract

Hybrid lateral superlattices composed of a square array of antidots and a periodic one-dimensional magnetic modulation are prepared in Ga [Al]As heterostructures. The two-dimensional electron gases exposed to these superlattices are characterized by magnetotransport experiments in vanishing average perpendicular magnetic fields. Despite the absence of closed orbits, the diagonal magnetoresistivity in the direction perpendicular to the magnetic modulation shows pronounced classical resonances. They are located at magnetic fields where snake trajectories exist which are quasi-commensurate with the antidot lattice. The diagonal magnetoresistivity in the direction of the magnetic modulation increases sharply above a threshold magnetic field and shows no fine structure. The experimental results are interpreted with the help of numerical simulations based on the semiclassical Kubo model. PACS numbers: 73.23.-b, 73.63.-b z , which allows a more direct comparison to the simulations. Even though the simulated function ρ xx (B max z ) deviates from the experimental trace in several aspects, the most prominent features are reproduced qualitatively, namely the positive magnetoresistivity around B max z = 0, minima close to B max z = 53 mT, 110 mT, 170 mT and 280 mT, the decrease of ρ xx at B max z ≈ 260 mT, and some weakly pronounced maxima and minima at larger magnetic fields. The sharp decrease of of ρ xx around B max z = 500 mT is not observed experimentally, most likely because our fringe fields are too weak. The simulation of ρ yy (B max z) is compared to the scaled experimental data in Fig. 3 (c). Very good agreement is found for B max z ≤ 0.3 T, while the strong increase of the resistivity around B max z ≈ 0.4 T is reproduced as well, though shifted to slightly higher magnetic fields. Further simulations 30 show that the presence of the antidots does influence ρ yy (B max z ) to some extent, but the overall behavior is dominated by the magnetic barriers and is not an effect of the hybrid superlattice.We proceed by interpreting the magnetoresistivity features in terms of the electron dynamics which determines the components of the magnetoconductivity tensor. 30 The off-diagonal elements σ xy and σ yx are approximately independent of B max z and of the order of 0.1 mS. σ yy decreases from 18 mS at B max z = 0 to almost zero at B max z ≈ 0.5 T. Only σ xx shows resonances as B max z is changed. This implies that ρ xx ≈ 1/σ xx and ρ yy ≈ 1/σ yy , while ρ xy (B y ) ≈ σ xy /(σ xx σ yy ). The sharp increase of ρ xy (see Ref. 30) and ρ yy at B max z = 0.5 T has thus its origin in the strongly suppressed diagonal conductivity in y-direction.FIG. 4. (color online). Poincaré sections for various values of B max z (a-e). Some characteristic trajectories are shown in (f), the initial conditions of which are indicated by full circles in the corresponding Poincaré sections.

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