Quantum interference Hall effect in nanopatterned two-dimensional electron gas systems

Abstract

We show that in mesoscopic two-dimensional electron gas systems, quantum interference caused by prede- signed nanopatterns can enhance the Hall effect by up to 500%. A quality factor Q is defined which optimizes the ratio of the Hall voltage to longitudinal voltage. Genetic algorithm and the Landauer-Buttiker formalism were used to search for the potential configuration that can achieve a large Q. We propose some realistic nanopatterns to realize this effect. Quantum Hall effect shows that electron's quantum wave nature can alter its classical Hall character under a strong magnetic field. 1 But can such wave characteristics persist in the limit of B →0? Some time ago it was shown that the giant Hall effect GHE in magnetic materials can persist even in the limit where magnetization has reached saturation and therefore cannot play a role. 2 It follows that there could be some alternative scenario for the enhancement of the Hall effect that are distinct from the usual GHE. 2,3 Motivated by this finding, subsequent experimental and theoretical studies on the nonmagnetic CuSiO2 composites have found that quantum interference may indeed play a crucial role in en- hancing the Hall coefficient. 4,5 This conclusion was sup- ported by the fact that only when the size of the metallic granules is much smaller than the coherent length of the electron, e.g., in the low-temperature regime so that the electron coherence length can reach its saturation value, can this GHE occur. Most dramatically, the effect vanishes in annealed samples, when the size of the metallic granules exceeds the quantum coherence length. Together with the fact that all the GHE was observed in the vicinity of the percolation threshold, it was concluded that the GHE arises from the quantum interference effect in the percolation geo- metric setting. By using mesoscopic transport calculations in the microscopic regions within a coherence length to evalu- ate the local Hall conductances, Wan and Sheng 5 built a model in which the local mesoscopic Hall conductance ten- sors thus obtained served as the inputs to the macroscopic classical electric network calculations. The results show ex- cellent agreement with the experiment data. The random nature of the composite geometry means that the GHE is manifest only in a statistically averaged sense. In this paper, we show in mesoscopic two-dimensional 2D electron gas systems one can utilize predesigned nanostruc- tures to maximize the Hall effect in the limit of small mag- netic field. Genetic algorithm was used to search the optimal 2D structure pattern. It is shown that for certain nanopat- terned configurations the Hall coefficient can be enhanced up to 300%-500% in 2D electron systems with parameters rel- evant to semiconductor heterostructures. By using designed nanostructures, the case for quantum interference Hall effect can be much better verified, as there can be a direct correla- tion between the nanostructure and the measured Hall char- acteristics. In what follows, the Hall effect in the mesoscopic context, i.e., in nanostructures, is described in Sec. II together with its calculational approach. In Sec. III we present the results on the Hall effect in homogeneous mesoscopic samples in order to set the stage for the consideration of patterned samples. In Sec. IV the definition of a quality factor for measuring the mesoscopic Hall effect is followed by pattern optimizations to achieve maximum Hall-effect enhancement. A few opti- mal nanopatterns are presented and their relevant parameter values compared with those of the homogeneous samples.