### Universal Modeling of Weak Antilocalization using Pseudo-Random Number Generator

2017.07.05

Takaaki Koga, Hokkaido University

The weak localization/antilocalization, recognized as a precursory state of the Anderson localization, was elucidated both theoretically and experimentally already in 1980's in the realm of “diffusion approximation” [1]. A theoretical model premised on the Rashba effect was then developed in 1990's, shortly before the “gate-induced” weak localization-to-antilocalization transition was confirmed experimentally [2]. After this experimental confirmation, the weak antilocalization effect has become recognized as a useful tool for investigating the spin-orbit interaction (SOI) in various two-dimensional electron systems (2DES). It is deemed that this tool will be also applied to so-called “2D materials” such as graphene and transition metal dichalgogenides in the near future. In this respect, we recently succeeded in developing a working universal model of the weak antilocalization that doesn’t rely on the “diffusion approximation” [3]. As a result, (1) our model ended up with being valid in wide magnetic field ranges. (2) It can take various SOIs and even multiple of these almost freely. (3) The numerical computation can be done easily using relatively simple coding. Return loop trajectories of two-dimensional electrons (2DES) are considered by the random walk in this model. These return trajectories, generated only once forever, can be used repeatedly in general-purpose way to all 2DESs because 2DESs are characterized by a single mean free path value and the associated return trajectories are scalable by this value. The utilization of the deterministic nature of the pseudo-random number generator provided a key for the fast computation in our proposed model.

[1] G. Bergmann, “Weak localization in thin films: a time-of-flight experiment with conduction electrons”, Phys. Rep.**107**, 1 (1984).

[2] T. Koga, J. Nitta, T. Akazaki, and H. Takayanagi, “Rashba Spin-Orbit Coupling Probed by the Weak Antilocalization Analysis in InAlAs/InGaAs/InAlAs Quantum Wells as a Function of Quantum Well Asymmetry”, Phys. Rev. Lett.

**89**, 046801 (2002).

[3] A. Sawada and T. Koga, “Universal modeling of weak antilocalization corrections in quasi-two-dimensional electron systems using predetermined return orbitals”, Phys. Rev. E

**95**, 023309 (2017).

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