Role of spin degrees of freedom in Anderson localization of two-dimensional particle gases with random spin-orbit interactions

Anderson localization of two-dimensional noninteracting high-spin particle gases subject to random spin-orbit coupling and random on-site potential is numerically studied on square lattices. Employing the finite-size scaling of localization length, we show that the Anderson localization transition occurs for high-spin fermions and belongs to the same universality class as two-dimensional systems with time-reversal symmetry and spin-orbit interaction characterized by the universal critical exponent of ν≃2.73, while all states of disordered bosons are localized in the thermodynamic limit. These observations are commensurate with the scaling theory. Moreover, a strong finite-size effect is observed for high-spin particles, which can be attributed to the large spin degrees of freedom acting as an extra spin dimension in finite lattices. As a consequence, the system indeed behaves as a three-dimensional system and the Anderson localization transition can even happen for bosons with very large spins when the spin degrees of freedom is comparable to the lattice size.