Anderson localization of the three-dimensional pseudospin-1 system

We report a systematic study of the Anderson localization of a three-dimensional (3D) pseudospin-1 system. From an analysis on the symmetry of the Hamiltonian, it can be inferred that the pseudospin-1 system belongs to the class of unitary symmetry according to Wigner's surmise. Such a result of Anderson localization is similar to the case of apseudospin-12 system which corresponds to the Weyl or Dirac topological semimetals. By carrying out the numerical calculations, we find that the statistical distributions of the adjacent energy level difference conform to the unitary distribution very well for both the pseudospin-1 and pseudospin- 12 systems. Furthermore, by taking a scaling analysis of the numerical result of the localization length, we obtain the critical exponent of the Anderson transition, nu = 1.42 +/- 0.04, for pseudospin-1 system, very close to the standard value of the unitary class systems (nu = 1.443 +/- 0.003). All these numerical results confirm unambiguously that the 3D pseudospin-1 system falls within the class of unitary symmetry, just like the pseudospin- 12 system. Furthermore, the numerical results demonstrate that the pseudospin-1 system exhibits Anderson localization at a lower critical disorder strength than the pseudospin- 12 system. We then generalize Ziman's approach to explain this phenomenon. Our findings indicate that the underlying physical reason for the result that the pseudospin-1 system can enter the localization regime at a smaller disorder strength than the pseudospin-12 system can be ascribed to the smaller average coordinate number.