Disorder-induced phase transitions in double Weyl semimetals

The double Weyl semimetal (DWSM) is a newly proposed topological material that hosts Weyl points with chiral charge $n=2$. The disorder effect in DWSM is investigated by adopting the tight-binding Hamiltonian. Using the transfer matrix method and the noncommutative Kubo formula, we numerically calculate the localization length and the Hall conductivity in the presence of the on-site nonmagnetic disorder or orbital (spin-flip) disorders, and give the corresponding global phase diagrams. For the on-site nonmagnetic disorder, the system undergoes the DWSM-3D quantum anomalous Hall (3D QAH) and normal insulator (NI)--DWSM phase transitions, and evolves into the diffusive metal phase before entering the gapless Anderson insulator phase, which is consistent with the Weyl semimetal. For ${\ensuremath{\sigma}}_x$ orbital disorder, increasing disorder strength can generate a pair of Weyl nodes at the boundary of the Brillouin zone and induce a 3D QAH--DWSM phase transition. Surprisingly, DOS calculations manifest that the insulator phase induced by the ${\ensuremath{\sigma}}_x$ disorder is gapped, which is different from the gapless DOS in the system with ${\ensuremath{\sigma}}₀$ disorders. Another difference is the direct DWSM-NI transition. These results indicate that the ${\ensuremath{\sigma}}₀$ and ${\ensuremath{\sigma}}_x$ disorders have a diverse impact on the system. Then we investigate the interplay of orbital disorders for both disordered 3D QAH phase and DWSM phase. The disorder-induced transitions at low disorders can be well understood in terms of the self-consistent Born approximation.