Ai Yamakage, Kentaro Nomura, Ken-Ichiro Imura, Yoshio Kuramoto
We study quantum criticality of the disordered topological insulator in two spatial dimensions, using a Wilson-Dirac Hamiltonian on a square lattice combined with Rashba spin-orbit coupling (SOC). Employing scaling analysis of the localization length, we estimate the critical exponent of metal-insulator transitions inherent to the system to be nu~2.7, which is consistent with that of the symplectic class. The phase diagram classifying different disordered topological phases is deduced from the size-scaling. In the phase diagram, the symplectic metal phase predominates over the weakly disordered region due to the effects of carrier-doping and Rashba SOC. In the generic carrier-doped case, i.e., away from the particle-hole symmetric point, our data implies a quantitative disagreement with a simple interpretation of the disorder-induced topological phase in terms of renormalization of the effective mass gap proposed earlier. Our model Hamiltonian determined by symmetry considerations is optimal for the description of systems under C4v point group symmetry, e.g., of the one implemented in the HgTe quantum well.
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http://arxiv.org/abs/1211.5026
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