Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2008-08-10
Physical Review B {\bf 79}, 045321 (2009)
Physics
Condensed Matter
Disordered Systems and Neural Networks
30 pages submitted to PRB. The standard WL calculation based on the Kubo formula is newly included, while the previous mode-mo
Scientific paper
10.1103/PhysRevB.79.045321
In this paper, we studied the nonmagnetic disorder effects onto the quantum critical point (QCP) which intervenes an ordinary insulator and the 3-dimensional $Z_2$ quantum spin Hall insulator. The minimal model describing this QCP is the single-copy of the 3+1 Dirac fermion, whose topological mass $m$ induces the quantum phase transition. We derived the phase diagram spanned by this mass-term $m$, chemical potential $\mu$ and strength of the disorder within the self-consistent Born approximation. To infer the structure of the low-energy effective theory, we further calculated the weak localization (WL) correction to the conductivity. By way of this, we have found that the diffuson consists of the two quasi-degenerate contributions having the diffusion pole; one always behaves as the diffusion mode. The other becomes the massless mode only at $m=0$. Based on this "two-mode picture", we will discuss the possible microscopic picture of the "levitation and pair annihilation" phenomena, recently discovered by Onoda et al.
Murakami Shuichi
Shindou Ryuichi
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