Disorder effect on 3-dimensional $Z_2$ quantum spin Hall systems

Abstract

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.

30 pages submitted to PRB. The standard WL calculation based on the Kubo formula is newly included, while the previous mode-mode coupling calculations are transferred to the appendices. The physical meaning of the "two-modes" is also made explicit

References in corpus (16)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Dissipationless Quantum Spin Current at Room Temperature
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling
• Topological delocalization of two-dimensional massless Dirac fermions
• Quantum criticality and minimal conductivity in graphene with long-range disorder
• Universal phase diagrams for the quantum spin Hall systems
• Topological aspects of quantum spin Hall effect in graphene: Z${}_2$ topological order and spin Chern number
• Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization
• Two-dimensional spin-filtered chiral network model for the Z_2 quantum spin-Hall effect