Stability of the quantum spin Hall effect: effects of interactions, disorder, and Z_2 topology

Details Stability of the quantum spin Hall effect: effects of interactions, disorder, and Z_2 topology Stability of the quantum spin Hall effect: effects of interactions, disorder, and Z_2 topology

2005-08-11

arxiv.org/abs/cond-mat/0508291v1

Phys. Rev. B 73, 045322 (2006)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

6 pages, 2 figures

Scientific paper

10.1103/PhysRevB.73.045322

The stability to interactions and disorder of the quantum spin Hall effect (QSHE) proposed for time-reversal-invariant 2D systems is discussed. The QSHE requires an energy gap in the bulk and gapless edge modes that conduct spin-up and spin-down excitations in opposite directions. When the number of Kramers pairs of edge modes is odd, certain one-particle scattering processes are forbidden due to a topological $\mathbb{Z}_2$ index. We show that in a many-body description, there are other scattering processes that can localize the edge modes and destroy the QSHE: the region of stability for both classes of models (even or odd number of Kramers pairs) is obtained explicitly in the chiral boson theory. For a single Kramers pair the QSHE is stable to weak interactions and disorder, while for two Kramers pairs it is not; however, the two-pair case can be stabilized by {\it either} finite attractive or repulsive interactions. For the simplest case of a single pair of edge modes, it is shown that changing the screening length in an edge with screened Coulomb interactions can be used to drive a phase transition between the QSHE state and the ordinary insulator.

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