Stability of the quantum spin Hall effect: Effects of interactions, disorder, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>topology

Abstract

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

Keywords

Affiliated Institutions

• University of California, Berkeley US
• Lawrence Berkeley National Laboratory US

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