Stability of the quantum spin Hall effect: Effects of interactions, disorder, and Z 2 topology
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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.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/8e94dfb20938adeb5ea21cd088d837b27ab28117
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In Atomic and Molecular Physics, and Optics
Citations in the corpus
- One-dimensional topologically protected modes in topological insulators with lattice dislocations (2008, background): “have provided evidence for the existence of these ‘helical’ edge state”
- Fractional charge and quantized current in the quantum spin Hall state (2007, background): “The edge states of the QSH insulator state differ from the quantum Hall effect and have a distinct helical property: two states with opposite spin polarization counterpropagate at a given edg”