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Abstract: The topological insulator is an electronic phase stabilized by spin-orbitcoupling that supports propagating edge states and is not adiabaticallyconnected to the ordinary insulator. In several ways it is a spin-orbit-inducedanalogue in time-reversal-invariant systems of the integer quantum Hall effect(IQHE). This paper studies the topological insulator phase in disorderedtwo-dimensional systems, using a model graphene Hamiltonian introduced by Kaneand Mele as an example. The nonperturbative definition of a topologicalinsulator given here is distinct from previous efforts in that it involvesboundary phase twists that couple only to charge, does not refer to edgestates, and can be measured by pumping cycles of ordinary charge. In thisdefinition, the phase of a Slater determinant of electronic states isdetermined by a Chern parity analogous to Chern number in the IQHE case.Numerically we find, in agreement with recent network model studies, that thedirect transition between ordinary and topological insulators that occurs inband structures is a consequence of the perfect crystalline lattice.Generically these two phases are separated by a metallic phase, which isallowed in two dimensions when spin-orbit coupling is present. The sameapproach can be used to study three-dimensional topological insulators.



Autor: Andrew M. Essin, J. E. Moore

Fuente: https://arxiv.org/







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