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      Zeeman Field-Tuned Transitions for Surface Chern Insulators

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          Abstract

          Mirror symmetric surfaces of a topological crystalline insulator host even number of Dirac surface states. A surface Zeeman field generically gaps these states leading to a quantized anomalous Hall effect. Varying the direction of Zeeman field induces transitions between different surface insulating states with any two Chern numbers between -4 and 4. In the crystal frame the phase boundaries occur for field orientations which are great circles with (111)-like normals on a sphere.

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          Topological Insulators with Inversion Symmetry

          Topological insulators are materials with a bulk excitation gap generated by the spin orbit interaction, and which are different from conventional insulators. This distinction is characterized by Z_2 topological invariants, which characterize the groundstate. In two dimensions there is a single Z_2 invariant which distinguishes the ordinary insulator from the quantum spin Hall phase. In three dimensions there are four Z_2 invariants, which distinguish the ordinary insulator from "weak" and "strong" topological insulators. These phases are characterized by the presence of gapless surface (or edge) states. In the 2D quantum spin Hall phase and the 3D strong topological insulator these states are robust and are insensitive to weak disorder and interactions. In this paper we show that the presence of inversion symmetry greatly simplifies the problem of evaluating the Z_2 invariants. We show that the invariants can be determined from the knowledge of the parity of the occupied Bloch wavefunctions at the time reversal invariant points in the Brillouin zone. Using this approach, we predict a number of specific materials are strong topological insulators, including the semiconducting alloy Bi_{1-x} Sb_x as well as \alpha-Sn and HgTe under uniaxial strain. This paper also includes an expanded discussion of our formulation of the topological insulators in both two and three dimensions, as well as implications for experiments.
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            Topological invariants of time-reversal-invariant band structures

            , (2013)
            The topological invariants of a time-reversal-invariant band structure in two dimensions are multiple copies of the \(\mathbb{Z}_2\) invariant found by Kane and Mele. Such invariants protect the topological insulator and give rise to a spin Hall effect carried by edge states. Each pair of bands related by time reversal is described by a single \(\mathbb{Z}_2\) invariant, up to one less than half the dimension of the Bloch Hamiltonians. In three dimensions, there are four such invariants per band. The \(\mathbb{Z}_2\) invariants of a crystal determine the transitions between ordinary and topological insulators as its bands are occupied by electrons. We derive these invariants using maps from the Brillouin zone to the space of Bloch Hamiltonians and clarify the connections between \(\mathbb{Z}_2\) invariants, the integer invariants that underlie the integer quantum Hall effect, and previous invariants of \({\cal T}\)-invariant Fermi systems.
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              Author and article information

              Journal
              29 September 2013
              Article
              1309.7682
              0962251b-709a-4e67-965a-8dadebaab279

              http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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              Custom metadata
              4 pages, 2 figures
              cond-mat.mes-hall cond-mat.str-el cond-mat.supr-con

              Condensed matter,Nanophysics
              Condensed matter, Nanophysics

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