Topological Insulators and Semimetals with Point Group Symmetries

ORAL

Abstract

In this work, we study the theory of topological phases in systems with point group symmetries (PGSs) in one-, two- and three-dimension. The systems we study in general do not require time-reversal symmetry, and hence may be realized in both non-magnetic and magnetic materials. We show that a point group symmetry introduces new quantum numbers which reveal themselves in the entanglement spectrum as mid-gap states. PGSs also define a series of topological semimetals, in which the band touching points are protected by certain symmetries. We apply our theory to 3D ferromagnetic semimetal HgCr$_2$Se$_4$ which possesses a double-vortex band crossing protected by $C_4$ rotation symmetry.

*ONR - N00014-11-1- 0635, Darpa - N66001-11-1-4110, AFOSR FA9550-10-1-0459, ONR N0014-11-1-0728 and a gift the Intel Corporation

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Authors

  • Chen Fang

    • Princeton University

  • Matthew Gilbert

    • Department of Electrical and Computer Engineering, the University of Illinois at Urbana-Champaign
    • Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign
    • University of Illinois at Urbana-Champaign
    • Department of Electrical and Computer Engineering, University of Illinois
    • Department of Electrical and Computer Engineering, University of Illinois, Urbana IL 61801
    • Department of Electrical and Computer Engineering, University of Illinois, Urbana, Il, 61801
    • University of Illinois at Urbana Champaign

  • Xi Dai

    • Institute of Physics, Chinese Academy of Sciences
    • Chinese Academy of Sciences
    • Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences

  • Andrei Bernevig

    • Princeton University