Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2012-01-31
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
changes in bibliography, and typos correction
Scientific paper
Two-dimensional 2-bands insulators breaking time reversal symmetry can present topological phases indexed by a topological invariant called the Chern number. Here we first propose an efficient procedure to determine this topological index. This tool allows in principle to conceive 2-bands Hamiltonians with arbitrary Chern numbers. We apply our methodology to gradually construct a quantum anomalous Hall insulator (Chern insulator) which can be tuned through five topological phases indexed by the Chern numbers {0,+/-1,+/-2}. On a cylindrical finite geometry, such insulator can therefore sustain up to two edge states which we characterize analytically. From this non-trivial Chern insulator and its time reversed copy, we build a quantum spin Hall insulator and show how the phases with a +/-2 Chern index yield trivial Z2 insulating phases.
Fuchs Jean-Noël
Kalugin Pavel
Piéchon Frédéric
Simon Pascal
Sticlet Doru
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