1201.6613 (Doru Sticlet et al.)

Geometrical engineering of a two-bands Chern insulator in two dimensions
with arbitrary topological index    [PDF]

Doru Sticlet, Frederic Piéchon, Jean-Noël Fuchs, Pavel Kalugin, Pascal Simon

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.

View original: http://arxiv.org/abs/1201.6613