One of the most exciting subjects in solid state physics is a single layer of
graphite which exhibits a variety of unconventional novel properties. The key
feature of its electronic structure are linear dispersive bands which cross in
a single point at the Fermi energy. This so-called Dirac cone is closely
related to the surface states of the recently discovered topological
insulators. The ternary compounds, such as LiAuSe and KHgSb with a honeycomb
structure of their Au-Se and Hg-Sb layers feature band inversion very similar
to HgTe which is a strong precondition for existence of the topological surface
states. In contrast to graphene with two Dirac cones at K and K' points, these
materials exhibit the surface states formed by only a single Dirac cone at the
\Gamma -point together with the small direct band gap opened by a strong
spin-orbit coupling (SOC) in the bulk. These materials are centro-symmetric,
therefore, it is possible to determine the parity of their wave functions, and
hence, their topological character. Surprisingly, the compound KHgSb with the
strong SOC is topologically trivial, whereas LiAuSe is found to be a
topological non-trivial insulator.Comment: 4 pages + 1 page supplementa