1202.2909 (Toshikaze Kariyado et al.)

Low-Energy Effective Hamiltonian and the Surface States of Ca_3PbO    [PDF]

Toshikaze Kariyado, Masao Ogata

The band structure of Ca_3PbO, which possesses a three-dimensional massive
Dirac electron at the Fermi energy, is investigated in detail. Analysis of the
orbital weight distributions on the bands obtained in the first-principles
calculation reveals that the bands crossing the Fermi energy originate from the
three Pb-p orbitals and three Ca-dx2y2 orbitals. Taking these Pb-p and Ca-dx2y2
orbitals as basis wave functions, a tight-binding model is constructed. With
the appropriate choice of the hopping integrals and the strength of the
spin-orbit coupling, the constructed model sucessfully captures important
features of the band structure around the Fermi energy obtained in the
first-principles calculation. By applying the suitable basis transformation and
expanding the matrix elements in the series of the momentum measured from a
Dirac point, the low-energy effective Hamiltonian of this model is explicitely
derived and proved to be a Dirac Hamiltonain. The origin of the mass term is
also discussed. It is shown that the spin-orbit coupling and the orbitals other
than Pb-p and Ca-dx2y2 orbitals play important roles in making the mass term
finite. Finally, the surface band structures of Ca_3PbO for several types of
surfaces are investigated using the constructed tight-binding model. We find
that there appear nontrivial surface states that cannot be explained as the
bulk bands projected on the surface Brillouin zone. The relation to the
topological insulator is also discussed.

View original: http://arxiv.org/abs/1202.2909