Low-Energy Effective Hamiltonian and the Surface States of Ca_3PbO

Abstract

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.

arXiv comment11 pages

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