Energy Gap and Averaged Inversion Symmetry of Tight-Binding Electrons on Generalized Honeycomb Lattice(Condensed matter: electronic structure and electrical, magnetic, and optical properties)

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We study the condition to open a finite gap in tight-binding electrons on an extended honeycomb lattice with the next-nearest-neighbor transfer integrals t_<2a>, t_<2b>, t_<2c>, t_<2d>, t_<2e>, and t_<2f>, where t_<2a>, t_<2b>, and t_<2c> are transfer integrals between the sublattice A and t_<2d>, t_<2e>, and t_<2f> are transfer integrals between the sublattice B. If the system has the inversion symmetry in this model, i.e., the sublattices A and B have the same on-site potential (∈_A=∈_B), the gap is zero. We find that although the finite gap is generally opened by inversion-symmetry breaking, the gap remains zero if the averaged inversion symmetry, which is defined as the sum of the transfer integrals and the on-site potentials of the sublattices are the same (t_<2a>+t_<2b>+t_<2c>+∈_A=t_<2d>+t_<2e>+t_<2f>+∈_B), is conserved.
2008-07-15