Quantum Hall effects of graphene with multi orbitals: Topological numbers, Boltzmann conductance and Semi-classical quantization

Hall conductance $\sigma_{xy}$ as the Chern numbers of the Berry connection in the magnetic Brillouin zone is calculated for a realistic multi band tight-band model of graphene with non-orthogonal basis. It is confirmed that the envelope of $\sigma_{xy}$ coincides with a semi-classical result when magnetic field is sufficiently small. The Hall resistivity $\rho_{xy}$ from the weak-field Boltzmann theory also explains the overall behaviour of the $\sigma_{xy}$ if the Fermi surface is composed of a single energy band. The plateaux of $\sigma_{xy}$ are explained from semi-classical quantization and necessary modification is proposed for the Dirac fermion regimes.Comment: 5pages, 3figure

Electron-energy-loss function of LiTaO3 and LiNbO3 by x-ray photoemission spectroscopy: Theory and experiment

We report experimental energy-loss structures in x-ray photoemission spectra of single crystalline LiTaO3 and LiNbO3, and then compare these with theoretical electron-energy-loss functions calculated from first principles using the full-potential linearized augmented plane-wave method in the local-density approximation. The energy-loss structure of core electrons can be approximated by a sum of four components: for LiTaO3, the peaks positioned at 8.0, 13.4, 15.8, and 22.6 eV; for LiNbO3, those positioned at 7.0, 12.0, 14.5, and 21.8 eV. The momentum matrix elements between Bloch functions were evaluated to determine the electron energy-loss functions. The theoretical electron-energy-loss functions agreed fairly well with the experimental one. The experimental peaks positioned at 8.0, 13.4, and 15.8 eV for LiTaO3 and those at 7.0, 12.0, and 14.5 eV for LiNbO3 were assigned to the interband transitions from the valence band to the conduction bands. The peaks at 22.6 eV for LiTaO3 and 21.8 eV for LiNbO3 were ascribed to the electron excitation from the O 2s level to the lower conduction band

Numerical study of quantum Hall effect in two-dimensional multi-band system: single- and multi-layer graphene

The Chern numbers which correspond to quantized Hall conductance $\sigma_{xy}$ were calculated for single- and bi-layer honeycomb lattices. The quantization of $\sigma_{xy}$ occurs in entire energy range. Several large jumps of Chern numbers appear at van-Hove singularities of energy bands without magnetic fields. The plateauxof $\sigma_{xy}$ are discussed from semi-classical quantization.Comment: 4 pages, submitted to Physica E as EP2DS-18 proceeding