Topological Chern Numbers in a Two-dimensional Triangular-Lattice

doi:10.19596/j.cnki.1001-246x.7696

Abstract

Abstract: We investigate numerically topological Chern number in a two-dimensional triangular-lattice with three bands, considering tight-binding Hamiltonian. Energy spectrum is obtained with Fourier transform and Hall conductance is calculated using Kubo formula. It is found that Chern number of energy band is modulated by next nearest neighbor hopping integral t'.Three bands own Chern numbers in sequence, {-4, 5,-1} at t'=1/2, {2,-4, 2} at t'=-1/2 and {2,-1,-1} at t'=±1/4, which leads to Hall plateaus in sequence, {-4, 1}e²/h, {2,-2}e²/h and {2, 1}e²/h, respectively. Peaks of density of states (DOS) are located at jumps of Hall conductance. Energy gap (DOS=0) gives width of corresponding Hall plateau. If energy band becomes more flat, corresponding peak of DOS becomes higher and sharper, and jump of Hall conductance becomes steeper.

Key words: integer quantum Hall effect, topological Chern number, Hall conductance, density of states, exact diagonalization method

CLC Number:

O469

YU Hualing, GAO Yu, ZHAI Zhangyin. Topological Chern Numbers in a Two-dimensional Triangular-Lattice[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 35(5): 606-612.

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