二维三角格点系统中的拓扑陈数

利用紧束缚模型对二维三角周期格点中各能带的陈数分布进行研究.通过严格对角化方法得到体系能量本征值和对应的本征态,再利用Kubo公式计算出量子化的霍尔电导、态密度及各扩展态对应的陈数.在傅里叶变换下将哈密顿量转换到k空间从而得到体系的能谱分布.研究表明：次近邻格点之间的跳跃积分t'的不同取值影响体系各能带对应的陈数分布,计算得到当t'=1/2时体系三个能带从低到高对应的陈数分布为{-4,5,-1},t'=-1/2时其对应陈数分布变化为{2,-4,2},而t'=±1/4时对应的陈数分布都为{2,-1,-1}.同时发现：能谱帯隙的宽度和对应霍尔平台的宽度一致,并且k空间的能带越平坦,其对应的在霍尔电导跳跃处的态密度峰就越高越尖锐,而该处霍尔电导跳跃就越陡峭.

Topological Chern Numbers in a Two-dimensional Triangular-Lattice

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.