Distribution of Chern number by Landau level broadening in Hofstadter butterfly

International Workshop on Dirac Electrons in Solids 2015

Yoshioka, Nobuyuki^1 ; Matsuura, Hiroyasu^1 ; Ogata, Masao^1

Department of Physics, University of Tokyo, Hongo, Bunkyo-ku

113-0033, Japan^1

关键词: Chern numbers;    Continued fraction expansion;    Hall conductance;    Hofstadter;    Landau levels;    Quantum hall;    Square lattices;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/603/1/012019/pdf
DOI  :  10.1088/1742-6596/603/1/012019

来源: IOP

【 摘 要 】

We discuss the relationship between the quantum Hall conductance and a fractal energy band structure, Hofstadter butterfly, on a square lattice under a magnetic field. At first, we calculate the Hall conductance of Hofstadter butterfly on the basis of the linear responce theory. By classifying the bands into some groups with a help of continued fraction expansion, we find that the conductance at the band gaps between the groups accord with the denominators of fractions obtained by aborting the expansion halfway. The broadening of Landau levels is given as an account of this correspondance.