Quantum Hall Effect of Massless Dirac Fermions and Free Fermions in Hofstadter's Butterfly

Nobuyuki Yoshioka, Hiroyasu Matsuura, Masao Ogata

We propose a new physical interpretation of the Diophantine equation of ${\sigma }_{xy}$ for the Hofstadter problem. First, we divide the energy spectrum, or Hofstadter's butterfly, into s…