2016/05/04 by Nobuyuki Yoshioka, Hiroyasu Matsuura, Masao Ogata · 3 citations
Physics and Astronomy · #Composite fermion #Dirac equation #Dirac fermion #Dirac sea #Energy spectrum #Fermion #Hamiltonian (control theory) #Landau quantization #Magnetic field #Massless particle #Mathematical physics #Physics #Quantization (signal processing) #Quantum Hall effect #Quantum Mechanics and Applications #Quantum and electron transport phenomena #Quantum mechanics #Quantum spin Hall effect #Theoretical physics #Topological Materials and Phenomena #cond-mat.str-el
paper · pdf · doi:10.7566/jpsj.85.064712
published in Journal of the Physical Society of Japan 85(6), 064712 (Physical Society of Japan) · 6 pages, 4 figures, To be published in J. Phys. Soc. Jpn
arxiv created 2016/05/04 · openalex publication_date 2016/05/30 · arxiv updated 2016/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose a new physical interpretation of the Diophantine equation of σxy for the Hofstadter problem. First, we divide the energy spectrum, or Hofstadter's butterfly, into smaller self-similar areas called "subcells", which were first introduced by Hofstadter to describe the recursive structure. We find that in the energy gaps between subcells, there are two ways to account for the quantization rule of σxy, that are consistent with the Diophantine equation: Landau quantization of (i) massless Dirac fermions or (ii) free fermions in Hofstadter's butterfly.