2021/02/24 by Yoshiyuki Matsuki, Kazuki Ikeda, Mikito Koshino · 11 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Fractal #Geometry #Lattice (music) #Magnetic field #Mathematical analysis #Mathematics #Physics #Quantum and electron transport phenomena #Quantum mechanics #Scaling #Square lattice #Theoretical and Computational Physics #Wave function #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.104.035305
published in Physical review. B./Physical review. B 104(3) (American Physical Society) · 10 pages, 10 figures
arxiv created 2021/02/24 · openalex publication_date 2021/07/26 · arxiv updated 2021/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We investigate the electronic properties in the Bloch electron on a two-dimensional lattice with vacancies in the uniform magnetic field. We show that a single vacancy site introduced to the system creates a defect energy level in every single innumerable fractal energy gap in the Hofstadter butterfly. The wave functions of different defect levels have all different localization lengths depending on their fractal generations, and they can be described by a single universal function after an appropriate fractal scaling. We also show that each defect state has its own characteristic orbital magnetic moment, which is exactly correlated to the gradient of the energy level in the Hofstadter diagram. Probing the spatial nature of the defect-localized states provides a powerful way to elucidate the fractal nature of the Hofstadter butterfly.