2024/04/04 by Igor N. Karnaukhov, Karnaukhov, Igor N.
Materials Science · Physics and Astronomy · #FOS: Physical sciences #Graphene research and applications #Quantum and electron transport phenomena #Strongly Correlated Electrons (cond-mat.str-el) #Surface and Thin Film Phenomena
paper · pdf · doi:10.48550/arxiv.2404.03289
openalex publication_date 2024/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The fractional quantum Hall effect (FQHE) is studied in the semiclassical limit in the framework of the Hofstadter model with a short-range interaction between fermions. In the mean-field approximation, the repulsion between fermions leads to a periodic potential. Numerical calculations show that in the case of the periodic potential with a period that is a multiple on \frac1ν of the magnetic cell (ν is filling of a separated band) composite Hofstadter bands (HBs) are formed. The composite HBs are split into \frac1ν subbands, which are separated by the Dirac points. The Chern number of γ-full filled composite HBs is equal to the Chern number Cγ of the corresponding HB. The Chern number, equal to νCγ, corresponds to ν-filling of γ-composite HB. Thus, FQHE is realized by fractional filling of composite HBs.