Hofstadter butterfly and integer quantum Hall effect in three dimensions

M. Koshino, H. Aoki, K. Kuroki, S. Kagoshima, T. Osada

Research output: Contribution to journalArticlepeer-review

79 Citations (Scopus)


The possibility of obtaining Hofstadter's butterfly inspite of three-dimensionality was addressed. This problem was solved by formally mapping the 3D Schrodinger's equation to 2D. The resulting mapping indicates that the ratio of the magnetic fluxes penetrating two facets of the 3D unit cell plays the role of the magnetic flux in 2D, so that 3D butterfly appears on the energy versus tilting angle of the magnetic field.

Original languageEnglish
Pages (from-to)1062-1065
Number of pages4
JournalPhysical review letters
Issue number6
Publication statusPublished - 2001 Feb 5
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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