Butterfly spectrum and integer quantum Hall effect in three dimensions - A mapping between 2D and 3D Hofstadter problems

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

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We have shown that Hofstadter's butterfly spectrum, which is usually conceived as peculiar to two-dimensional systems in magnetic fields, can occur, unexpectedly, in three-dimensional lattices as well under certain criteria. Curiously, the butterfly arises due to the third-direction transfer rather than as a remnant of a 2D butterfly. A formal mapping between 2D and 3D Harper's equations enables us to calculate the Hall conductivity in terms of Kohmoto-Halperin-Wu's topological invariants, where each of σxy, σzx is found to be quantized.

Original languageEnglish
Pages (from-to)97-100
Number of pages4
JournalPhysica B: Condensed Matter
Volume298
Issue number1-4
DOIs
Publication statusPublished - 2001 Apr 1

Keywords

  • Hofstadter butterfly
  • IQHE
  • Organic conductors

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics

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