Berry phase, hyperorbits, and the Hofstadter spectrum: Semiclassical dynamics in magnetic Bloch bands

Ming Che Chang, Qian Niu

Research output: Contribution to journalArticle

278 Citations (Scopus)

Abstract

We have derived a set of semiclassical equations for electrons in magnetic Bloch bands. The velocity and energy of magnetic Bloch electrons are found to be modified by the Berry phase and magnetization. This semiclassical approach is used to study general electron transport in a dc or ac electric field. We also find a close connection between the cyclotron orbits in magnetic Bloch bands and the energy subbands in the Hofstadter spectrum. Based on this formalism, the pattern of band splitting, the distribution of Hall conductivities, and the positions of energy subbands in the Hofstadter spectrum can be understood in a simple and unified picture.

Original languageEnglish
Pages (from-to)7010-7023
Number of pages14
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume53
Issue number11
DOIs
Publication statusPublished - 1996 Jan 1

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Bloch band
Electrons
Cyclotrons
Magnetization
Orbits
electrons
Electric fields
cyclotrons
energy
formalism
orbits
conductivity
magnetization
electric fields

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

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AB - We have derived a set of semiclassical equations for electrons in magnetic Bloch bands. The velocity and energy of magnetic Bloch electrons are found to be modified by the Berry phase and magnetization. This semiclassical approach is used to study general electron transport in a dc or ac electric field. We also find a close connection between the cyclotron orbits in magnetic Bloch bands and the energy subbands in the Hofstadter spectrum. Based on this formalism, the pattern of band splitting, the distribution of Hall conductivities, and the positions of energy subbands in the Hofstadter spectrum can be understood in a simple and unified picture.

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