Berry curvature, orbital moment, and effective quantum theory of electrons in electromagnetic fields

Ming Che Chang*, Qian Niu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

139 Citations (Scopus)


Berry curvature and orbital moment of the Bloch state are two basic ingredients, in addition to the band energy, that must be included in the formulation of semiclassical dynamics of electrons in crystals, in order to give proper account of thermodynamic and transport properties to first order in the electromagnetic field. These quantities are gauge invariant and have direct physical significance as demonstrated by numerous applications in recent years. Generalization to the case of degenerate bands has also been achieved recently, with important applications in spin-dependent transport. The reader is assured that a knowledge of these ingredients of the semiclassical dynamics is also sufficient for the construction of an effective quantum theory, valid to the same order of the field, using a new quantization procedure that generalizes the venerable Peierls substitution rule. We cite the relativistic Dirac electron and the carrier in semiconductors as two prime examples to demonstrate our theory and compare with previous work on such systems. We also establish general relations between different levels of effective theories in a hierarchy.

Original languageEnglish
Article number193202
JournalJournal of Physics Condensed Matter
Issue number19
Publication statusPublished - 2008 May 14

ASJC Scopus subject areas

  • General Materials Science
  • Condensed Matter Physics


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