Ming-Che Chang and Qian Niu 2008 J. Phys.: Condens. Matter 20 193202 doi:10.1088/0953-8984/20/19/193202
Ming-Che Chang1 and Qian Niu2
Show affiliationsBerry 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.
72.10.-d Theory of electronic transport; scattering mechanisms
03.65.Sq Semiclassical theories and applications
71.70.Ej Spin-orbit coupling, Zeeman and Stark splitting, Jahn-Teller effect
03.65.Ta Foundations of quantum mechanics; measurement theory
Condensed matter: electrical, magnetic and optical
Issue 19 (14 May 2008)
Received 9 January 2008, in final form 20 March 2008
Published 11 April 2008
Ming-Che Chang and Qian Niu 2008 J. Phys.: Condens. Matter 20 193202
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