M J Rave and W C Kerr 2010 Eur. J. Phys. 31 15 doi:10.1088/0143-0807/31/1/002
M J Rave1 and W C Kerr2
Show affiliationsBerry's phase, although well known since 1984, has received little attention among textbook authors of solid state physics. We attempt to address this lack by showing how the presence of the Berry's phase significantly changes a standard concept (effective mass) found in most solid state texts. Specifically, we show that the presence of a non-zero Berry curvature in Bloch systems makes the traditional concept of an inverse effective mass tensor M−1 problematic, since a routine application of Newton's second law leads to a circular definition. As a consequence, the related concept of cyclotron effective mass m* also requires modification. It is shown that m* is magnetic-field dependent in non-inversion symmetric systems. This has important ramifications for cyclotron resonance experiments, since such experiments yield m* and thereby purportedly give the components of M−1. This work represents a 'case study' in how Berry's phase effects can modify 'standard' solid-state topics in ways that students and instructors may find surprising.
03.65.Ta Foundations of quantum mechanics; measurement theory
Issue 1 (January 2010)
Received 12 August 2009, in final form 14 September 2009
Published 4 November 2009
M J Rave and W C Kerr 2010 Eur. J. Phys. 31 15
E G Kalnins and W Miller Jr 1982 J. Phys. A: Math. Gen. 15 2699
W.J. Hogan et al 2001 Nucl. Fusion 41 567
F De Zela 2005 J. Opt. B: Quantum Semiclass. Opt. 7 372
A van den Bos 1977 J. Phys. E: Sci. Instrum. 10 753
S Djordjevic et al 2008 Metrologia 45 429
H Ezawa and M Leventhal 1975 J. Phys. B: At. Mol. Phys. 8 1824
1998 Phys. Educ. 33
A Bäcker et al 2002 Nonlinearity 15 1417
Norman E Booth et al 1999 Supercond. Sci. Technol. 12 538