| We examine several aspects of Berry's phase (BP) in the context of solid state physics. We first present several simple models that lead to BP effects, and then introduce a generalized Kronig-Penney potential that yields a non-trivial BP when inversion symmetry is broken. Next, we present an alternative derivation of the BP-modified Bloch electron semiclassical equations of motion (EOM) using a Poisson bracket formalism. The presence of a non-zero Berry curvature in the EOM is investigated, in particular for a spinless gas of Bloch electrons. Next, the concepts of effective mass and cyclotron mass are reconsidered in light of the presence of a BP. Finally we examine the feasibility of creating a simple 2D model to study BP effects; an asymmetric hexagonal lattice is studied and suggestions are made for further research. |
