Wave-packet dynamics of Bloch electrons—Role of Berry phase

Motivated by a recent proposal on the possibility of observing a monopole in the band structure, and by an increasing interest in the role of Berry phase in spintronics, we reconsidered the problem of adiabatic motion of a wave packet of Bloch functions, under a perturbation varying slowly and incommensurately to the lattice structure. We showed, using only the fundamental principles of quantum mechanics, that the effective wave-packet dynamics of Bloch electrons is conveniently described by a set of equations of motion (EOM) in which a non-Abelian Berry phase associated with the internal degree of freedom appears.