Berry's phase realized in solids with broken time-reversal symmetry: Application to anyon superconductivity

Abstract

We show that the Berry's phase arises when the phenomenological Hamiltonian for the fast variable in the system consisting of fast and slow variables violates the time-reversal symmetry. This type of Berry's phase is distinguished from the usual monopole-type Berry's phase which is created by the degeneracy of states acting as a topological singularity in the parameter space. Effects of this phase on the transverse phonon modes of solids are studied and the results are applied to the anyon superconductors. Using the semion model for the highz. sbnd; T c superconductors, we predict that, under specified conditions, degenerate TO phonons are split in energy by ≲0.001 meV. Rotation of the polarization of the TA and TO phonons is also predicted.