Berry’s phase originated from the broken time-reversal symmetry: Theory and application to anyon superconductivity

We prove that Berry's phase arises when the (phenomenological) Hamiltonian for the fast variable in the system violates time-reversal symmetry. Our derivation demonstrates the existence of a current-type Berry's phase based on the time-reversal-odd part of the Hamiltonian, in contrast to the usual monopole-type Berry's phase where the degeneracy of states acts 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 model of the high-Tc superconductors.