Theory of Berry Phases in the Cuprate Pseudogap Phase

The geometric Berry phase is part of the phase accumulated by a quantum system undergoing adiabatic evolution around a closed loop in parameter space \footnote{Berry, M.~V. Quantal Phase Factors Accompanying Adiabatic Changes. \emph{Proceedings of the Royal Society of London.~A.~Mathematical and Physical Sciences} \textbf{392}, 45-57 (1984).}. Recently, data from quantum oscillations experiments, in which Berry's phase is accessible via its contribution to the phase offset, were used to determine Berry's phase in certain electron- and hole-doped cuprate superconductors in high-magnetic-field regimes \footnote{Doiron-Leyraud, N.,~et al. Berry Phase in Cuprate Superconductors. \emph{arXiv preprint arXiv:1407.1388} (2014).}. The data reveal a trivial Berry phase of $0$ in the hole-doped materials examined, while a phase of $\sim 1.4\pi$ was found in the electron-doped material. These findings set new, significant constraints on the possible descrpitions of the pseudogap phase of the cuprates. This is used as a test of validity for some proposed models of cuprate superconductors. Berry's phase is computed within the framework of these models in high-field regimes and compared to the experimental findings.