Berry Phase in Cuprate Superconductors

TL;DR

This paper investigates the Berry phase in cuprate superconductors using quantum oscillation data, revealing trivial phases in hole-doped and non-zero phases in electron-doped materials, which impacts understanding of their normal states.

Contribution

It provides the first systematic analysis of Berry phases in various cuprates, highlighting contrasting behaviors between hole- and electron-doped compounds.

Findings

Hole-doped cuprates show trivial Berry phase of 0 mod 2π.

Electron-doped Nd₂₋ₓCeₓCuO₄ exhibits a significant non-zero Berry phase.

Results constrain theories of the high-field normal state in cuprates.

Abstract

Geometrical Berry phase is recognized as having profound implications for the properties of electronic systems. Over the last decade, Berry phase has been essential to our understanding of new materials, including graphene and topological insulators. The Berry phase can be accessed via its contribution to the phase mismatch in quantum oscillation experiments, where electrons accumulate a phase as they traverse closed cyclotron orbits in momentum space. The high-temperature cuprate superconductors are a class of materials where the Berry phase is thus far unknown despite the large body of existing quantum oscillations data. In this report we present a systematic Berry phase analysis of Shubnikov - de Haas measurements on the hole-doped cuprates YBa$_2$Cu$_3$O$_{y}$, YBa$_2$Cu$_4$O$_8$, HgBa$_2$CuO$_{4 + \delta}$, and the electron-doped cuprate Nd$_{2-x}$Ce$_x$CuO$_4$. For the hole-doped materials, a trivial Berry phase of 0 mod $2\pi$ is systematically observed whereas the electron-doped Nd$_{2-x}$Ce$_x$CuO$_4$ exhibits a significant non-zero Berry phase. These observations set constraints on the nature of the high-field normal state of the cuprates and points towards contrasting behaviour between hole-doped and electron-doped materials. We discuss this difference in light of recent developments related to charge density-wave and broken time-reversal symmetry states.