Fermi pockets and quantum oscillations of the Hall coefficient in high temperature superconductors

TL;DR

This paper explains quantum oscillation experiments in high-temperature superconductors by proposing a hidden $d$-density wave order that reconstructs the Fermi surface, revealing electron and hole pockets with specific symmetry-breaking properties.

Contribution

The paper introduces a theoretical model involving a $d$-density wave order to account for Fermi surface reconstruction and quantum oscillations observed in high-temperature superconductors.

Findings

Fermi surface consists of electron and hole pockets with reconstructed topology.

Oscillation frequencies depend on the commensurability of the order with the lattice.

Oscillation amplitudes are influenced by charge carrier mobilities.

Abstract

Recent quantum oscillation measurements in high temperature superconductors in high magnetic fields and low temperatures have ushered in a new era. These experiments explore the normal state from which superconductivity arises and provide evidence of a reconstructed Fermi surface consisting of electron and hole pockets in a regime in which such a possibility was previously considered to be remote. More specifically, the Hall coefficient has been found to oscillate according to the Onsager quantization condition, involving only fundamental constants and the areas of the pockets, but with a sign that is negative. Here we explain the observations with the theory that the alleged normal state exhibits a hidden order, the $d$-density wave, which breaks symmetries signifying time reversal, translation by a lattice spacing, and a rotation by an angle $\pi/2$, while the product of any two symmetry operations is preserved. The success of our analysis underscores the importance of spontaneous breaking of symmetries, Fermi surface reconstruction, and conventional quasiparticles. We primarily focus on the version of the order that is commensurate with the underlying crystalline lattice, but also touch upon the consequences if the order were to incommensurate. It is shown that while commensurate order results in two independent oscillation frequencies as a function of the inverse of the applied magnetic field, incommensurate order leads to three independent frequencies. The oscillation amplitudes, however, are determined by the mobilities of the charge carriers comprising the Fermi pockets.