Time-reversal symmetry breaking by a $(d+id)$ density-wave state in underdoped cuprate superconductors

TL;DR

This paper demonstrates that a small $d_{xy}$ component added to the $id_{x^2-y^2}$ density-wave state in underdoped cuprates breaks time-reversal symmetry, explaining the observed polar Kerr effect in the pseudogap phase.

Contribution

It introduces a modified density-wave state with a $d_{xy}$ component that accounts for time-reversal symmetry breaking in underdoped cuprates.

Findings

Breaking of symmetry between orbital currents due to $d_{xy}$ admixture.

Non-zero polar Kerr effect observed in pseudogap phase.

Theoretical explanation for experimental Kerr measurements.

Abstract

It was proposed that the $id_{x^2-y^2}$ density-wave state (DDW) may be responsible for the pseudogap behavior in the underdoped cuprates. Here we show that the admixture of a small $d_{xy}$ component to the DDW state breaks the symmetry between the counter-propagating orbital currents of the DDW state and, thus, violates the macroscopic time-reversal symmetry. This symmetry breaking results in a non-zero polar Kerr effect, which has recently been observed in the pseudogap phase.