Probing time reversal symmetry breaking topological superconductivity in twisted double layer copper oxides with polar Kerr effect

TL;DR

This paper predicts a large polar Kerr effect as a signature of time reversal symmetry breaking topological superconductivity in twisted bilayer cuprates, providing a measurable way to identify topological phases.

Contribution

It introduces a model predicting a significant Kerr angle in twisted cuprate bilayers, enabling experimental detection of topological superconducting phases via optical measurements.

Findings

Kerr angle predicted to be 10-100 μrad, much larger than in Sr₂RuO₄.

Optical Hall conductivity can distinguish topological from trivial phases.

Large intrinsic Hall response serves as a signature of time reversal symmetry breaking.

Abstract

Recent theoretical work predicted emergence of chiral topological superconducting phase with spontaneously broken time reversal symmetry in a twisted bilayer composed of two high-$T_c$ cuprate monolayers, such as Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. Here we identify large intrinsic Hall response that can be probed through the polar Kerr effect measurement as a convenient signature of the $\mathcal{T}$-broken phase. Our modelling predicts the Kerr angle $\theta_K$ to be in the range of 10-100 $\mu$rad, which is a factor of $10^3-10^4$ times larger than what is expected for the leading chiral supercondutor candidate Sr$_2$RuO$_4$. In addition we show that the optical Hall conductivity $\sigma_H(\omega)$ can be used to distinguish between the topological $d_{x^2-y^2}\pm id_{xy}$ phase and the $d_{x^2-y^2}\pm is$ phase which is also expected to be present in the phase diagram but is topologically trivial.