Probing Time Reversal Symmetry Breaking Topological Superconductivity in Twisted Double Layer Copper Oxides with Polar Kerr Effect

Recent theoretical work predicted the emergence of a 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+δ}. Here, we identify a large intrinsic Hall response that can be probed through the polar Kerr effect measurement as a convenient signature of the T-broken phase. Our modeling predicts the Kerr angle θ_{K} to be in the range of 10-100  μrad, which is a factor of 10^{3} to 10^{4} times larger than what is expected for the leading chiral superconductor candidate Sr_{2}RuO_{4}. In addition, we show that the optical Hall conductivity σ_{H}(ω) can be used to distinguish between the topological d_{x^{2}-y^{2}}±id_{xy} phase and the d_{x^{2}-y^{2}}±is phase, which is also expected to be present in the phase diagram but is topologically trivial.