Does 45-degree twisted $\mathrm{Bi2Sr2CaCu2O8}+x$ break time-reversal symmetry
In plain words
Stacking two thin flakes of the cuprate Bi2Sr2CaCu2O8+x rotated by 45 degrees is predicted to create a superconducting state whose pairs circulate in one sense, breaking time-reversal symmetry; Josephson experiments by different groups disagree.
Precise statement
For c-axis Josephson junctions between Bi2Sr2CaCu2O8+x flakes twisted by $\theta$ near 45 degrees, pure $d_{(x^2-y^2)}$ pairing makes the first-order Josephson coupling vanish, and second-order coupling is predicted to stabilize a $d + i d$ state with spontaneous time-reversal breaking (Can et al., Nature Physics 2021). Determine whether the critical current $I_c(\theta)$ is suppressed at 45 degrees as pure d-wave requires, and whether half-integer Shapiro steps, a Josephson diode effect and spontaneous magnetization near 45 degrees arise from time-reversal breaking rather than from interface disorder or an s-wave admixture. An answer is a reproducible $I_c(\theta)$ on junctions with characterized interfaces plus a direct probe of time-reversal breaking at 45 degrees.
What would settle it
Independent groups measuring $I_c(\theta)$ on atomically sharp junctions, with local magnetometry or polar Kerr detection (or exclusion) of spontaneous time-reversal breaking at $\theta = 45\,\mathrm{degrees}$.
Status in the literature
Zhao et al. (Science 2023) reported a Josephson diode effect and half-integer Shapiro steps near 45 degrees, while Zhu et al. (PRX 2021, PRB 2023) found Josephson tunneling persisting at 45 degrees across the doping dome and attributed it to s-wave pairing.