Time-reversal symmetry breaking in microscopic single-crystal Sr$_2$RuO$_4$ devices

Abstract: Time-reversal symmetry breaking superconductivity is a quintessential unconventional quantum state. In Josephson junctions, time-reversal symmetry breaking manifests itself in the supercurrent interference pattern as the invariance of the critical current under the reversal of both transport and magnetic field directions, i.e., $I_\text{c+}(H) = I_\text{c-}(-H)$. So far, such systems have been realized in devices where superconductivity is injected into a deliberately constructed weak link medium, usually carefully tuned by external magnetic fields and electrostatic gating. In this work, we report time-reversal symmetry breaking in spontaneously emerging Josephson junctions without intentionally constructed weak links. This is realized in ultra-pure single-crystal microstructures of Sr$2$RuO$_4$, an unconventional superconductor with a multi-component order parameter. Here, the Josephson effect emerges intrinsically at the superconducting domain wall, where the degenerate states partially overlap. In addition to violating $I\text{c+}(H) = I_\text{c-}(-H)$, we find a rich variety of exotic transport phenomena, including a supercurrent diode effect present in the entire interference pattern, two-channel critical current oscillations with a period that deviates from $\Phi_0$, fractional Shapiro steps, and current-switchable bistable states with highly asymmetric critical currents. Our findings provide direct evidence of TRSB in unstrained Sr$_2$RuO$_4$ and reveal the potential of domain wall Josephson junctions, which can emerge in any superconductor where the pairing symmetry is described by a multi-component order parameter.