Spontaneous rotational symmetry breaking in KTaO$_3$ interface superconductor

Strongly correlated electrons can display intriguing spontaneous broken symmetries in the ground state. Understanding these symmetry breaking states is fundamental to elucidating the various exotic quantum phases in condensed matter physics. Here, we report a pronounced spontaneous rotational symmetry breaking of the superconductivity at the interface of YAlO$_3$/KTaO$_3$ with superconducting transition temperature of 1.86 K and the thickness of superconducting layer as thin as 4.5 nm. Both the magnetoresistance and upper critical field under an applied in-plane magnetic field manifest striking asymmetric twofold oscillations deep inside the superconducting state, whereas the anisotropy vanishes in the normal state, demonstrating that it is an intrinsic property of the superconducting phase. We attribute this behavior to the mixed-parity superconducting state with a mixture of $s$-wave and $p$-wave pairing components induced by strong electron correlation and spin-orbit coupling inherent to the inversion symmetry breaking at the interface of YAlO$_3$/KTaO$_3$. Our work demonstrates the unconventional character of the pairing interaction in the KTaO$_3$ interface superconductor and sheds new light on the pairing mechanism of unconventional superconductivity with inversion symmetry breaking.