Determining the superconducting order parameter of UPt$_3$ using scanning tunneling microscopy

Abstract: Superconductivity, a state in which electrical currents can flow without resistance, occurs because of pairing of electrons into quasiparticles with integer spin $S$. In practically all known superconducting materials, these pairs form a singlet with $S=0$. Finding a material that has triplet pairing, $S=1$, would have profound fundamental and technological implications. UPt$_3$ has been a key candidate material for spin-triplet superconductivity. Because of a lack of direct evidence for the pairing symmetry, the nature of the superconducting pairing remains under debate. Here, we use ultra-low temperature scanning tunneling microscopy to resolve this question. Our data reveals a zero-bias Andreev bound state within the gap for a surface normal to the $c$-axis of UPt$_3$. The superconducting origin of the features is confirmed through vortex imaging. For triplet pairing, such an Andreev state is fragile against Rashba spin-splitting, whereas for singlet pairing it remains robust, classifying UPt$_3$ as a spin-singlet superconductor with a chiral order parameter.