Unconventional superconductivity in strongly correlated systems marked by non-s-wave pairing is an important problem to explore in condensed matter physics. The newly discovered heavy fermion superconductor UTe₂ is believed to be a non-s-wave, spin-triplet superconductor based primarily on the observations of the large upper critical field which greatly exceeds the Pauli limit, the reentrance of superconductivity seen at high magnetic field, and a small drop of Knight shift across the superconducting transition temperature. However, direct evidence for UTe₂ being a spin-triplet superconductor is lacking, at least in low applied magnetic fields. In this talk I will first give a brief introduction of the concept of unconventional superconductivity and show that Josephson-effect-based phase-sensitive experiment is an effective tool to probe the symmetry of the superconducting order parameter. I will then present the results on the selection rule of the Josephson effect we observed recently in planar tunnel junctions of s-wave superconductor In and UTe₂ and discuss their implications on the pairing symmetry of this novel superconducting material.

 This work done in collaboration with Zixuan Li and Nathan McKee, Pennsylvania State University (PSU), Camilla M. Moir, Eric Lee-Wong, and M. Brian Maple, University of California San Diego (UCSD), and Ryan E. Baumbach, National High Magnetic Field Laboratory and Department of Physics, Florida State University (FSU), supported at Penn State by NSF, at UCSD by DOE and NSF, and at FSU also by NSF.