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A revolutionary new direction in the field of superconductivity emerged recently with the synthesis of superconductors with strong inherent spin-orbit coupling of electrons, such as the half-Heusler compounds YPtBi or LuPdBi. Due to band inversion, the low-energy degrees of freedom are electrons at a three-dimensional quadratic band touching point with an effective spin 3/2, which allows for Cooper pairs with spins ranging from 0 to 3. I will illuminate some of the unconventional superconducting properties that arise from this band structure and attractive short-range interaction: (i) At strong coupling, the system features an s-wave superconducting quantum critical point with non-Fermi liquid scaling of fermions and several other unusual scaling properties. (ii) The system may further undergo a transition into a phase with complex tensor order, which is a superconducting state captured by a complex-valued matrix order parameter describing Cooper pairs having spin 2. Here the interplay of both tensorial and complex nature results in a rich and intriguing phenomenology. I will discuss the mean-field phase structure as a function of doping and temperature, and relate our finding to experiments in YPtBi. Further, the critical properties of this new paradigm for superconductivity will be addressed.

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Igor Boettcher
Seminar Room of the Institute of Physics II
Contact: Sebastian Diehl