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Exotic multi-gap structure in UPt$_3$ unveiled by the first-priniciples analysis

A heavy-fermion superconductor UPt$_3$ is a unique spin-triplet superconductor with multiple superconducting phases. Here we provide the first report on the first-principles analysis of the microscopic superconducting gap structure. We find that the promising gap structure is an unprecedented $E_{2u}$ state, which is completely different from the previous phenomenological $E_{2u}$ models. Our obtained $E_{2u}$ state has in-plane twofold vertical line nodes on small Fermi surfaces and point nodes with linear dispersion on a large Fermi surface. These peculiar features cannot be explained in the conventional spin $1/2$ representation, but is described by the group-theoretical representation of the Cooper pairs in the total angular momentum $j=5/2$ space. Our findings shed new light on the long-standing problems in the superconductivity of UPt$_3$