Topology and symmetry in multiple superconducting phases of U_1-xTh_xBe₁₃

We theoretically investigate the topological aspect of the multiple superconducting phases in the heavy-fermion compound U_1-xTh_xBe₁₃. The gap symmetry and the multiple phase transitions in this superconductor (SC) have been longstanding unsolved issues. Recent measurements with high-quality single crystals suggests the odd-parity E_u state as a possible scenario [Y. Shimizu et al., arXiv:1709.00128]. In this scenario, the multiple superconducting phases are composed of uniaxial nematic, biaxial nematic, and nonunitary cyclic phases, corresponding to the DIII topological SC, Dirac SC, and Weyl SC, respectively. In this talk, we show that all the phases are accompanied by different types of topological quasiparticles: surface helical Majorana fermions in nematic phases and itinerant Majorana fermions in the cyclic phase. In particular, in the cyclic phase, surface states evoluve from a Majorana cone to Majorana arcs under rotation of surface orientation. The cone is protected solely by an accidental spin rotation symmetry and fragile against spin-orbit coupling, while the arcs are protected by the first Chern number and one-dimensional winding number. Lastly, we discuss how topological quasiparticles can be captured from tunneling conductance spectra in U_1-xTh_xBe₁₃.