Pairing symmetries and Majorana surface states of multiple superconducting phases in UTe2

We discuss a possible scenario of multiple superconducting phases under applied pressure in the putative spin-triplet superconductor UTe2. Since the coexistence of ferromagnetic (FM) and antiferromagnetic (AFM) spin fluctuations with Ising-type anisotropy is supported by various experimental studies such as NMR and neutron scattering measurements, it is expected that the interplay between these spin fluctuations plays a crucial role in the emergence of the multiple superconducting phases. Motivated by this observation, we examine spin-fluctuation-mediated pairing mechanisms, analyzing the linearized Eliashberg equations for an effective model of f -electron bands. It is found that the growth of the AFM fluctuation due to applied pressure give rise to the transition between spin-triplet odd-parity pairing states with different symmetries. We, furthermore, discuss Majorana surface states which are expected for the odd-parity pairing states of UTe2. According to the recent dHvA and quantum oscillation measurements, it is strongly suggested that the Fermi surfaces of UTe2 are quasi-two-dimensional, which implies that topological superconductivity protected by time-reversal symmetry is not realized. However, even in this case, Majorana surface states protected by crystalline symmetry are still possible. We present a detection scheme for these Majorana surface states with the use of magnetic probes.