Spontaneous symmetry breaking has been a paradigm to describe the phase transitions in condensed matter physics. In addition to the continuous electromagnetic gauge symmetry, an unconventional superconductor can break discrete symmetries simultaneously, such as time reversal and lattice rotational symmetry. In this work we report a characteristic in-plane 2-fold behaviour of the resistive upper critical field and point-contact spectra on the superconducting semimetal PbTaSe2 with topological nodal-rings, despite its hexagonal lattice symmetry (or D_3h in bulk while C_3v on surface, to be precise). However, we do not observe any lattice rotational symmetry breaking signal from field-angle-dependent specific heat. It is worth noting that such surface-only electronic nematicity is in sharp contrast to the observation in the topological superconductor candidate, CuxBi2Se3, where the nematicity occurs in various bulk measurements. In combination with theory, superconducting nematicity is likely to emerge from the topological surface states of PbTaSe2, rather than the proximity effect. The issue of time reversal symmetry breaking is also addressed. Thus, our results on PbTaSe2 shed new light on possible routes to realize nematic superconductivity with nontrivial topology.
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