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Among the family of odd-parity topological superconductors derived fromBi$_2$Se$_3$, Cu$_x$(PbSe)$_5$(Bi$_2$Se$_3$)$_6$ has been elucidated to havegap nodes. Although the nodal gap structure has been established byspecific-heat and thermal-conductivity measurements, there has been no directobservation of the superconducting gap of CPSBS using scanning tunnellingspectroscopy (STS). Here we report the first STS experiments on CPSBS down to0.35 K, which found that the vortices generated by out-of-plane magnetic fieldshave an elliptical shape, reflecting the anisotropic gap structure. Theorientation of the gap minima is found to be aligned with the bulk directionwhen the surface lattice image shows twofold symmetry, but, surprisingly, it isrotated by 30$^{\circ}$ when twofold symmetry is absent. In addition, thesuperconducting gap spectra in zero magnetic field suggest that the gap nodesare most likely lifted. We argue that only an emergent symmetry at the surface,allowing for a linear superposition of gap functions with different symmetries,can lead to the rotation of the gap nodes. The absence of inversion symmetry atthe surface additionally lifts the nodes. This result establishes the subtlebut crucial role of crystalline symmetry in topological superconductivity.

Rotation of gap nodes in the topological superconductor Cu$_x$(PbSe)$_5$(Bi$_2$Se$_3$)$_6$