  Superconductivity mediated by phonons is typically conventional, exhibiting a
momentum-independent s-wave pairing function, due to the isotropic interactions
between electrons and phonons along different crystalline directions. Here, by
performing inelastic neutron scattering measurements on a superconducting
single crystal of Sr0.1Bi2Se3, a prime candidate for realizing topological
superconductivity by doping the topological insulator Bi2Se3, we find that
there exist highly anisotropic phonons, with the linewidths of the acoustic
phonons increasing substantially at long wavelengths, but only for those along
the [001] direction. This observation indicates a large and singular
electron-phonon coupling at small momenta, which we propose to give rise to the
exotic p-wave nematic superconducting pairing in the MxBi2Se3 (M = Cu, Sr, Nb)
superconductor family. Therefore, we show these superconductors to be example
systems where electron-phonon interaction can induce more exotic
superconducting pairing than the s-wave, consistent with the topological
superconductivity.
