Phononic nodal points with quadratic dispersion and multifold degeneracy in the cubic compound Ta3Sn

Topological states with quadratic dispersion and multiple-fold band degeneracy have not only fundamentally updated our knowledge of the phases of matter but also become a major cutting-edge research direction in condensed matter physics. Note that the sixfold band degeneracy corresponds to the maximum degeneracy in phononic systems. Remarkably, in this work, based on first-principles calculations, we proposed an authentic material, ${\mathrm{Ta}}_{3}\mathrm{Sn}$, which hosts phononic nodal points with both quadratic dispersion and maximum band degeneracy, i.e., quadratic contact triple point, quadratic contact Dirac point and sixfold-degenerate point. Furthermore, the corresponding symmetry analysis with the help of the $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ model further deepens the understanding of the relative physics. Evident arc-shaped surface states, originating from the projected phononic nodal points, can strongly benefit the experimental detection. It is hoped that the rich types of phonon points with quadratic dispersion and multiple-fold band degeneracy as well as the surface states can be confirmed in experiments soon.