Motivated by the relation between the Dirac/Schrodinger hamiltonians, the square root topological phase (SRTI) has been discussed in several cases recently. Here the roles of symmetries in SRTI are focused and discussed with several examples in our recent paper, “Square-root topological phase with time-reversal and particle-hole symmetry” by Tsuneya Yoshida, Tomonari Mizoguchi, Yoshihito Kuno, and Yasuhiro Hatsugai, Phys. Rev. B 103, 235130 – Published 14 June 2021. See also arXiv:2103.11305.