  Square-root topological phases have been discussed mainly for systems with
chiral symmetry. In this paper, we analyze the topology of the squared
Hamiltonian for systems preserving the time-reversal and particle-hole
symmetry. Our analysis elucidates that two-dimensional systems of class CII
host helical edge states due to the nontrivial topology of the squared
Hamiltonian in contrast to the absence of ordinary topological phases. The
emergence of the helical edge modes is demonstrated by analyzing a toy model.
We also show the emergence of surface states induced by the non-trivial
topology of the squared Hamiltonian in three dimensions.
