  The Nambu-Goldstone (NG) modes in a nonrelativistic system can be classified
into two types from their characteristic features: being of either an odd (type
I) or an even (type II) power energy-momentum dispersion. Conventionally, the
type-II NG modes may universally arise from spontaneous breaking of
noncommutative symmetry pairs. Here, we predict a novel type of quadratically
dispersed NG modes that emerges in mixed $s$ and $p$ band Bose superfluids in
an optical lattice and, unlike the conventional type-II NG modes, cannot be
solely interpreted with the celebrated symmetry-based argument. Instead, we
show that the existence of such modes has a profound connection to the
topological transition on projective complex order-parameter space. The
detection scheme is also proposed. Our Letter reveals a new universal mechanism
for emergence of type-II NG modes, which bridges intrinsically the Landau
symmetry-breaking and topological theories.
