  Superfluid $^4$He (He-II) is a widely studied model system for exploring
finite-size effects in strongly confined geometries. Here, we study He-II
confined in mm-scale channels of 25 and 50 nm height at high pressures using a
nanofluidic Helmholtz resonator. We find that the superfluid density is
measurably suppressed in the confined geometry from the transition temperature
down to 0.6 K. Importantly, this suppression can be accounted for by roton-like
thermal excitation with an energy gap of 5 K. We show that the surface-bound
excitations lead to the previously unexplained lack of finite-size scaling of
suppression of the superfluid density.
