  We revisit the problem of adsorption of a single He-4 layer on graphene,
focusing on the commensurate C1/3 crystalline phase, specifically on whether it
may possess a nonzero superfluid response, and on the existence of superfluid
phases, either (metastable) liquid or vacancy-doped crystalline. We make use of
canonical Quantum Monte Carlo simulations at zero and finite temperature, based
on a realistic microscopic model of the system. Our results confirm the absence
of any superfluid response in the commensurate crystal, and that no
thermodynamically stable uniform phase exists at lower coverage. No evidence of
a possibly long-lived, metastable superfluid phase at C1/3 coverage is found.
Altogether, the results of ground-state projection methods and
finite-temperature simulations are entirely consistent.
