  Monolayers of hexagonal boron nitride (h-BN) can in principle be identified
by a Raman signature, consisting of an upshift in the frequency of the E2g
vibrational mode with respect to the bulk value, but the origin of this shift
(intrinsic or support-induced) is still debated. Herein we use density
functional theory calculations to investigate whether there is an intrinsic
Raman shift in the h-BN monolayer in comparison with the bulk. There is
universal agreement among all tested functionals in predicting the magnitude of
the frequency shift upon a variation in the in-plane cell parameter. It is
clear that a small in-plane contraction can explain the Raman peak upshift from
bulk to monolayer. However, we show that the larger in-plane parameter in the
bulk (compared to the monolayer) results from non-local correlation effects,
which cannot be accounted for by local functionals or those with empirical
dispersion corrections. Using a non-local-correlation functional, we then
investigate the effect of finite temperatures on the Raman signature. We
demonstrate that bulk h-BN thermally expands in the direction perpendicular to
the layers, while the intralayer distances slightly contract, in agreement with
observed experimental behavior. Interestingly, the difference in in-plane cell
parameter between bulk and monolayer decreases with temperature, and becomes
very small at room temperature. We conclude that the different thermal
expansion of bulk and monolayer partially "erases" the intrinsic Raman
signature, accounting for its small magnitude in recent experiments on
suspended samples.

Materials Science