Borophane as substrate for adsorption of 4He: A journey across dimensionality

In search of substrates for the adsorption of He atoms allowing for novel quantum phases in restricted geometry, we study the case of borophane, a hydrogenated compound of borophene. We consider two allotropes of borophane, 𝛼′−4⁢𝐻 and rect-2⁢𝐻. With a suitable density functional theory we characterize the adsorption potential of a He atom on such crystalline substrates, finding its corrugation, the preferential adsorption sites, and the energy barrier between sites. In the case of 𝛼′−4⁢𝐻 borophane the adsorption potential has some similarity to that of graphite but with much larger energy barriers between adsorption sites, so that the first adsorbed layer of 4He should be localized in a registered triangular crystal similar to the √3×√3⁢R⁢30∘ phase of graphite. Rect-2⁢𝐻 borophane appears more interesting due to the presence of ridges in the adsorption potential with modest energy barriers in one direction of the basal plane and a much higher barrier in the orthogonal direction, thus forming channels for motion of the adsorbed atoms. Using path integral Monte Carlo (PIMC) simulations, we find that in the first adsorbed layer the 4He atoms are rather delocalized along a channel with no exchanges between channels. This strong anisotropy is present also in the first few additional adsorption layers with the presence of ordered and disordered regions. In the second, fourth, and fifth layers we find superfluidity on the length scale of the simulated systems. In the second layer, the superfluidity is one-dimensional (1D) along the grooves. In a narrow low-coverage region of the fourth layer we observe an intriguing state with one unidirectional structure across the grooves which supports a tiny superfluid signal. In the fifth layer we find a two-dimensional (2D) superfluid, with a crossover from strongly anisotropic at low coverage to isotropic at layer completion. Starting from the sixth layer, the adsorbed 4He film evolves towards a three-dimensional (3D) superfluid. Our main prediction is that adsorption of 4He on rect-2⁢𝐻 borophane will allow us to probe 1D superfluidity in the second and possibly the fourth layers, the evolution from a 2D anisotropic superfluid to an isotropic one in the fifth layer, and, eventually, the onset of 3D superfluidity for higher coverages.