Vacancy-induced supersolidity of the second He4 layer on a biphenylene carbon sheet

Abstract

We have performed path-integral Monte Carlo calculations to investigate various quantum phases of $^{4}\mathrm{He}$ layers adsorbed on a biphenylene sheet, a recently synthesized two-dimensional network of carbon atoms. Three different commensurate solid phases are identified in the first $^{4}\mathrm{He}$ layer, which is found to be completed to a ${\mathrm{C}}_{2/2}$ commensurate solid at an areal density of 0.119 ${\AA{}}^{\ensuremath{-}2}$. We have also found that the commensurate structure of the completed first layer allows second-layer $^{4}\mathrm{He}$ atoms to constitute a stable commensurate ${\mathrm{C}}_{2/3}$ structure at a total helium coverage of 0.199 ${\AA{}}^{\ensuremath{-}2}$. Furthermore, this second-layer commensurate structure is observed to be stable even with the formation of vacancies that are mobile to instigate the superfluid response at low temperatures. This unequivocally shows that vacancy-induced supersolidity can be realized in the second $^{4}\mathrm{He}$ layer on biphenylene.