Vacancy-induced supersolidity of the second He 4 layer on a biphenylene carbon sheet

We have performed path-integral Monte Carlo calculations to investigate various quantum phases of He4 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 He4 layer, which is found to be completed to a C2/2 commensurate solid at an areal density of 0.119 Å-2. We have also found that the commensurate structure of the completed first layer allows second-layer He4 atoms to constitute a stable commensurate C2/3 structure at a total helium coverage of 0.199 Å-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 He4 layer on biphenylene.