Effects of 3He impurities on the superfluid response of the 4He monolayer on a C20 molecule

The path-integral Monte Carlo calculations have been performed to investigate the effects of (3)He impurities on structural and superfluid properties of the (4)He monolayer on a single C(20) molecule. According to our previous study, the helium monolayer exhibits different quantum states for different numbers of (4)He adatoms and is completed to form a commensurate solid where nanoscale supersolidity can be realized through the activation of mobile vacancy states. We first observe that different structures for different numbers of helium atoms are mostly preserved with the replacement of a few (4)He atoms with the same number of (3)He atoms, whether the helium layer is a fluid or a solid. However, the substitution of (3)He impurities is found to have different effects on the superfluid response of the helium layer, depending on its quantum state. For a partially-filled fluid layer the superfluid fraction decreases monotonically with the increasing (3)He concentration, which can be understood in terms of the suppression of exchange couplings among (4)He atoms due to the presence of (3)He impurities. On the other hand, the substitution of a few (3)He impurity atoms may increase the superfluid fraction of a near-complete monolayer that is in a crystalline solid state. The enhancement of superfluidity in a solid layer is interpreted to be due to interstitial and vacancy defects promoted by larger quantum fluctuations of lighter (3)He atoms. This provides strong evidence that the (4)He monolayer on C(20) shows the vacancy-based supersolidity near its completion.