^{1}and Yongkyung Kwon

^{1,a)}

### Abstract

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.

Y. Kwon thanks Professor D. M. Ceperley for helpful discussion. This work was supported by the Basic Science Research Program (2012R1A1A 2012006887) and the WCU Program (R31-2008-000-10057-0) through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology.

I. INTRODUCTION

II. METHODOLOGY

III. PIMC RESULTS

IV. CONCLUSION

## Figures

Radial density distributions of the total 32 helium atoms adsorbed on C_{20} at *T* = 0.31 K. The black solid line represents the density distribution of the pure ^{4}He layer and the red solid line corresponds to the total density distribution of the mixed layer with 28 ^{4}He atoms and 4 ^{3}He atoms. The red dotted line and the red dashed one represent the ^{4}He density distribution and the ^{3}He distribution of the mixed layer, respectively. *R* is the distance from the C_{20} molecular center.

Radial density distributions of the total 32 helium atoms adsorbed on C_{20} at *T* = 0.31 K. The black solid line represents the density distribution of the pure ^{4}He layer and the red solid line corresponds to the total density distribution of the mixed layer with 28 ^{4}He atoms and 4 ^{3}He atoms. The red dotted line and the red dashed one represent the ^{4}He density distribution and the ^{3}He distribution of the mixed layer, respectively. *R* is the distance from the C_{20} molecular center.

Angular pair correlation functions of total 32 helium atoms on C_{20} at *T* = 0.31 K. Here the number of ^{3}He atoms varies while the total number of ^{3}He and ^{4}He atoms is fixed to 32. γ represents the angle between the position vectors of two helium atoms on the C_{20} molecular surface.

Angular pair correlation functions of total 32 helium atoms on C_{20} at *T* = 0.31 K. Here the number of ^{3}He atoms varies while the total number of ^{3}He and ^{4}He atoms is fixed to 32. γ represents the angle between the position vectors of two helium atoms on the C_{20} molecular surface.

Contour plots of angular density distributions of the ^{3}He–^{4}He mixed layer on C_{20} for (a) *N* _{ tot } = 14, (b) *N* _{ tot } = 24, (c) *N* _{ tot } = 30, and (d) *N* _{ tot } = 32, where the number of ^{3}He atoms is fixed to 4. The horizontal axis corresponds to the azimuthal angle ϕ and the vertical one to the cosine of the polar angle θ. The characters *C* and *P*’s represent the angular positions of the carbon atoms and those of the pentagon centers, respectively. All contour plots are in the same color scale denoted by the color table in the upper right hand corner.

Contour plots of angular density distributions of the ^{3}He–^{4}He mixed layer on C_{20} for (a) *N* _{ tot } = 14, (b) *N* _{ tot } = 24, (c) *N* _{ tot } = 30, and (d) *N* _{ tot } = 32, where the number of ^{3}He atoms is fixed to 4. The horizontal axis corresponds to the azimuthal angle ϕ and the vertical one to the cosine of the polar angle θ. The characters *C* and *P*’s represent the angular positions of the carbon atoms and those of the pentagon centers, respectively. All contour plots are in the same color scale denoted by the color table in the upper right hand corner.

Contour plots of the ^{3}He angular distributions of the mixed layer with (a) *N* _{ tot } = 24 and (b) *N* _{ tot } = 30, where the number of ^{3}He atoms is fixed to 4. The horizontal axis corresponds to the azimuthal angle ϕ and the vertical one to the cosine of the polar angle θ. The characters *C* and *P*’s represent the angular positions of the carbon atoms and those of the pentagon centers, respectively. Different color scales of two contour plots are represented by the color tables on their right hand sides.

Contour plots of the ^{3}He angular distributions of the mixed layer with (a) *N* _{ tot } = 24 and (b) *N* _{ tot } = 30, where the number of ^{3}He atoms is fixed to 4. The horizontal axis corresponds to the azimuthal angle ϕ and the vertical one to the cosine of the polar angle θ. The characters *C* and *P*’s represent the angular positions of the carbon atoms and those of the pentagon centers, respectively. Different color scales of two contour plots are represented by the color tables on their right hand sides.

^{4}He superfluid fractions of the mixed helium layer on a C_{20} molecule as a function of the system size, , at *T* = 0.31 K. The PIMC results for the pure ^{4}He monolayer are from Ref. ^{ 2 } .

^{4}He superfluid fractions of the mixed helium layer on a C_{20} molecule as a function of the system size, , at *T* = 0.31 K. The PIMC results for the pure ^{4}He monolayer are from Ref. ^{ 2 } .

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