Quantized Vortices in Mixed ${}_{}{}^3{}_{}{}^{}He-{}_{}{}^4{}_{}{}^{}He$ Drops

Using density functional theory, we investigate the structure of mixed ${}^3{\mathrm{He}}_{N_3}{-}^4{\mathrm{He}}_{N_4}$ droplets with an embedded impurity (Xe atom or HCN molecule) which pins a quantized vortex line. We find that the $\mathrm{dopant}+\mathrm{vortex}{+}^4{\mathrm{He}}_{N_4}$ complex, which in a previous work [F. Dalfovo et al., Phys. Rev. Lett. 85, 1028 (2000)] was found to be energetically stable below a critical size $N_{\mathrm{cr}}$, is robust against the addition of ${}^3\mathrm{He}$. While ${}^3\mathrm{He}$ atoms are distributed along the vortex line and on the surface of the ${}^4\mathrm{He}$ drop, the impurity is mostly coated by ${}^4\mathrm{He}$ atoms. Results for $N_4=500\mathrm{}$ and a number of ${}^3\mathrm{He}$ atoms ranging from 0 to 100 are presented, and the binding energy of the dopant to the vortex line is determined.