Quantum prewetting transitions in liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$

Multilayer ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ film growth on weak-binding alkali substrates is investigated with a nonlocal density functional theory. Although ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ wets all substrates down to zero temperature, prewetting transitions are predicted to occur on Cs, Rb, and K. Emphasis is put on the role played by the Fermi statistics. Continuous wetting is recovered with increasing strength of substrate potential. The heat capacity and the magnetization of the films exhibits steps associated with the occupation of two-dimensional Fermi disks.