Layered ⁴He and ³He-⁴He mixture between two surfaces

We examine the static, dynamic, and low-temperature thermodynamic properties of liquid ⁴He and the low-concentration limit of ³He-⁴He mixtures confined between two walls. A generalized variational Jastrow-Feenberg ansatz with time-dependent correlations is used for describing the excited states; the present variant accounts for up to three-phonon effects. We show that with decreasing wall separation the quantum liquid goes though a sequence of confined layering transitions familiar from classical fluids. These transitions are due to the geometry and have potentially observable effects in the roton excitations near wave vector k ∼ 2 Å^-1. In high-density liquid ⁴He, ³He impurities assemble in the middle of the gap forming a nearly perfect two-dimensional Fermi-liquid layer.