One-Dimensional Phonon State of 4He Films Adsorbed in Straight Nanopores

We have studied heat capacities of ⁴He adsorbed in straight nanopores 1.8, 2.2, and 2.8 nm in diameter. Heat capacities of the ⁴He fluid film on the solid layer at 0.08–0.4 K show power laws close to T in 1.8 nm pores, close to T ² in 2.8 nm pores, and a crossover from T to T ² with increasing temperature in 2.2 nm pores. These heat capacities are explained by a model assuming a phonon dispersion with continuous one-dimensional (1D) states in the axial direction and discrete energy levels in the azimuthal direction. By fitting experimental data to the model, the phonon velocity along the pore axis and the energy gap for propagation in the cross section are derived. At temperatures sufficiently lower than the energy gap, where the thermal wave length of phonons is much longer than the effective pore diameter, the ⁴He fluid films show a T-linear heat capacity of 1D phonons propagating only along the pore axis. At higher temperatures, a 1D-2D crossover of phonons occurs.