Possible Dimensional Crossover to 1D of $$^3$$ 3 He Fluid in Nanochannels Observed in Susceptibilities

Abstract

Dimensional crossover to the one-dimensional (1D) state from higher dimensions has been studied for dilute \(^3\)He fluid adsorbed in 2.4 nm \(^4\)He-preplated nanochannels, by susceptibility measurements down to 70 mK using 4.29 MHz nuclear magnetic resonance. In nanochannels, since energy states of \(^3\)He motion perpendicular to the channel axis are discrete, a genuine 1D \(^3\)He fluid is expected when the Fermi energy is less than the first excitation \(\Delta _{01}\) for azimuthal motion. The susceptibilities \(\chi \) above 0.3 K show the Curie-law susceptibilities independent of the \(^3\)He density, which are characteristic of nondegenerate fluid in higher dimensions. With decreasing the temperature, a significant reduction of \(\chi T\) was observed from about 0.3 K for all \(^3\)He densities. It is considered to be due to the dimensional crossover below \(\Delta _{01}\sim 0.5\) K to the 1D \(^3\)He state in the semi-degenerate regime above the Fermi temperature. In the 1D state at lower temperatures, T-independent \(\chi \) were observed for \(^3\)He of 0.019 layers below 0.1 K. It suggests that the 1D \(^3\)He fluid enters the quantum degenerate regime.