Possible Dimensional Crossover to 1D of $^3$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.