On the Novel Superfluidity in the Second Layer of $^4$He on Graphite

Abstract

Evidence for a new type of superfluid phase in second-layer $^4$He on graphite has been obtained from simultaneous measurements of torsional-oscillator response and heat-capacity on exactly the same sample down to 30 mK, which resolve substrate-related uncertainties in the previous studies. The new phase hosts both superfluidity and enhanced viscoelasticity, and is stable over a finite density interval, strongly supporting the proposed superfluid liquid-crystal hypothesis. A random-Josephson-network analysis shows that the widely reported log-$T$ dependence of the superfluid density is likely due to substrate imperfections.

Figures (6)

• Figure 1: (a) Normalized TO superfluid responses in the second layer of $^4$He on graphite (Grafoil) (obtained from Refs. Nyeki2017aChoi2021) plotted using each group's original density axis (dashed curves): the density for each group (solid curves) was rescaled by the respective authors themselves to conform to the thermodynamic phase diagram determined by the HC measurement Nakamura2016 (shown at the top). However, no established protocol exists to perform the rescaling. (b) Experimental apparatus specifically designed to measure TO signals and HCs simultaneously on the same He sample Usami2022.
• Figure 2: HC data at densities corresponding to (a) liquid (16.95), (b) QLC (19.80), and (c) solid (21.09) phases obtained in this work (dots). They show characteristic melting anomalies with different sharpness centered at different temperatures. Close agreement is observed with the HC data obtained at nearby densities by Greywall Greywall1993 using a Grafoil substrate (dashed curves). All numbers denote total $^4$He densities in units of nm$^{-2}$. Atomic structures of the three phases are illustrated by cartoons at the top of each panel.
• Figure 3: Frequency shifts $\Delta f$ associated with superfluid NCRI for coverages between (a) 16.95--18.35, (b) 18.35--18.61, (c) 19.00--20.80, and (d) 21.09--23.92 nm$^{-2}$. (e) Plot of $\Delta f$ at $T = 30$ mK vs. $^4$He density shows a systematic change at characteristic densities $\rho_1$--$\rho_5$ indicated by the vertical dashed lines, along with the thermodynamic phase diagram Nakamura2016 shown at the top. Note that the low-density bound of the liquid+QLC coexistence has been set to $\rho_2$ (the same hereinafter). Here, $\rho_1$, $\rho_2$, $\rho_3$, $\rho_4$, and $\rho_5$ are 16.95, 18.35, 18.8, 20.9, and 21.6 nm$^{-2}$, respectively. $\rho_0 = 16.5$ nm$^{-2}$ is the high-density bound of the gas+liquid coexistence region. The thick grey curve is a guide for the eyes. The red solid curve ($\rho \leq \rho_{2}$) and the red dashed curve ($\rho \geq \rho_{2}$) are calculated density dependences based on the RJN model (see text). (f) Fitting parameter $\zeta$ in Eq. \ref{['eq-1']} representing the stiffness of $^{4}$He film shows a stepwise increase at $\rho_2$ and above.
• Figure 4: (a) Temperature dependences of measured resonant-frequency raw data $f(T)$ before subtracting the substrate-He composite background $f_{\rm{cBG}} (T, \rho)$, for various He sample densities. The numbers denote total densities in atoms/nm$^2$. The data are vertically shifted to coincide at 1.5 K. The small but rather sharp decrease in $f_{\rm{emp}}$ below 50 mK is characteristic of BeCu torsion rods Agnolet1989, and has properly been included in the $T$-dependence of $f_{\rm{emp}}$. (b) Resonance frequency shifts $\Delta f$ after subtracting $f_{\rm{cBG}} (T, \rho)$ determined by fitting the raw data shown in (a) to Eq. \ref{['eq-1']} in the temperature range between $0.5$ and $1.5$ K. Upturns below 0.4--0.5 K in the liquid and QLC phases are due to superfluid mass decoupling. Each dataset is vertically shifted for clarity.
• Figure 5: Fitted $\zeta$ parameter values for the second layer of bilayer $^3$He on graphite. $\zeta$ shows a stepwise increase near the phase boundary ($\approx 18.0$ nm$^{-2}$) between the liquid and the liquid+QLC coexistence region. Note that, due to different zero-point energies, the thermodynamic phase diagram of $^3$He Nakamura2016, shown at the top, is slightly shifted to lower densities compared with $^4$He. (Inset) Like the other five densities, no superfluid signal is observed in the temperature dependence of $\Delta f$ at $17.1$ nm$^{-2}$ either.