Observation of Self-Binding in Monolayer ${}^3\mathrm{He}$

We report clear experimental signatures of the theoretically unexpected gas-liquid transition in the first three monolayer systems of ${}^3\mathrm{He}$ adsorbed on graphite. The transition is inferred from the linear density dependence of the gamma coefficient of the heat capacity measured in the degenerate region ($2\le T\le 80\mathrm{mK}$) below a critical liquid density (${\rho }_{c0}$). Surprisingly, the measured ${\rho }_{c0}$ values ($0.6–0.9{\mathrm{nm}}^{-2}$) are nearly the same for all these layers in spite of their quite different environments. We conclude that the ground state of ${}^3\mathrm{He}$ in strictly two dimensions is not a dilute quantum gas but a self-bound quantum liquid with the lowest density ever found.

Figure 1

(a) Heat capacities ($C$) of the first layer ${}^3\mathrm{He}$ on Grafoil. The numbers are densities in ${\mathrm{nm}}^{-2}$, and those not denoted are 1.05, 1.25, 1.45, and $1.70{\mathrm{nm}}^{-2}$, respectively, from bottom to top. The solid lines are fittings to Eq. (1). The dashed line is $C={\gamma }_{\mathrm{ideal}}T$ for a degenerate Fermi gas spreading over the whole surface. (b) Density dependence of the fitting parameter $\beta$ in Eq. (1). (c) Density dependence of the fitting parameter $\gamma$ in Eq. (1). The open circles are from Ref. 29. Only after the growth of $\beta$ is saturated, $\gamma$ starts to increase linearly with $\rho$ above $0.6{\mathrm{nm}}^{-2}$. The horizontal dashed line represents $\gamma ={\gamma }_{\mathrm{ideal}}$.

Figure 2

(a) Heat capacities of the second layer of ${}^3\mathrm{He}$ on Grafoil preplated with a monolayer of ${}^4\mathrm{He}$. The solid lines are fittings to Eq. (2). (b) Density variation of the fitting parameter $\gamma$ in Eq. (2). The open circles are from Matsumoto et al. [22]. Note that their data point at $2.38{\mathrm{nm}}^{-2}$ is not shown in Ref. 22. Otherwise, notation here is the same as in Fig. 1.

Figure 3

(a) Density variation of $\gamma$ deduced from measured heat capacities of the third-layer liquid ${}^3\mathrm{He}$ on graphite preplated with a monolayer of ${}^4\mathrm{He}$; present work (closed circles), Ref. 10 (open circles). The magnetic contribution from the second-layer solid ${}^3\mathrm{He}$ has already been subtracted as described in Ref. 10. The solid line is a guide for eye. The uniform liquid region above $8.1{\mathrm{nm}}^{-2}$ is divided into two regions, ($\mathrm{C}2+\mathrm{IC}2$) and IC2, depending on the structure of the second-layer solid ${}^3\mathrm{He}$ (see Ref. 10). Schematic cross sectional views of the first (b), second (c), and third-layer (d) ${}^3\mathrm{He}$ puddles on graphite. Only the topmost three graphene-layers are drawn here.

Figure 4

Low-density phase diagram of monolayer ${}^3\mathrm{He}$ on graphite. The thick solid lines are the gas-liquid (G-L) transition lines determined from this experiment. The dash dotted line is a calculated one normalized to ${\rho }_{c0}=0.6{\mathrm{nm}}^{-2}$ and $T_c^{\max }=130\mathrm{mK}$ (Ref. 25). The dashed line represents $T_F$ of 2D ${}^3\mathrm{He}$ gas. The arrows denote sample densities at which we made the $C$ measurements for the second layer of ${}^3\mathrm{He}$. The inset shows a schematic top view of phase-separated liquid puddles in the second layer.