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Physical Review Letters

Quasiparticle interactions in two-dimensional fluid He3 films adsorbed on graphite

C. P. Lusher, Brian P. Cowan, J. Saunders

Published Oct 28, 1991• 95 citations
Publisher

Abstract

The nuclear magnetic susceptibility of $^{3}\mathrm{He}$ adsorbed on the surface of graphite, plated with a monolayer of solid $^{4}\mathrm{He}$, has been measured at surface densities less than 0.055 \AA{} $^{\mathrm{\ensuremath{-}}2}$ and at temperatures down to 6 mK. A temperature-independent susceptibility is observed at low temperatures, which is strongly enhanced over the ideal-gas value, due to quasiparticle interactions. The inferred Landau-Fermi-liquid parameters allow a comparison with microscopic theories of interacting Fermi systems.

DOI
10.1103/physrevlett.67.2497

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The nuclear magnetic susceptibility of 3He^{3}\mathrm{He}3He adsorbed on the surface of graphite, plated with a monolayer of solid 4He^{4}\mathrm{He}4He, has been measured at surface densities less than 0.055 \AA{} \ensuremath−2^{\mathrm{\ensuremath{-}}2}\ensuremath−2 and at temperatures down to 6 mK. A temperature-independent susceptibility is observed at low temperatures, which is strongly enhanced over the ideal-gas value, due to quasiparticle interactions. The inferred Landau-Fermi-liquid parameters allow a comparison with microscopic theories of interacting Fermi systems.
3He^{3}\mathrm{He}3He adsorbed on graphite is an almost ideal two-dimensional (2D) fermionic system. The 2D solid, where the interaction between the nuclear spins S=12S=\frac{1}{2}S=21​ is due to multiple spin exchange, has been extensively studied as a model system for strongly interacting fermions in 2D. At high densities in the second layer, three-body exchange dominates and leads to Heisenberg ferromagnetism. We report on nuclear magnetic resonance measurements at ultralow temperatures and low magnetic fields of the second layer of 3He^{3}\mathrm{He}3He on graphite preplated by one layer of 4He^{4}\mathrm{He}4He. By adding controlled amounts of 4He^{4}\mathrm{He}4He, 3He^{3}\mathrm{He}3He atoms are pushed out from the ferromagnetic domains, which become smaller and denser. We can evaluate the properties of these clusters, and control their size from a few tens to a few hundreds of atoms. These sizes are comparable to today's computing capabilities for exact numerical calculations on small clusters, and should lead to direct comparison between measurements on this model Heisenberg system and theory.
We report clear experimental signatures of the theoretically unexpected gas-liquid transition in the first three monolayer systems of 3He^{3}\mathrm{He}3He 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 ($2\ensuremath{\le}T\ensuremath{\le}80\text{ }\text{ }\mathrm{mK}$) below a critical liquid density (${\ensuremath{\rho}}_{c0}$). Surprisingly, the measured ${\ensuremath{\rho}}_{c0}$ values ($0.6--0.9\text{ }\text{ }{\mathrm{nm}}^{\ensuremath{-}2}$) are nearly the same for all these layers in spite of their quite different environments. We conclude that the ground state of 3He^{3}\mathrm{He}3He in strictly two dimensions is not a dilute quantum gas but a self-bound quantum liquid with the lowest density ever found.
Nuclear magnetic susceptibility measurements of the 3He^{3}\mathrm{He}3He in dilute 3He^{3}\mathrm{He}3He-4He^{4}\mathrm{He}4He mixture films are presented. At low 3He^{3}\mathrm{He}3He coverages (d3<0.1{d}_{3}<0.1d3​<0.1 layer), the 3He^{3}\mathrm{He}3He behaves approximately as a 2D ideal Fermi gas. For larger submonolayer 3He^{3}\mathrm{He}3He coverages, the low-temperature susceptibility is enhanced, increasing with increasing amounts of 3He^{3}\mathrm{He}3He, contrary to the 2D ideal Fermi-gas model. No evidence for a phase transition in the 3He^{3}\mathrm{He}3He is seen.
The specific heat and susceptibility data for 3He^{3}\mathrm{He}3He on Grafoil are analyzed in the framework of the Landau Fermi-liquid theory. The data suggest that the dominant interaction between 3He^{3}\mathrm{He}3He quasiparticles is an attraction in the p-wave channel. We have calculated explicitly the superfluid transition temperature in a two-dimensional Fermi gas and found that the prefactor in Tc{\mathit{T}}_{\mathit{c}}Tc​ is very small (\ensuremath{\sim}${10}^{\mathrm{\ensuremath{-}}2}$--${10}^{\mathrm{\ensuremath{-}}3}$ depending on the form of the potential). For moderate areal densities of 3He^{3}\mathrm{He}3He, Tc{\mathit{T}}_{\mathit{c}}Tc​ is estimated to be on the scale of several millikelvin. The relevance of these results to the change in the temperature behavior of the specific heat observed below Tk{\mathit{T}}_{\mathit{k}}Tk​=3.2 mK is discussed.
At low densities (ρ ≲ 4.2 nm -2 ), measured heat capacities satisfy the C = γT dependence at low T , which is characteristic of the degenerate Fermi liquid.With increasing density effective mass of a 3 He quasiparticle, deduced from γ, shows the divergence up to m * /m = 4.4 ± 0.3 until 4.2 nm -2 .At the lowest densities (0.1 ≲ ρ ≲ 0.7 nm -2 ), we observed the formation of the self-condensed liquid, judging from the γ coefficient smaller than the value of the noninteracting Fermi gas.Its critical density (0.7 nm -2 ) is quantitatively consistent with that of 1 -3 layers on graphite [1], but contradict recent Monte Carlo studies which claims that the potential corrugation play an essential role to stabilize the self-condensed liquid.
We study the thermodynamic response, effective masses, and collective excitations for thin (submonolayer) 3{}^{3}3He films as a function of density and polarization using Fermi liquid theory. The Landau parameters ${f}^{\ensuremath{\uparrow}\ensuremath{\uparrow}},{f}^{\ensuremath{\uparrow}\ensuremath{\downarrow}},{f}^{\ensuremath{\downarrow}\ensuremath{\downarrow}}$ are obtained to quadratic order in the low-density sss-wave and ppp-wave TTT-matrix interaction parameters. Values for the effective interaction components are determined by fitting zero-polarization experimental data for the cases of thin 3{}^{3}3He films on graphite and also thin 3{}^{3}3He films in surface states of thin superfluid 4{}^{4}4He films. By fitting the interaction parameters, we can calculate the Landau parameters to all orders, and we show results for the behavior of ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{F}}_{\ensuremath{\ell}}^{\ensuremath{\uparrow}\ensuremath{\uparrow}}\phantom{\rule{4.pt}{0ex}}\text{for}\phantom{\rule{4.pt}{0ex}}\ensuremath{\ell}\ensuremath{\leqslant}30$. With knowledge of the Landau parameters we calculate the polarization dependence of the state-dependent effective masses, compressibility, spin susceptibility, and zero-sound spectra for the mobile submonolayer range of areal densities. Our results predict a dramatic decrease in the effective masses for 3{}^{3}3He on graphite as a function of polarization at higher coverages. At fixed density, the compressibility is shown to decrease monotonically with increasing polarization. At small polarization the inverse spin susceptibility is largest for small density whereas at large polarization it is largest for large density. We show that zero sound will propagate at all densities and polarizations whereas spin zero sound does not propagate in these systems. The condition for thermodynamic stability in an arbitrarily polarized Fermi liquid film is derived and discussed. We show explicitly the Fermi surface distortion due to the presence of a zero-sound mode. A table of predicted values for the zero polarization Fermi liquid parameters F0sandF1a{F}_{0}^{\text{s}}\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}{F}_{1}^{\text{a}}F0s​andF1a​ is provided.