A liquid ground state for 2D helium-3?

A liquid ground state for 2D helium-3?Ashley G. Smart Citation: Phys. Today 66(1), 16 (2013); doi: 10.1063/PT.3.1842 View online: http://dx.doi.org/10.1063/PT.3.1842 View Table of Contents: http://www.physicstoday.org/resource/1/PHTOAD/v66/i1 Published by the American Institute of Physics. Additional resources for Physics TodayHomepage: http://www.physicstoday.org/ Information: http://www.physicstoday.org/about_us Daily Edition: http://www.physicstoday.org/daily_edition

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Because helium-3 is so light, and be-cause, as a fermion, it can’t crowdinto low energy levels, ensembles

of 3He atoms have unusually large ki-netic energy in the ground state. Whenthat energy is partitioned among twodimensions instead of three, it’s thoughtto be sufficient to overcome van derWaals attractions and prevent the sys-tem from condensing into a 2D liquid—even at absolute zero.

It came as a surprise, then, when ina 1985 experiment1 by Bidyut Bhat-tacharyya and Francis Gasparini (StateUniversity of New York at Buffalo) 3Heappeared to form a quasi-2D liquid. Theresearchers had added 3He to a thin filmof 4He and chilled the mixture to milli -kelvin temperatures. In such a system,the 3He atoms strongly prefer to sit atthe film’s surface, and because 4He be-comes a superfluid, they can moveabout that surface almost as easily asthey would in free space. (See the articleby Robert Hallock, PHYSICS TODAY, June1998, page 30.)

The heat capacity of such a weaklyinteracting 2D group of fermions isknown to grow linearly with tempera-ture. The slope, γ, can be shown to beproportional to the atomic mass andthe occupied surface area—but inde-

pendent of the total number of atoms.But Bhattacharyya and Gasparini foundthat under certain conditions, γ grew as3He atoms were added. The only rea-sonable interpretation, they concluded,was that 3He atoms weren’t spreadingout over the entire film surface, as a gaswould, but instead were collecting intopuddles of fixed, low density that occu-pied a growing fraction of the film surface as atoms were added.

The Buffalo team’s finding runscounter to nearly five decades of theoretical and numerical work on 2Dquantum systems. And subsequent ex-periments have only muddied the picture: Work by Moses Chan’s groupat the Pennsylvania State Universityseemingly corroborated the results,but a later study by Hallock and colleagues at the University of Massa-chusetts Amherst found no signs of aliquid phase.

Some theorists speculate that thesurface of a thin film just doesn’t suit-ably approximate a 2D environment.Surely, atoms at the free surface retainsome freedom to move in the normal direction, and such imperfect confine-ment should effectively reduce theatoms’ ground state energy in the planeof interest. Furthermore, the superfluid

film used in the experiment might havehosted ripple-like quantum excitations,or ripplons, which could mediate inter-atomic interactions not appearing intheoretical models.

Now, work from a University ofTokyo team led by Hiroshi Fukuyamamay dispel notions that the apparent liq-uid phase is an artifact of hydrodynamicor 3D effects.2 Their new experimentsseem to show that the precise nature ofthe underlying film has little bearing onwhether or not 3He condenses.

Flat liquidThe Tokyo group’s recent work grewout of previous efforts to elucidate how magnetically disordered systemsknown as spin liquids transform to ferromagnetic states. Fukuyama andhis colleagues sought to re-create sucha transformation in the lab by graduallyincreasing the density of a 3He mono-layer adsorbed on graphite. Before thetransition occurred, however, some 3Heatoms leapt out of the densely packedmonolayer to form a new top layer.Those atoms seemed to form puddlesmuch like the ones observed in the Buffalo experiment.

Figuring that the appearance of theliquid phase was probably connectedto the atoms’ out-of-plane motions,Fukuyama, Tomohiro Matsui, andgraduate students Daisuke Sato andKimiaki Naruse decided to probe3He’s behavior in the three differentquasi-2D systems depicted in figure 1.In one case (top image in figure), the3He layer of interest was adsorbed di-rectly onto a graphite substrate; in asecond (center), it was deposited on adense monolayer of 4He; in a third(bottom), it was deposited atop twodense monolayers—a layer of 3Heoverlying a layer of 4He. The 4Hemonolayers serve to mitigate the ef-fects of surface heterogeneities.

Each system imposes varying de-grees of 2D confinement on the topmost3He atoms: Those adsorbed directlyonto graphite have the least freedom tomove normal to the plane, whereasthose sitting atop two monolayers havethe most. So if the purported liquidphase was indeed an artifact of out-of-plane motion, the Tokyo group shouldhave seen quantitative differences inthe phase behavior of the three systems,and perhaps no liquid phase at all for3He deposited directly on the graphitesubstrate. Because the underlying

A liquid ground state for 2D helium-3?

New experiments hint at what could be the lowest-density liquid everfound in nature.

3He

4He

Graphite

Figure 1. Mimicking two dimensions. When chilled to millikelvin temperatures,helium-3 atoms atop a graphite substrate (top), a dense 4He monolayer (center),or dense 4He and 3He monolayers (bottom) closely approximate a 2D quantumfluid. In the multilayer films, the bottom monolayer of 4He serves to mitigate theeffects of heterogeneities in the graphite substrate. (Adapted from ref. 2.)

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monolayers in both multilayer films be-have as 2D solids, ripplons shouldn’tfactor into any of the three scenarios.

To the team’s surprise, calorimetricdata obtained at temperatures of 80 mKand below were quite similar for allthree systems. Figure 2 shows represen-tative results obtained from 3He atop asingle layer of 4He: As in the Buffalo ex-periment, γ grows proportionally to theaverage areal density ρ—the number ofsurface atoms per unit area of sub-strate—at small ρ. And as in the Buffaloexperiment, that linear-growth regionis thought to signal puddle formation.Notably, the linear trend can be extrap-olated to the origin, which suggests thatthe liquid phase is stable in the infi-nitely dilute limit.

The researchers infer from theirdata that the areal density inside thepuddles lies roughly in the range of0.6–0.9 nm−2. That would make it thelowest-density liquid ever discoveredin nature, with a mean interatomicspacing of more than a nanometer,more than twice that of 3D 3He.

Implied interactionsFukuyama isn’t yet sure how to recon-cile the experiments with theory, but thedata in figure 2 may hold an importantclue. They show that at a critical averagedensity, γ shifts from a linear function ofρ to a nonlinear one. Presumably, thatdensity marks the point at which liquid3He covers the entire substrate surface,and the nonlinear behavior reflectsstrengthening atomic interactions as theliquid becomes more densely packed.

Extrapolating the nonlinear branchto ρ = 0 should, in theory, yield γ corre-

sponding to an ideal, noninteractingFermi gas. The actual value, however,is roughly 25% larger. The implicationis that there must be some as-yetunidentified interaction—possibly me-diated by quasiparticles—that drivescondensation.

Washington State University theo-rist Michael Miller thinks there may bea simpler answer: The Tokyo groupmay be seeing not condensation but ag-gregation, driven by preferential ad-sorption at heterogeneities in thegraphite substrate. “If it turns out thatthis can’t be explained away in terms ofsurface inhomogeneities,” Miller com-ments, “then something very strangehas to be going on.”

A key next step for the Tokyo groupwill be to determine the critical temper-ature at which the 2D liquid transitionsto a pure gas. That temperature is ex-pected to lie somewhere in the range of80–700 mK. To pinpoint it, Fukuyamaand his colleagues will need to do sometinkering with their calorimeter: It cur-rently relies on a superconducting zincheat switch that fails at temperaturesabove 80 mK.

Theorists will have plenty to mullover in the meantime. In the opinion ofGasparini, “One might say the score isnow three experiments in favor of a 2Dliquid phase and one against it.”

Ashley G. Smart

References1. B. K. Bhattacharyya, F. M. Gasparini,

Phys. Rev. B 31, 2719 (1985).2. D. Sato, K. Naruse, T. Matsui, H.

Fukuyama, Phys. Rev. Lett. 109, 235306(2012).

0 1 2 3 4

0

100

ρ (nm−2)

γ(m

J/K

2 )

Ideal Fermi gas

Figure 2. Calorimetric data for ultracold helium-3 atop a dense 4He monolayershow signatures of a liquid phase: At low coverage densities, γ—the slope of the

heat capacity as a function oftemperature—grows linearlywith the average coveragedensity ρ. In that regime, 3Hecollects into liquid puddles offixed, low density. Above thecritical density of ρ ≈ 0.6 nm−2,at which the puddles presumably cover the entiresubstrate surface area, γgrows nonlinearly, indicatingstrengthening atomic interactions. Extrapolated toρ = 0 (dot–dash line), thenonlinear branch yields a γthat’s roughly 25% largerthan the ideal Fermi gasvalue, indicated by the redline. (Adapted from ref. 2.)

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