A liquid ground state for 2D helium-3? Ashley G. Smart

7/29/2019 A liquid ground state for 2D helium-3? Ashley G. Smart

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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 Today

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ecause helium-3 is so ligh, and be-cause, as a ermion, i can’ crowd

ino low energy levels, ensembleso 3He aoms have unusually large ki-neic energy in he ground sae. Whenha energy is pariioned among wodimensions insead o hree, i’s hougho be sufficien o overcome van derWaals atracions and preven he sys-em rom condensing ino a 2D liquid—even a absolue zero.

I came as a surprise, hen, when ina 1985 experimen1  by Bidyu Bha-acharyya and Francis Gasparini (SaeUniversiy o New York a Buffalo) 3Heappeared o orm a quasi-2D liquid. The

researchers had added 3He o a hin filmo 4He and chilled he mixure o milli-kelvin emperaures. In such a sysem,he 3He aoms srongly preer o si ahe film’s surace, and because 4He be-comes a superfluid, hey can moveabou ha surace almos as easily ashey would in ree space. (See he aricle

 by Rober Hallock, PHYSICS TODAY , June1998, page 30.)

The hea capaciy o such a weaklyineracing 2D group o ermions isknown o grow linearly wih empera-

ure. The slope, γ , can be shown o beproporional o he aomic mass andhe occupied surace area—bu inde-

penden o he oal number o aoms.Bu Bhatacharyya and Gasparini ound

ha under cerain condiions, γ grew as3He aoms were added. The only rea-sonable inerpreaion, hey concluded,was ha 3He aoms weren’ spreadingou over he enire film surace, as a gaswould, bu insead were collecing inopuddles o fixed, low densiy ha occu-pied a growing racion o he filmsurace as aoms were added.

The Bualo eam’s inding runscouner o nearly ive decades oheoreical and numerical work on 2Dquanum sysems. And subsequen ex-perimens have only muddied he

picure: Work by Moses Chan’s groupa he Pennsylvania Sae Universiyseemingly corroboraed he resuls,

 bu a laer sudy by Hallock andcolleagues a he Universiy o Massa-chuses Amhers ound no signs o aliquid phase.

Some heoriss speculae ha hesurace o a hin film jus doesn’ sui-ably approximae a 2D environmen.Surely, aoms a he ree surace reainsome reedom o move in he normaldirecion, and such imperec confine-

men should effecively reduce heaoms’ ground sae energy in he planeo ineres. Furhermore, he superfluid

film used in he experimen migh havehosed ripple-like quanum exciaions,or ripplons, which could mediae iner-aomic ineracions no appearing inheoreical models.

Now, work rom a Universiy oTokyo eam led by Hiroshi Fukuyamamay dispel noions ha he apparen liq-uid phase is an ariac o hydrodynamicor 3D effecs.2 Their new experimensseem o show ha he precise naure ohe underlying film has litle bearing onwheher or no 3He condenses.

Flat liquidThe Tokyo group’s recen work grewou o previous effors o elucidaehow magneically disordered sysemsknown as spin liquids ransorm oerromagneic saes. Fukuyama andhis colleagues sough o re-creae sucha ransormaion in he lab by graduallyincreasing he densiy o a 3He mono-layer adsorbed on graphie. Beore heransiion occurred, however, some 3Heaoms leap ou o he densely packedmonolayer o orm a new op layer.Those aoms seemed o orm puddlesmuch like he ones observed in heBuffalo experimen.

Figuring ha he appearance o heliquid phase was probably connecedo he aoms’ ou-o-plane moions,Fukuyama, Tomohiro Masui, andgraduae sudens Daisuke Sao andKimiaki Naruse decided o probe3He’s behavior in he hree dierenquasi-2D sysems depiced in igure 1.In one case (op image in igure), he3He layer o ineres was adsorbed di-recly ono a graphie subsrae; in asecond (cener), i was deposied on adense monolayer o 4He; in a hird(boom), i was deposied aop wodense monolayers—a layer o 3Heoverlying a layer o 4He. The 4Hemonolayers serve o miigae he e-ecs o surace heerogeneiies.

Each sysem imposes varying de-grees o 2D confinemen on he opmos3He aoms: Those adsorbed direclyono graphie have he leas reedom omove normal o he plane, whereashose siting aop wo monolayers havehe mos. So i he purpored liquidphase was indeed an ariac o ou-o-plane moion, he Tokyo group shouldhave seen quaniaive differences inhe phase behavior o he hree sysems,and perhaps no liquid phase a all or3He deposied direcly on he graphiesubsrae. Because he 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 boh mulilayer films be-have as 2D solids, ripplons shouldn’acor ino any o he hree scenarios.

To he eam’s surprise, calorimericdaa obained a emperaures o 80 mKand below were quie similar or allhree sysems. Figure 2 shows represen-aive resuls obained rom 3He aop asingle layer o 4He: As in he Buffalo ex-perimen, γ grows proporionally o heaverage areal densiy ρ—he number osurace aoms per uni area o sub-srae—a small ρ. And as in he Buffaloexperimen, ha linear-growh regionis hough o signal puddle ormaion.Noably, he linear rend can be exrap-olaed o he origin, which suggess hahe liquid phase is sable in he infi-niely dilue limi.

The researchers iner rom heirdaa ha he areal densiy inside hepuddles lies roughly in he range o0.6–0.9 nm−2. Tha would make i helowes-densiy liquid ever discoveredin naure, wih a mean ineraomicspacing o more han a nanomeer,more han wice ha o 3D 3He.

Implied interactionsFukuyama isn’ ye sure how o recon-cile he experimens wih heory, bu hedaa in figure 2 may hold an imporanclue. They show ha a a criical averagedensiy, γ shifs rom a linear uncion oρ o a nonlinear one. Presumably, hadensiy marks he poin a which liquid3He covers he enire subsrae surace,and he nonlinear behavior reflecssrenghening aomic ineracions as heliquid becomes more densely packed.

Exrapolaing he nonlinear brancho ρ = 0 should, in heory, yield γ corre-

sponding o an ideal, nonineracingFermi gas. The acual value, however,is roughly 25% larger. The implicaionis ha here mus be some as-yeunidenified ineracion—possibly me-diaed by quasiparicles—ha drivescondensaion.

Washingon Sae Universiy heo-ris Michael Miller hinks here may bea simpler answer: The Tokyo groupmay be seeing no condensaion bu ag-gregaion, driven by preerenial ad-sorpion a heerogeneiies in he

graphie subsrae. “I i urns ou hahis can’ be explained away in erms osurace inhomogeneiies,” Miller com-mens, “hen somehing very srangehas o be going on.”

A key nex sep or he Tokyo groupwill be o deermine he criical emper-aure a which he 2D liquid ransiionso a pure gas. Tha emperaure is ex-peced o lie somewhere in he range o80–700 mK. To pinpoin i, Fukuyamaand his colleagues will need o do someinkering wih heir calorimeer: I cur-renly relies on a superconducing zinc

hea swich ha ails a emperauresabove 80 mK.

Theoriss will have pleny o mullover in he meanime. In he opinion oGasparini, “One migh say he score isnow hree experimens in avor o a 2Dliquid phase and one agains i.”

Ashley G. Smart

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

Phys. Rev. B 31 , 2719 (1985).2. D. Sao , K. Naruse, T. Masui, 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 of temperature—grows linearlywith the average coveragedensity ρ. In that regime, 3Hecollects into liquid puddles of fixed, low density. Above the

critical density of ρ ≈ 0.6 nm−2,at which the puddlespresumably cover the entiresubstrate surface area, γ grows nonlinearly, indicatingstrengthening atomicinteractions. Extrapolated toρ = 0 (dot–dash line), thenonlinear branch yields a γ 

that’s roughly 25% largerthan the ideal Fermi gasvalue, indicated by the redline. (Adapted from ref. 2.)

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