Presentation on theme: "Can a solid be superfluid?"— Presentation transcript:
1 Can a solid be superfluid? Symposium on Quantum Phenomena and Devicesat Low Temperatures, 2008Helsinki Univ. of TechnologyMoses Chan - Penn State
2 Outline Introduction Torsional oscillator measurements. Origin of supersolidity :zero point vacancies, grain boundariesglassy regions or dislocations?Specific heat and dc flow experimentsConclusions
3 Theoretical ‘consensus’ in 1970s: Superfluidity in solid is not impossible!- If solid 4He can be described by a Jastraw-type wavefunction that is commonly used to describe liquid helium then crystalline order (with finite fraction of vacancies) and BEC can coexist.G.V. Chester, Lectures in Theoretical Physics Vol XI-B(1969);Phys. Rev. A 2, 256 (1970)J. Sarfatt, Phys. Lett. 30A, 300 (1969)L. Reatto, Phys. Rev. 183, 334 (1969)- Andreev and Liftshitz assume the specific scenario of zero-point vacancies and other defects ( e.g. interstitial atoms) undergoing BEC and exhibit superfluidity.Andreev & Liftshitz, Zh.Eksp.Teor.Fiz. 56, 205 (1969).
4 R I(T)=Iclassical[1-fs(T)] The ideal method of detection of superfluidity is to subject solid to dc or ac rotation.Leggett, “Can a solid be superfluid?” PRL 25, 1543(1970)Quantum exchange of particles arranged in an annulus under rotation leads to a measured moment of inertia that is smaller than the classical valueSolid HeliumRI(T)=Iclassical[1-fs(T)]fs(T) is the supersolid or nonclassical rotational inertia (NCRI) fraction.Its upper limit is estimated by different theorists to range from 10-6 to 0.4; Leggett: 10-4
5 Torsional Oscillator Technique is ideal for the detection of superfluidity AmpDriveDetection3.5 cmTorsion rodTorsion cellQuality FactorQ= f0 / f ~106Stability in the period is ~0.1 nsFrequency resolution of 1 part in 107Mass sensitivity of ~10-7 gf~ 1kHz
6 Torsional oscillator studies of superfluid films VycorΔI total= I cell+ I helium film,Above Tc the adsorbed normal liquid film behaves as solid and oscillates with the cell. In the superfluid phase, helium film decouples from oscillation.Hence Itotal and drops.Berthold,Bishop, Reppy, PRL 39,348(1977)
7 Bulk solid helium in annulus Torsion cellwith helium in annulusFilling lineChannel OD=10mmWidth=0.9mmTorsion rod3.5 cmMg diskTorsion cellAl shellDetectionSolid helium in annular channelDrive
8 E. Kim & M.H.W. Chan, Science 305, 1941 (2004) Bulk solid helium in annulusf0=912Hz51barTotal mass loading = 3012nsMeasured decoupling, -o=41nsNCRIF = 1.4%E. Kim & M.H.W. Chan, Science 305, 1941 (2004)
9 Non-Classical Rotational Inertia Fraction |v|maxTotal mass loading=3012ns at 51 bars
10 Irrotational Flow Superfluids exhibit potential (irrotational) flow For our exact dimensions, NCRIF in the blocked cell should be about 1% that of the annulus**E. Mueller, private communication.
11 Reversibly blocked annulus Rittner & Reppy, Cornell Top View: BlockedTop View: Opensolid inertiaNonclassicalrotationalinertiaGap 73 mm, NCRI = 16 %
12 Nonclassical rotational inertia results have been replicated in five other labs. The temperature dependence of NCRI is reproduced.However, the magnitude of NCRIF varies from 0.015% up to 16%.Simulations studies indicate NCRI is not possible in a ‘perfect’ crystal and that quantum zero point vacancies concentration is too low to account for the observations.(this conclusion not universally accepted).This leaves other defects, e.g. grain boundaries, glassy regions and dislocations as possible origins or at least ‘enhancer’ for NCRI.
13 Grain boundariesIt has been suggested that the observed NCRI are due to atomically thin superfluid (liquid) films along the grain boundaries, if true, NCRI should scales with total grain boundary area.Grain size of solid 4He inside Vycor glass is ~ 7nm and in bulk it is ~0.1 mm. This means the grain boundary surface differs by many orders of magnitude, but observed NCRI is about the same, ~1%.Nevertheless, most bulk solid samples grown by the blocked capillary method is polycrystalline. Does NCRI exists in a single crystal ?
14 E. Kim & M.H.W. Chan, Nature 427, 225 (2004). Solid helium in Vycor glass7nmf0=1024Hz62barTotal mass loading = 4260nsMeasured decoupling, -o=17nsNCRI fraction, or NCRIF = 0.4%(with tortuosity, 2% )-*[ns]E. Kim & M.H.W. Chan, Nature 427, 225 (2004).*=971,000ns
15 Crystal GrowthHigh quality single crystals have been grown under constant temperature1 and pressure2Best crystals grownin zero temperaturelimit1. O.W. Heybey & D.M. Lee, PRL 19, 106 (1967); S. Balibar, H. Alles & A. YaParshin, Rev. Mod. Phys. 77, 317 (2005).2. L.P. Mezhov-Deglin, Sov. Phys. JETP 22, 47 (1966); D.S. Greywall, PRA 3, 2106(1971).
16 Constant T/P growth from superfluid (1ppb 3He) Heat in Heat outQ ~ 500,000Tony Clark and Josh West
17 Solid 4He (1ppb 3He) grown under constant P/T from superfluid
18 Solid 4He (1ppb 3He) grown under constant P/T from superfluid
19 Solid 4He (1ppb 3He) grown under constant P/T from superfluid
20 Solid 4He (1ppb 3He) grown under constant P/T from superfluid
21 Solid 4He (1ppb 3He) grown under constant P/T from superfluid
22 Solid 4He (1ppb 3He) grown under constant P/T from superfluid
23 Samples grown under constant P/T from superfluid collapse onto one curve for T > 40mK and share common onset temperature, TC ~ 80mK. Superfluid film flow along grain boundary cannot be the ‘origin’ of NCRI.
24 High temperature tail of NCRI Transition broadened in BC samples (probably “polycrystalline”) and by 3He impurities
25 Superfluid film along the grain boundaries cannot be the mechanism for NCRI. What is the most likely origin for the large variation in NCRI from cell to cell?Dislocation lines density in solid 4He ranges from ~10 to 109 cm-2 , sensitive to how the solid is nucleated and grown. But how does dislocations enable or enhance NCRI?
26 Dislocations Two of the common types: edge & screw In solid 4He Dislocation density, L = ~5 <1010 cm-2
27 3He impurities at “high” T Network pinning at the nodes3He impurities are not ‘attached’ to the dislocation lines.
28 Increasing fraction of 3He atoms condense onto and stiffen dislocation network with decreasing T Iwasa et.al., J.Phys. Soc. Jpn. 46, 1119( 1979);Paalanen, Bishop and Dail,PRL 46, 664(1981)
29 3He Effect ( bulk samples) E. Kim, J. S. Xia, J. T. West, X. Lin, A. C Clark, and M. H. W. Chan, , PRL 100, ( 2008)
30 Onset of NCRI tracks the expected temp Onset of NCRI tracks the expected temp. of 3He condensation onto dislocation
31 Direct measurement of the Shear Modulus James Day and John Beamish, Nature (London) 450, 853 (2007).
32 Shear Modulus mirrors NCRI James Day and John Beamish, Nature (London) 450, 853 (2007).
33 The increase in shear modulus and the onset of NCRI at low T must be related, but how? An increase in shear modulus of solid 4He in TO can result an increase in its resonant freq., ie. the same sign as the observed NCRI. But simulation studies shows the magnitude of the ‘Beamish’ effect is typically orders of magnitudes smaller than that observed in most TOs.The ‘Beamish’ effect or shear modulus stiffening cannot explain the blocked annulus experiments.It has been suggested (Anderson) that the onset of supersolidity stiffens the shear modulus.Simulations show the dislocation lines are ‘superfluid’ and it has been suggested that the onset of NCRI requires a ‘rigid’ dislocation network.
34 What about the superglass model? Since glass has no crystalline order, it is thought superfluidity is more likely to occur.If this is the case there should be thermodynamic signatures ( e.g. thermal hysteresis, and linear specific heat)
35 Heat capacity Is there a thermodynamic signature of the transition? There is no specific heat information on solid 4He below 200 mK. The heat capacity of metal container swamps the contribution of solid 4He
36 Heat Capacity measurements in a Silicon cell Reasons for Si:Low heat capacity:High thermal conductivity:Helium Volume= 0.926ccSiAlGlass CapillaryStycast 2850HeaterThermometer0.1mm ID1.5 cmLattice Materials CorP., MT, USAOptical Silicon purity : >99.999%Heat capacity of solid 4He is more than 10 times largerthan the Si cell over the entire temp. range
37 AC Calorimetry KΘ Kb Sample Kh Internal time constant << 1/ω External time constant >> 1/ωKbSampleThermal BathThermometerKΘHeaterKhPaul F. Sullivan, G. Seidel, Phys Rev. 173, 679 (1968).Yaakov Kraftmakher, Physics Reports, 356 (2002)
38 Specific heat of commercially pure 4He (0.3ppm 3He) log C vs. log TConstant volumetechnique.20 hours to finish solidification.No long time constant.No hysteresisNo annealing effectNo thermal cycle effect
39 Specific heat of solid 4He (0.3ppm & 1ppb) log C vs. log T
40 C/T vs. T2 Data above 140 mK extrapolate to zero the data seem to diverge in the low-temperature limit. This behaviour, which is more prominent in the 30 p.p.m. sample, suggests the presence of a temperature-independent term in addition to the Debye contribution.Data above 140 mK extrapolate to zero
41 ‘Linear T’ term from Pressure measurements ? PHYSICAL REVIEW B 76,V. N. Grigor'ev et alFreshly grown sampleAnnealed sample (19.83cc/mole)— Grüneisen constant ρ — molar volumeCV~Tn P~Tn+1
42 Specific heat with Debye phonon term subtracted T3 subtracted~20 mJ mol−1 K−1~2.5×10-6 kB per 4He atomExplain the Scatter.
43 Higher resolution in 2008 sample cell Minimum Temperature 25mKNew preliminary result with a more sensitive thermometer.Disadvantage of Si?8 out of 10 cells leaks under high pressure4 hours to solidify a sample.Solid sample grown under constant pressure condition has the smallest peak.T3 subtractedT3 subtracted
44 Comparison with the Helsinki melting curve measurement. Constant volume 1ppb 2008Constant pressure 1ppb 2008No anomaly in melting curve after correction for instrumental effect.Discrepancy we don’t understandTodoschenko et al., PRL 97, (2006); JETP Lett. 85, 555 (2007).
45 dc ( superfluid-like ) flow? Greywall and Beamish carried out experiments by increasing pressure on one end of a solid ( bulk or in Vycor glass) sample. No evidence of flow.Balibar and collaborators saw flow in liquid-solid coexistence samples. The observed phenomenon is likely a consequence of liquid film flow through the ‘crack’ in the solid.
46 DC superflow reported by ‘pushing’ on superfluid in contact with solid : ‘UMass Sandwich’ (R.B. Hallock)312R, reservoirsV, VycorS, sampleC1C2
47 ConclusionsNCRI or superfluid like behavior seen in solid 4He in 7 labs.Shear modulus increases at low temperature, the temperature dependence of the increases mimics that of NCRIIt is possible that either (1) NCRI ‘requires’ a rigid dislocation network, or (2) onset of NCRI stiffens the solid lattice.No evidence of linear T term in specific heat, but a peak near NCRI onset is seen, size of peak is smaller for a ‘higher’ quality sample.Preliminary dc superfluid flow through solid helium reported.
50 Lindemann Parameterthe ratio of the root mean square of the displacement of atoms to the interatomic distance (da)A classical solid will melt if the Lindemann’s parameter exceeds the critical value of ~0.1 .X-ray measurement of the Debye-Waller factor of solid helium at ~0.7K and near melting curve shows this ratio to be(Burns and Issacs, Phys. Rev. B 55, 5767(1997))total energyzero-point energyZero-point EnergyInter-atomic potential
51 Solid 4He at 62 bars in Vycor glass Period shifted by ns due to mass loading of solid helium*=966,000ns
52 Strong and ‘universal’ velocity dependence in all annular samplesωRvC~ 10µm/s=3.16µm/sfor n=1Vortices are important
58 Specific heat with the temperature independent constant term subtracted
59 Previous solid 4He heat capacity measurements below 1K Year Low temperature limitSwenson1 1962, KEdwards KGardner KAdams KHebral KClark KThey all observed T3 phonon contribution.Their sample cells used in these experiments were all constructed with heavy wall metal or epoxy which contribute significantly to the heat capacity at low temperature.E. C. Heltemes and C. A. Swenson, Phys. Rev. 128, 1512 (1962); H. H. Sample and C. A. Swenson, Phys. Rev. 158, 188 (1967).D. O. Edwards and R. C. Pandorf, Phys. Rev. 140, A816 (1965).W. R. Gardner et al., Phys. Rev. A 7, 1029 (1973).S. H. Castles and E. D. Adams, J. Low Temp. Phys. 19, 397 (1975).B. Hébral et al., Phonons in Condensed Matter, edited by H. J. Maris (Plenum, New York, 1980), pg. 169.A. C. Clark and M. H. W. Chan, J. Low Temp. Phys. 138, 853 (2005).
60 Results: 4He at different 3He concentrations in glass capillary cell Constant volume techniqueNo long time constant.No hysteresisNo change due to annealingNo thermal cycle effect
61 C vs T3 10ppm sample 0.7+/-0.2 kB per 3He 30ppm sample Constant contribution from 3He impurity10ppm sample0.7+/-0.2 kB per 3He30ppm sample1.7+/-0.3 kB per 3He
62 Is there a linear T term?For 0.3ppm, T>0.14K T3 relation only
63 NMR measurement of spin (3He) diffusion: A. R. Allen, M. G. Richards & J. Schratter J. Low Temp. Phys. 47, 289 (1982).M. G. Richards, J. Pope & A. Widom, Phys. Rev. Lett. 29, 708 (1972).
64 Results: pure 4He (0.3ppm & 1ppb) Ln C vs. Ln TWhat is the deviation?
65 Previous solid 4He heat capacity measurements below 1K Year Low temperature limitSwenson1 1962, KEdwards KGardner KAdams KHebral KClark KThey all observed T3 phonon contribution.Their sample cells used in these experiments were all constructed with heavy wall metal or epoxy which contribute significantly to the heat capacity at low temperature.E. C. Heltemes and C. A. Swenson, Phys. Rev. 128, 1512 (1962); H. H. Sample and C. A. Swenson, Phys. Rev. 158, 188 (1967).D. O. Edwards and R. C. Pandorf, Phys. Rev. 140, A816 (1965).W. R. Gardner et al., Phys. Rev. A 7, 1029 (1973).S. H. Castles and E. D. Adams, J. Low Temp. Phys. 19, 397 (1975).B. Hébral et al., Phonons in Condensed Matter, edited by H. J. Maris (Plenum, New York, 1980), pg. 169.A. C. Clark and M. H. W. Chan, J. Low Temp. Phys. 138, 853 (2005).
66 Results from Edwards and Hebral The background problemEdwardsHebralEffect of changing 1% of the empty cell
67 Temperature scale based on Results: pure 4He (0.3ppm)The heat capacity of the empty cell at 0.2 K and 0.05 mK are respectively less than 3 % and 10 % of the heat capacity of solid helium at 27 bar.0.3ppmMinimum temperature 40mKTemperature scale based on3He melting curve
68 Specific heat peak is found when T3 term subtracted The peak is independent of 3He concentration Peak height: 20 μJ mol-1 K-1(2.5 x 10-6 kB per 4He atom)Excess entropy: 28 μ J mol-1 K-1(3.5 x 10-6 kB per 4He atom)
69 BC samples can also be grown Heat outQ ~ 500,000
70 Granato-Lucke applied to 4He Dislocations pinned by network, 3He, jogs?Typical LN in pure 4He crystals ~ 5mm
79 Specific heat with T3 term subtracted Specific heat peak is independent of 3He concentrations.Assuming 3D-xy universality class (same as the lambda transition in liquid 4He).Use two-scale-factor universality hypothesis, ρs ~0.06%. 1ppb study of TO found this number lays between 0.03% and 0.3%.Peak height:20 μJ mol-1 K-1 (2.5 x 10-6 kB per 4He atom)Excess entropy:28 μ J mol-1 K-1 (3.5 x 10-6 kB per 4He atom)
82 Dislocations Two of the common types: edge & screw Dislocation density, L = ~5 <1010 cm-23-d network, LN ~ 1 to 10 mm (L~105 to 107)[LN ~ 0.1 to 1 mm (L~109)]
83 Granato-Lucke applied to 4He Dislocations intersect on a characteristic length scale of LN ~ 1 5mmDislocations can also be pinned by 3He impuritiesDistance between 3He atoms (if uniformly distributed):1ppb 1000a ~ 0.3mm0.3ppm 150a ~ 45nm1% a ~ 15nm
84 3He-dislocation interaction Actual 3He concentration on dislocation line is thermally activated*Typical binding energy, W0 is 0.3K to 0.7K
85 3He-dislocations interaction Line considered as crossover from network pinning to 3He impurity pinning of dislocations (LNetwork ~ L3He spacing)Average lengthLNetwork ~ 1 to 10mmFor L ~ 105 to 106cm-2Smaller lengths(< 1mm) are expectedfor larger dislocation densities
86 Solid helium in Vycor glass Weak pressure dependence…from 40 to 65barStrong velocity dependence
87 3He-4He mixtures-*[ns]*=971,000nsQuestion: If there is a transition between the normal and supersolid phases, where is the transition temperature?