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Superfluidity in solid helium and solid hydrogen E. Kim*, A. Clark, X. Lin, J. West, E. Kim*, A. Clark, X. Lin, J. West, M. H. W. Chan M. H. W. Chan Penn.

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Presentation on theme: "Superfluidity in solid helium and solid hydrogen E. Kim*, A. Clark, X. Lin, J. West, E. Kim*, A. Clark, X. Lin, J. West, M. H. W. Chan M. H. W. Chan Penn."— Presentation transcript:

1 Superfluidity in solid helium and solid hydrogen E. Kim*, A. Clark, X. Lin, J. West, E. Kim*, A. Clark, X. Lin, J. West, M. H. W. Chan M. H. W. Chan Penn State University * KAIST, Korea

2 Introduction Introduction Theoretical background for supersolid Theoretical background for supersolid Experimental setup Experimental setup - Torsional oscillator technique - Torsional oscillator technique Supersolid in porous media Supersolid in porous media Supersolid in bulk 4 He Supersolid in bulk 4 He Heat Capacity of solid helium. Heat Capacity of solid helium. Results in para-hydrogen Results in para-hydrogen Summary Summary Outline

3 Solid Superfluid ( He II ) Normal Liquid, ( He I ) Fritz London is the first person to recognize that superfluidity in liquid 4 He is a BEC phenomenon. Condensation fraction was predicted and measured to be 10% near T=0. Superfluid fraction at T=0, however is 100%. Phase diagram of 4 He

4 Can a solid be superfluid?* - In a perfect solid when each atom is localized at a specific lattice site and symmetry is ignored, then there is no BEC at T=0. Penrose and Onsager, Phys. Rev. 104, 576 (1956 ) Penrose and Onsager, Phys. Rev. 104, 576 (1956 ) - Off Diagonal Long Range Order, or superfluidity, which is directly related to Bose-Einstein Condensation, may occur in a solid phase if particles are not localized. C. N. Yang, Rev. Mod. Phys. 34, 694 (1962) C. N. Yang, Rev. Mod. Phys. 34, 694 (1962) *A.J.Leggett,PRL 25, 1543 (1970)

5 Lindemann Parameter Lindemann Parameter the ratio of the root mean square of the displacement of atoms to the interatomic distance (d a ) the ratio of the root mean square of the displacement of atoms to the interatomic distance (d a ) A classical solid will melt if the Lindemanns parameter exceeds the critical value of ~0.1. A classical solid will melt if the Lindemanns 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 0.262. (Burns and Issacs, Phys. Rev. B 55, 5767(1997)) Zero-point Energy Inter-atomic potential total energy zero-point energy

6 Superfluidity in solid: Superfluidity in solid: not impossible! not impossible! - If solid 4 He 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. - If solid 4 He 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); G.V. Chester, Lectures in Theoretical Physics Vol XI-B(1969); Phys. Rev. A 2, 256 (1970) Phys. Rev. A 2, 256 (1970) J. Sarfatt, Phys. Lett. 30A, 300 (1969) J. Sarfatt, Phys. Lett. 30A, 300 (1969) L. Reatto, Phys. Rev. 183, 334 (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 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). Andreev & Liftshitz, Zh.Eksp.Teor.Fiz. 56, 205 (1969).

7 The ideal method to detect superflow would be to subject solid helium to undergo dc or ac rotation to look for evidence of Non-Classical Rotational Inertia. The ideal method to detect superflow would be to subject solid helium to undergo dc or ac rotation to look for evidence of Non-Classical Rotational Inertia. Leggett, Phys. Rev. Lett. 25, 1543 (1970) Leggett, Phys. Rev. Lett. 25, 1543 (1970) f s (T) is the supersolid fraction Its upper limit is estimated by different theorists to range from 10 -6 to 0.4; Leggett: 10 -4 Solid Helium R I(T)=I classical [1-f s (T)] Quantum exchange of particles arranged in an annulus under rotation leads to a measured moment of inertia that is smaller than the classical value

8 Plastic flow measurement Andreev et al. Sov. Phys. JETP Lett 9,306(1969) Suzuki J. Phys. Soc. Jpn. 35, 1472(1973) Tsymbalenko Sov. Phys. JETP Lett. 23, 653(1976) Dyumin et al.Sov. J. Low Temp. Phys. 15,295(1989); Torsional oscillator Bishop et al. Phys. Rev. B 24, 2844(1981) Mass flow Greywall Phys. Rev. B 16, 1291(1977) Bonfait, Godfrin and Castaing, J. de Physique 50, 1997(1989) Day, Herman and Beamish, Phys. Rev. Lett. 95, 035301 (2005) P V (T) measurement Adams et al. Bull. Am. Phys. Soc. 35,1080(1990) Haar et al. J. low Temp. Phys. 86,349(1992) However, interesting results are found in Ultrasound Measurements at UCSD. Goodkind Phys. Rev. Lett. 89,095301(2002) and references therein No experimental evidence of superfluidity in solid helium prior to 2004

9 9.3 MHz x 28MHz 46MHz P.C. Ho, I.P. Bindloss and J. M. Goodkind, J. Low Temp. Phys. 109, 409 (1997) Ultrasound velocity and dissipation measurements in solid 4 He with 27.5ppm of 3 He The results are interpreted by the authors as showing BEC of thermally activated vacancies above 200mK.

10 Amorphous boundary layer Solidification proceeds in two different directions: 1) In the center of the pore a solid cluster has crystalline order identical to bulk 4 He 2) On the wall of a pore amorphous solid layers are found due to the van der Waals force of the substrate Elbaum et al. Adams et al. Brewer et al. Solid helium in a porous medium should have more disorder and defects, which may facilitate the appearance of superflow in solid? Crystalline solid TEM of Vycor glass

11 Torsional oscillator is ideal for the detection of superfluidity Be-Cu Torsion Rod Torsion Bob containing helium Drive Detection Q=f 0 /f ~ 2×10 6 Resolution Resonant period ( o ) ~ 1 ms stability in is 0.1ns / o = 5×10 -7 Mass sensitivity ~10 -7 g f0f0 f Amp

12 Torsional oscillator studies of superfluid films Above Tc the adsorbed normal liquid film behaves as solid and oscillates with the cell, since the viscous penetration depth at 1kHz is about 3 m. Vycor Berthold,Bishop, Reppy, PRL 39,348(1977) Δ

13 Solid helium in Vycor glass 5cm Detect Torsion Bob (vycor glass) Torsion Rod Drive 2.2mm 0.38mm f 0 = 1024Hz Q ~ 1*10 6 A=A 0 sinωt v=|v| max cosωt |v| max =rA 0 ω

14 Solid 4 He at 62 bars in Vycor glass Period shifted by 4260ns due to mass loading of solid helium *=966,000ns

15 Supersolid response of helium in Vycor glass Period drops at 175mK appearance of NCRI size of period drop - ~17ns *=971,000ns

16 Superfluid response - * [ns] *=971,000ns Total mass loading =4260ns Measured decoupling - o =17ns Apparent supersolid fraction= 0.4% (with tortuosity correction s / =2% ) Weak pressure dependence

17 Δ 0 [ns] Strong velocity dependence For liquid film adsorbed on Vycor glass v c > 20cm/s Chan et. al. Phys. Rev. Lett. 32, 1347(1974). For superflow in solid 4 He v c < 30 µm/s

18 Control experiment I : Solid 3 He? Nature 427,225(2004)

19 4 He solid diluted with low concentration of 3 He

20 Effect of the addition of 3 He impurities At 0.3ppm, the separation of the 3 He atoms is about 450Å

21 Be-Cu Torsion Rod OD=2.2mm I D=0.4mm Filling line Detection Drive Torsion cell with helium in annulus Mg disk Filling line Solid helium in annulus channel Al shell Channel OD=10mm Width=0.63mm Search for the supersolid phase in the bulk solid 4 He.

22 Torsional Oscillator (bulk solid helium-4) Drive Detection 3.5 cm Torsion rod Torsion cell

23 Solid 4 He at 51 bars NCRI appears below 0.25K Strong |v| max dependence (above 14µm/s) Amplitude minimum, Tp 0 = 1,096,465ns at 0 bar 1,099,477ns at 51 bars (total mass loading=3012ns due to filling with helium) Science 305, 1941(2004) 4µm/s corresponds to amplitude of oscillation of 7Å Porous media are not essential !

24 Non-Classical Rotational Inertia Fraction Total mass loading =3012ns at 51 bars NCRIF ρS/ρρS/ρ |v| max

25 Total mass loading =3012ns at 51 bars ρS/ρρS/ρ |v| max Non-Classical Rotational Inertia Fraction

26 Control experiment II With a barrier in the annulus, there should be NO simple superflow and the measured superfluid decoupling should be vastly reduced With a barrier in the annulus, there should be NO simple superflow and the measured superfluid decoupling should be vastly reduced Torsion cell with blocked annulus Solid helium Mg barrier Al shell Mg Disk Mg disk Filling line Solid helium in annulus channel Al shell Mg barrier Channel OD=15mm Width=1.5mm

27 If there is no barrier, then the supersolid fraction appears to be stationary in the laboratory frame; with respect to the torsional oscillator it is executing oscillatory superflow. Superflow viewed in the rotating frame - *[ns]

28 With a block in the annulus, irrotational flow of the supersolid fraction contributes about 1% (Erich Mueller) of the barrier-free decoupling. Δ~1.5ns Irrotational flow pattern in a blocked annular channel (viewed in the rotating frame) - *[ns] A. L. Fetter, JLTP(1974) * If no block, the expected Δ =90ns

29 Similar reduction in superfluid response is seen in liquid helium at 19 bars in the same blocked cell measured superfluid decoupling in the blocked cell Δ(T=0) 93ns. While the expected decoupling in unblocked cell is 5270ns. Hence the ratio is 1.7% similar to that for solid. [ns] Conclusion : superflow in solid as in superfluid is irrotational.

30 Superflow persists up to at least 136 bars ! ρs/ρρs/ρ 136bar ρs/ρρs/ρ 108bar

31 Strong and universal velocity dependence in all samples v C ~ 10µm/s =3.16µm/s for n=1 ω R

32 Pressure dependence As a function of pressure the supersolid fraction shows a maximum near 55bars. The supersolid fraction extrapolates to zero near 170 bars. As a function of pressure the supersolid fraction shows a maximum near 55bars. The supersolid fraction extrapolates to zero near 170 bars.

33 Superfluidity in ultra-pure Solid Helium: 1ppb 3 He 0 ~ 0.77ms [1300Hz] 0 ~ 0.77ms [1300Hz] 4He - 0 = 3920ns 4He - 0 = 3920ns NCRIF ~ 1.25/3920 = 0.03% NCRIF ~ 1.25/3920 = 0.03% Exp. done at at U. of Florida

34 Phase Diagram of 4 He

35 Heat Capacity signature? No reliable heat capacity measurement of solid 4 He below No reliable heat capacity measurement of solid 4 He below 200mK because of large background 200mK because of large background contribution due to the sample cell. contribution due to the sample cell.

36 Experimental cell of Xi Lin and Tony Clark Silicon!!

37 Results: pure 4 He (0.3ppm 3 He)

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41 Heat capacity peak near the supersolid transition

42 Is the supersolid phase unique with 4 He? Apparently not! Preliminary torsional oscillator data of Tony Clark and Xi Lin indicate similar supersolid- like decoupling in solid H 2. 3 He 3.09 4 He 2.68 H 2 1.73 HD 1.41 D 2 1.22 de Boer parameter More quantum mechanical

43 Q = 1.6million P 0 = 560,400ns P ~0.05ns Inside Mg bob: Hydrogen space BeCu wall Hydrogen in a cylindrical cell

44 Inside Mg bob: Hydrogen space BeCu wall HD P HD = 4014ns (93% filling) Hydrogen in a cylindrical cell

45 HD H2 P H2 = 1638ns (64% filling) Inside Mg bob: Hydrogen space BeCu wall Hydrogen in a cylindrical cell

46 HD H2 Temperature below 50mK uncertain, thermometer not on the torsional cell Ortho concentration is most likely less than 0.5% HD concentration uncertain NCRIF ~ 0.015%

47 Inside Mg bob: Hydrogen space (h=3.5mm w=2.3mm) Mg Q = 350,000 P 0 = 709,700ns P <0.1ns Hydrogen in an annular cell Samples contain < 50ppm HD BeCu wall X is the ortho conc,

48 Inside Mg bob: Hydrogen space BeCu wall Mg Hydrogen in an annular cell Comparison of 50 and 200ppm HD

49 Summary Superflow is seen in solid helium confined in Vycor glass with pores diameter of 7nm and also in bulk. Results in bulk have been replicated in three other labs. Superflow is seen in solid helium confined in Vycor glass with pores diameter of 7nm and also in bulk. Results in bulk have been replicated in three other labs. Supersolid fraction is on the order of 1% for He-4 sample with 0.3ppm of He-3 impurities. For ultra-high purity sample (1ppb He-3) the supersolid fraction is on the order of 0.03% and the transition temp. is depressed. Supersolid fraction is on the order of 1% for He-4 sample with 0.3ppm of He-3 impurities. For ultra-high purity sample (1ppb He-3) the supersolid fraction is on the order of 0.03% and the transition temp. is depressed. There is preliminary evidence of a heat capacity peak at the transition. There is preliminary evidence of a heat capacity peak at the transition. Superflow is also seen in para-hydrogen. Superflow is also seen in para-hydrogen. The supersolid fraction is on the order of The supersolid fraction is on the order of 0.05% 0.05%

50 We are grateful for many informative discussions with many colleagues, too numerous to acknowledge all of them. P.W. Anderson P.W. Anderson J. R. Beamish, J. R. Beamish, D. J. Bishop, D. J. Bishop, D. M. Ceperley, D. M. Ceperley, J. M. Goodkind, J. M. Goodkind, T. L. Ho, T. L. Ho, J. K. Jain, J. K. Jain, A. J. Leggett, A. J. Leggett, E. Mueller, E. Mueller, M. A. Paalanen, M. A. Paalanen, J. D. Reppy, J. D. Reppy, W. M. Saslow, W. M. Saslow, D.S. Weiss D.S. Weiss

51 Xi, Tony, Eunseong, Josh

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