1. The case for and against dislocation network as the relevant disorder for the supersolid phenomenon & other puzzles Fondation des Treilles Workshop July 17, 2008 Moses Chan - Penn State Supported by NSF

2. The puzzle Assumptions and model Effect of 3 He impurities Shear modulus experiment and FEM simulations Dilute impurities in solid ( aerogel) Problems with the model

3. NCRIF from different samples differs by 3 orders of magnitude! Temperature dependence reproducible, but NCRIF varies by more than 3 orders of magnitude! NCRIF seems to show an Interesting depend, on S/V ratio From Rittner and Reppy

4. The model In a perfect crystal NCRIF is either very small ( ~0.015%) or nonexistent The core of the dislocation line is superfluid ( Shevchenko( 1987); Boningsegni et.al ( 2007)); Luttinger liquid. Large NCRIF observed in TO experiments and specific heat peak is a consequence of inter-connected superfluid dislocation network.

5. Two of the common types: edge & screw Dislocation density,  = <10 10 cm -2 –3-d network, L N ~ 1 to 10  m (  ~10 5 to 10 7 ) Information on Λcomes mostly from ultrasound attenuation measurements between 15 to 50 MHz. Dislocations

6. Dislocations intersect on a characteristic length scale of L N ~ 1  5  m Granato-Lucke applied to 4 He 3 He atoms also can condense onto and pin the dislocation Wo~0.3 to 0.7K ΛL 2 =0.2 ( okay for Λ~10 6 cm -2 )

7.  -  *[ns]  *=971,000ns Data shifted vertically for easy comparison Effect of 3 He impurities ( in Vycor)

8. Effects of 3 He impurities In bulk solid samples in cylindrical torsion cells Kim et. al, PRL 100,065301 (2008)

9. Effect of 3 He impurities in bulk samples

10. L IP =1.9  m W 0 =0.42 K Onset T vs. 3 He impurities Kim et. al, PRL 100,065301 (2008) L IP 3 He pinning length , shear modulus, b, Burger’s vector

11. L IP =0.5  m W 0 =0.6 K

12. The characteristic (onset ) temperature of NCRI tracks the condensation (pinning) temperature of 3 He atoms onto the dislocation line. The pinning of 3 He would stiffens the dislocation network This implies NCRI is possible only with a rigid dislocation network. As a sample of a fixed x 3 is warmed above Ts, the temperature where NCRI saturates, the continual evaporation of 3 He atoms from the dislocation network softens the solid, which concomitantly destroy NCRI. It is surprising (interesting) that 1ppb of 3 He impurity can completely immobilize the dislocation network below 30 mK.

13. Direct measurement of the Shear Modulus James Day and John Beamish, Nature (London) 450, 853 (2007).

14. Shear Modulus mirrors NCRI James Day and John Beamish, Nature (London) 450, 853 (2007).

15. An enhancement of to the overall rigidity of the (helium+ torsion cell) system will lead to a higher resonant frequency( or drop in period). Is this the sole cause for the observed increase in frequency in TO and hence there is no need to invoke NCRI or superfluidity? No! (1)The blocked annulus experiments showed macroscopic phase coherence. (2) The magnitude of the frequency shift due to an increase of shear modulus were calculated by finite element methods (FEM) for a number of torsion cells and found to be at 10 to 100 times smaller than the measured frequency increase. ( Clark, Maynard and Chan, PRB 77, 184513 (2008)) The increase in shear modulus and NCRI are related, but how?

16. Sheer Modulus results with solid 3 He and 4 He Syshenko & Beamish

17. Helium Space: OD = 10 mm Annulus Width = 1.2 mm Height = 6.4 mm ( no epoxy!) FEM Calculations (for 20% c 44 change) Predicted Shifts:  < 0.02 ns  f/f < 10 ppb Josh West

18. A few more details Cell is purged with Argon during welding to prevent oxidation Frequency = 341 Hz Q  1.6 x 10 6 Mass Loading  4500 ns (for 60 bar solid)

19. Shear Effect Torsional oscillator results with solid 4 He

20. No NCRI signal from either HCP or BCC solid 3 He. Torsional oscillator results with solid 3 He and 4 He Same 3 He gas used in Alberta

21. Comments on the Alberta-Penn State 3 He control experiment Smallest NCRI observed to date (0.015%) in 4 He Still a factor of at least 25 above the calculated shear effect HCP solid 3 He show a sheer modulus increase at low T, similar to HCP 4 He. No observable NCRI for solid 3 He in BCC or HCP phases. ( less than 0.1ns out of 4500 ns mass loading; or less than 0.002%) NCRI is not the cause for shear modulus increase, but a stiff dislocation network enable NCRI in solid 4 He.

22. Solid 4 He in aerogel Torsional oscillator and X-ray diffraction study. Inside such a random media, NCRI is expected to be very large? Norbert Mulders, Clem Burns, Larry Lurio, Tony Clark, Josh West

23. 20nm Aerogels Very porous silica glass, 95% open space Large surface area, 1000 m 2 /g  Small primary particles, 2 – 5 nm diameter TEM picture of 5% dense silica aerogel Herman and co-workers, U. Alberta

24. 24

25. Samples 95% porous SiO 2 aerogel 2 mm thick, 5 mm dia. In copper frame sandwiched between Be windows P = 60 bar, T M = 2.6 K X-ray scattering with E ph = 30 keV Bulk Solid 4 He 4 He in aerogel

26. X-ray Diffraction in bulk solid 4 He Liquid Solid

27. liquid solid X-ray powder diffraction for solid 4 He in aerogel rings from Be windows rings from solid helium

28. Powder pattern liquid minus solid 1,0,0 1,0,1 0,0,2 1,0,2 1,1,0 - liquid ring

29. From the diffraction peak width we can obtain the grain size: ~ 1000Å

30. Torsional Oscillator h d AgCu Al CuNi fo = 732 Hz Mass Loading ~ 3000 ns h = 6.4 mm, d = 10 mm Q = 1x10 6 at 20 mK Solid helium in 95% porous aerogel ( same batch as in X-ray) no “glue”

31. Note the small NCRIF of ~4x10 -2 % in bulk and in aerogel!

32. The temperature dependence most closely matches bulk sample grown under constant pressure with the same 3 He concentration.

33. Conclusions We have made very disordered samples, consisting of 1000 Å diameter HCP crystallites. We observe a super solid transition similar to that in “high quality” samples. Grain boundaries are not the important defects for NCRI; Aerogel strands are very different from dislocation lines.( it is not superfluid!)

34. Problems with the dislocation network model [A] The line density of dislocation network, as given by ultrasound attenuation measurements even for samples grown with blocked capillary method is at most ~10 9 cm -2. The superfluid core according to Boninsegni et.al is 6 Angstrom in diameter. Then if we assume the dislocation lines are aligned along the flow path, then NCRIF is only 3x10 -4 %. Anyway out? (1) Effective superfluid core is much larger? (2) Dislocation line density is much higher? Note that the ultrasound used in the studies of dislocation all have frequency smaller than 50 MHz ( with λ> 10 µm).These experiment will not see L n less than 1  m, and hence will not conclude a line density higher than 10 9 cm -2, [with L n ~3  m]

35. Problems with dislocation network model [B] Can we understand the three orders of magnitude difference seen with different cells? NCRIF does not scale linearly with dislocation line density; It is a percolation problem so it scale with line density with the power of 2.5(?), an order of difference in Λ will results in 2.5 orders’ change in NCRI. [C] Can we understand qualitatively Rittner and Reppy’s plot of NCRIF dependence on S/V ratio? Kosevich & Svatko, [SJLTP 9, 99(1983)] suggested that the density of dislocation is proportional to S/V ratio and sensitive to smoothness of the walls of the sample cell.

36. Problems with dislocation network model [D] How do we understand the results in porous media particularly in Vycor glass with a tortuous porous structure and NCRIF of 2.5%? The dislocation network conforms to the porous structure? Simulation studies will be helpful.

37. Log C vs. Log T Peak height and position decreases with higher quality crystal 4 h: BC 20h: BC CP T 3 subtracted

38. Specific heat height and position is independent of 3 He concentration T 3 subtracted ~20  J mol −1 K −1 ~2.5×10 -6 k B per 4 He atom Lin, Clark and Chan, Nature 449, 1025 (2007).

39. Confirmed at higher precision and to higher x 3, in contrast to NCRI data. Why?

40. Anderson’s vortex liquid model ”Free” vortices (relative to time scale of oscillator = resonant period) can respond to motion of oscillator and screen supercurrents, reducing measured NCRIF -NCRI related to susceptibility of vortices: NCRIF largest when they are “pinned” - 3 He may attach to vortices and slow them down (higher T O ) -Dissipation peak: vortex rate of motion ~ oscillator frequency (higher frequency, higher T O ); confirmed by experiment by Aoki,Graves and Kojima, PRL 99, 015301 P.W. Anderson, Nature Phys. 3, 160 (2007). Is this model related with and consistent with the dislocation network model?

41. Frequency dependence -T O increases with frequency -Low temperature NCRIF unchanged Aoki, Graves & Kojima, PRL 99, 015301 (2007). ~150mK ~220mK X 3 =0.3ppm Frequency effect should be much larger for samples of higher X 3

42. Perhaps the specific heat peak locates the ‘real’ transition in the zero frequency limit. NCRI results on the other hand are non-zero frequency measurements, as noted by Anderson’s vortex liquid model. f~1kHz Zero f limit ?

43. High oscillation speed trace always below that of low speed –Quick decay for large differences in metastable and stable NCRIF values –BC: T O is smallest at high speed, CT: T O is independent of speed Metastability of NCRIF, pinning and unpinning of vortices, or response of dislocation network to oscillation BC  Cooling and warming, 1.3  m/s  Cooling, 21  m/s  -Cycling, 21  m/s CT/CP  Cooling, 22  m/s <  -, cooling, 2.2  m/s , cycling, 22  m/s

44. Different velocity dependence for samples grown at CT/CP and by BC -No saturation in the (presumably) worst quality crystals -If there is a “critical velocity,” it is very low ; 3.5  m/s=k=h/m Data extracted from cooling scans!!

45. For T < 60mK, different decay above & below the low velocity field track. T>60mK, decay is exponential! NCRIF decay 60 mK is T of specific heat peak.

46. Summary and future experiments There are strong evidence that rigid inter-connected dislocation network enable or enhances superfluidity in solid 4 He. Experiments are need to determine and correlate the density of dislocation lines to NCRIF in solid samples. Ultrasound at gigahertz? X-ray imaging and TO measurements on the same sample cell? Specific heat measurement on solid sample that is confirmed to have large NCRIF ( in narrow gaps) DC flow experiment.

47. Collaborators: Xi Lin, Josh West, Zhigang Cheng, Eunseong Kim (KAIST); Tony Clark ( Basel); J.S. Xia ( Univ. of Florida); Norbert Mulders ( University of Delaware) Clem Burns ( Western Michigan U.,) Larry Lurio ( Northern Illinois); Alex Syshenko, John Beamish ( University of Alberta)