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Harry Kojima Rutgers University in collaboration with Yuki Aoki and Joe Graves

Harry Kojima Rutgers University in collaboration with Yuki Aoki and Joe Graves. Compound Torsional Oscillator: Frequency Dependence and Hysteresis of Supersolid 4 He (and Search for Superfluid Sound Mode). outline. Compound Torsional Oscillator motivation oscillator

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Harry Kojima Rutgers University in collaboration with Yuki Aoki and Joe Graves

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  1. Harry Kojima Rutgers University in collaboration with Yuki Aoki and Joe Graves Compound Torsional Oscillator: Frequency Dependence and Hysteresis of Supersolid 4He(and Search for Superfluid Sound Mode)

  2. outline • Compound Torsional Oscillator • motivation • oscillator • results on NCRI(T, ), dissipation(T, ), dependence of NCRI on drive displacement, velocity and acceleration • relaxation effects of dissipation • vortex analogies with HTSC • Search for superfluid sound mode • motivation • generator and detector – heater/bolometer • ballistic phonon propagation • search for propagation with low velocity

  3. Compound Torsional Oscillatormotivation probing NCRI of identical solid 4He as function of frequency • glassy solid 4He (Nussinov, et al, cond-mat/0610743) • critical displacement, velocity or acceleration? • vortex liquid (Anderson, Nature Physics 3, 160(2007)) “Clearly the crucial experiment for our hypothesis is to change the torsional vibration frequency, holding all other variables constant. This has not been done. It would seem to be urgent to do so, because no other hypothesis yet proposed is consistent with any appreciable fraction of the data.”

  4. Compound Torsion Oscillator dilution refrigerator in-phase mode: 496 Hz, Q~1.3106 out-phase mode: 1.2 kHz, Q~ 0.76 106 BeCu rods driver detector1 sample cell (stycast 1266) Cell volume=0.6 cm3 Inner Diameter=10 mm Inner Height= 8 mm S/V=7 cm-1 detector2

  5. “raw” data, 496 Hz mode

  6. “raw” data, 1.2 kHz mode

  7. NCRI fraction:rim velocity < 20 m/s

  8. Change in Dissipation due to Solid 4He rim velocity ~ 20 m/s

  9. dissipation vs. frequency shift

  10. Critical Velocity and Hysteresis T = 19 mK

  11. velocity =100- 200mm/s T = 63 mK Note: no hysteresis! reversible!

  12. hysteresis at 30 mK Start here.

  13. supersolid – type II HTSC vortex – flux lines analogy rotation --- magnetic field ac oscillation --- ac magnetic field angular momentum --- magnetization picture (T): increasing superfluid fraction (or NCRIf)  decreasing number of vortices

  14. T < 45 mK: vortices cannot enter as, V is increased. 1172.8 Hz rs/r [%] T < 45 mK: vortices can go out, as V is decreased. zero field cooled T > 45 mK: vortices can go in and out reversibly. 19 mK 62 mK T [mK] Velocity [mm/sec] field cooled analogies to vortices in sc T < 45 mK: hysteresis  “vortex glass state” T > 45 mK: reversible  “vortex liquid state”

  15. relaxation effects T = 30 mK

  16. relaxation at T = 10 mK drive level time

  17. “relaxation time” vs. T ring down time ~ 120 s

  18. long time behavior after decreasing drive

  19. V vortex liquid vortex glass T vortex-matter phase diagram supersolid

  20. Summary • Small ρs/ρ : ~ 0.1% • No frequency dependence in rs/r below 20 mK, v=20 mm/sec. • Possible frequency dependence at higher temperature and at high velocity. • Comparison with glassy solid 4He theory on-going. • Hysteresis and reversible regimes in NCRIf and oscillator response. • Analogy with vortex phase diagram of HTSC.

  21. Heat Pulse Experiment (Experimental Setup) Heater Pressure gauge Fill line 2.8 mm 4.3 mm bolometer 0.5 mm Magnet M.C. 3 mm Ti bolometer Pulse Method with 0.5~10 msec width heat pulse.

  22. signal (t, T)

  23. time derivative of signal(t,T)

  24. P=53. 6bar (rs/r Penn State) P=30bar (rs/r from Penn State) 37 bar 56 bar P=30 bar (Rutgers) 56 bar 37 bar pulse propagation velocity vs. T“expected” velocity shift = C – C0 ~ (1/2)(rs/r)C0

  25. Search for fourth sound 3D plotexpected T dependence of fourth sound

  26. Temperature dependence of the transverse ballistic phonon velocity below 200 mK did not change within ±0.15 % which is expected to increase 0.5 % from the theory at low temperature if the rs is 1 % (Pulse energy = 3 nJ/pulse). conclusions Transverse ballistic phonon propagation Search of the Fourth sound like propagation mode. Heat pulse response of solid 4He was measured up to 10 msec(=0.4 m/sec), using the high sensitivity Ti bolometer at 38 bar. Signature of new mode has not been observed within DT=5 mK.

  27. conclusions • compound torsional oscillator with cylinder • frequency dependence of NCRIf and dissipation • critical velocity (not amplitude or acceleration) • hysteresis – possible analogy with HTSC • fourth sound • not yet observed, but crucial • search is continuing by increasing sensitivity, etc

  28. Vortex Liquid comparison with vortex liquid theory Anderson (Nature Physics 3, 160(2007))

  29. Nussinov et. al. (cond-mat/0610743) comparison with glassy behaviour f0=495.8 Hz Using;s0, D Fitting parameters; A=2.0x10-3 sec-1 s0=6.7 msec D/kB=219 mK Fitting parameter; B=0.3 sec-2 f0=1172.8 Hz Using;A, s0, D Using;B, s0, D

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