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C C Can supersolidity be Can supersolidity be lidit lidit b b suppressed in stiffened suppressed in stiffened suppressed in stiffened suppressed in stiffened solid 4 He? solid He? solid solid He? He? Eunseong Eunseong Eunseong

  1. C C Can supersolidity be Can supersolidity be lidit lidit b b suppressed in stiffened suppressed in stiffened suppressed in stiffened suppressed in stiffened solid 4 He? solid He? solid solid He? He? Eunseong Eunseong Eunseong Eunseong Kim Kim Kim Kim Center for Center for Center for Center for Supersolid Supersolid Supersolid Supersolid & Quantum & Quantum matter & Quantum & Quantum matter matter Research matter Research Research Research KAIST, Republic of KAIST, Republic of Korea KAIST, Republic of KAIST, Republic of Korea Korea Korea

  2.  Shear  Shear Shear Modulus Shear Modulus Modulus Anomaly odulus Anomaly Anomaly Anomaly  Simultaneous Measurements : Simultaneous Measurements : NCRI& Shear NCRI& NCRI& Shear NCRI& Shear Modulus hear Modulus Modulus Modulus - What is common? hat is common? - What is different? hat is different?  Summary  Summary Summary Summary

  3. J. Day, and J. Beamish, Nature 450 , 853 (2007). J. Day, and J. Beamish, Nature 450 , 853 (2007). 2 d D I   2 A 15   2 A fV fV

  4. A. Granato, K. Lucke, J. of Appl. Phys. 27, 27, 583 (1956). With most dislocations strongly pinned by impurities strongly pinned by impurities at low temperatures, the shear modulus is close to that of a perfect crystal. The detachment of impurities by thermal evaporation • reduces μ by a fraction proportional to Λ L 2 at high μ y p p g temperatures.     2 C L 

  5. • Drive dependence • Frequency dependence • 3 He concentration dependence Y A ki J C G Y. Aoki, J. C. Graves, and H. d H Kojima, PRL 99, 99, (2007) Two phenomena should be closely related !

  6. Reduction in the resonant period can be understood by stiffening of can be understood by stiffening of solid helium ? Shear modulus stiffening possibly mimic the Shear modulus stiffening possibly mimic the NCRI.           df d ln f d ln f      5 ~10 ppm        f d ln d ln However, the estimated value is too small. Elastic stiffening alone cannot explain the NCRI. Clark et al., PRB (2008) ( )

  7. NCRI occurs only in a NCRI occurs only in a stiffened Bose solid. NCRI occurs only in a NCRI occurs only in a stiffened Bose solid. stiffened Bose solid. stiffened Bose solid. Effect in Fermi solid 3 He ? Effect in Fermi solid Effect in Fermi solid Effect in Fermi solid He ? He ? He ? J. T. West, O. Syshchenko, J. Beamish, M. H. W. Chan, Nat Phys 5, 598 (2009) NCRI is quantum Shear modulus is crystal statistics dependent. structure dependent. p

  8. How NCRI and How NCRI and How NCRI and shear modulus are How NCRI and shear modulus are shear modulus are shear modulus are relate re re relate l l l l ated? ated? d? d? d d d? d? Striking similarities found, but NCRI shows Striking similarities found, but NCRI shows Striking similarities found, but NCRI shows Striking similarities found, but NCRI shows quantum statistics dependence quantum statistics dependence quantum statistics dependence quantum statistics dependence  The  The The appearance The appearance appearance of ppearance of of NCRI of NCRI NCRI seems NCRI seems seems to eems to to require the require the stiffening of solid helium. stiffening of solid helium.  It It It i It is s bett b tt tt tter er to measure t o measure both b th b t th p phenomena h enomena simultaneously simultaneously

  9.  Torsional Oscillator ◦ Resonant Freq: 911 Hz q ◦ Q factor: 6 x 10 5 ◦ Annular channel  Diameter:16 mm Diameter:16 mm  width: 400 μ m  PZT shear transducer ◦ Area : 1 cm x 1 cm ◦ Area : 1 cm x 1 cm ◦ gap : 400 μ m ◦ d 15 at low temperature 1.5x 10 -10 m/V ◦ frequency range: ◦ 10 Hz ~ 40 kHz 10 Hz 40 kHz

  10.  Sample preparation l ◦ 10 samples with Blocked capillary method capillary method ◦ Pressure of samples: 30 ~ 49 bar  Same thermodynamic path path  Same 3 He concentration  Compatible S/V ratio  Compatible S/V ratio

  11. Tem perature dependence Tem perature dependence  NCRI and the shear NCRI and the shear 1.0 modulus increase were modulus increase were modulus increase were modulus increase were -6 3.0x10 ] hase [deg] observed in a similar observed in a similar 0.5 -6 2.0x10 Q temperature range. temperature range. temperature range. temperature range. -1 -6 1.0x10 1 0x10  ph 0.0 0.0 50 Shear modulus 1.5 NCRI 40  /  0 [%] ] NCRIF [% 1.0 30 0.5 20  %] 10 10 0 0 0.0 0 -0.5 0.2 0.5 0.02 0.1 T [K] T [K]

  12. Tem perature dependence Tem perature dependence Temperature Temperature dependence in dependence in 1.0 shear modulus increase can be shear modulus increase can be -6 3.0x10 ] hase [deg] understood by 3 He impurity understood by He impurity 0.5 -6 2.0x10 pinning of dislocation network pinning of dislocation network Q -1 -6 1 0x10 1.0x10  ph ( ith b (with broad range of activation (with broad range of activation ( ith b d d f f ti ti ti ti 0.0 energies). energies) . 0.0 50 Indeed, characteristic Indeed, c haracteristic Shear modulus 1.5 NCRI 40 te temperature mperature of NCRI traces the p of NCRI traces the  /  0 [%] ] NCRIF [% 1.0 30 pinning temperature of 3 He on pinning temperature of He on 0.5 20 dislocation lines. dislocation lines .  %] 10 10 0 0 0.0 0 NCRI probably appears in a -0.5 0.02 0.1 stiffened solid! tiff d lid! T [K] T [K]

  13.  No No correlation between the magnitude o No No correlation between the magnitude o correlation between the magnitude of NCRI correlation between the magnitude of NCRI f NCRI NCRI and shear modulus change and shear modulus change and shear modulus change and shear modulus change  Critical Stress Critical Stress Critical Stress Critical Stress Supersolidity can be suppressed in a stiffened Supersolidity can be suppressed in a stiffened Supersolidity can be suppressed in a stiffened Supersolidity can be suppressed in a stiffened solid helium. solid helium. solid helium. solid helium.  Relaxation Relaxation Relaxation Relaxation NCRI shows extremely slower relaxation NCRI shows extremely slower relaxation NCRI shows extremely slower relaxation NCRI shows extremely slower relaxation

  14. Average NCRIF ~ 2%, SM increase 25.7% SM increase ~ 25.7% over 10 samples      df d ln f        ln f d 0.20 F [%] 0.15 0.10 ced NCRI 0.053% 0.05 0.00 • Eigen frequency analysis Ei f l i -0.05 mimic 25.7% -0.10 -0.15  Empty cell : Empty cell : 908.88 Hz 908.88 Hz -60 -40 -20 0 20 40 60 80 100 SM increase [%] SM increase [%]  Solid Helium (SM=1.5x10 7 Pa) : 907.06 Hz

  15. No linear relation between NCRI and No linear relation between NCRI and SM increase SM increase The magnitude of The magnitude of The magnitude of The magnitude of NCRI seems to have a NCRI seems to have a NCRI seems to have a NCRI seems to have a correlation correlation rather correlation correlation rather rather rather with the absolute with with with the absolute the absolute the absolute va value o va value o l l l l ue of s ue of s f f f f shear shear h h ear ear modulus modulus modulus modulus at at low at at low low low temperatures than temperatures t temperatures than temperatures t h an an the shear modulus the shear modulus the shear modulus the shear modulus increase at increase at low increase at increase at low l ow ow temperatures. temperatures. temperatures. temperatures.

  16. Interference I Interference I NO interference from hi high drive am g g h drive amplitude in p p litude in PZT PZT. The softening of solid helium in the center h li i h channel does not affect NCRI NCRI PZT shear transducer Normal stress on solid Softened solid h li helium in the center i th t channel induced by the large torsional large torsional Wh When the reduction in the period th d ti i th i d oscillation do reduce the is due to SM increase of 25%. shear modulus. The period shift is expected to be Th i d hift i t d t b Torsional Oscillator Solid Helium reduced to 1.2%

  17. NCRI and shear modulus change with g Drive dependence Drive dependence drive sweep Critical stress of shear modulus shear modulus   0.37 Pa c

  18. Different low temperature excitation Different low temperature excitation Drive dependence Drive dependence destroys NCRI in a destroys NCRI in a stiffened solid helium stiffened solid helium Critical stress of shear modulus shear modulus   0.37 Pa c Critical stress of NCRI   0.002 Pa c Stress for solid helium is calculated from the S rim velocity of the oscillators. ( σ = ρ t ω v /2)

  19. Different low temperature excitation Different low temperature excitation destroys NCRI in a destroys NCRI in a stiffened solid helium stiffened solid helium Critical stress for NCRI is always 2 Critical stress for NCRI is always 2 orders of orders of magnit magn it it d itude sma e small ller ll er th than th an th th t that o of s f shear mo h ear modulus d l us

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