The effect of 3 He impurity on supersolid E. Kim, Korea Advanced Institute of Science and Technology J. T. West, X. Lin, and M. H. W. Chan J. T. West, X. Lin, and M. H. W. Chan Penn State University J. S. Xia University of Florida

 NCRI  Low 3 He concentration mixtures in Vycor glass  The effect of 3 He in open cylindrical geometry

ideal for detection of superfluid mass Be-Cu Torsion rod Torsion cell containing helium Drive Detection I : rotational inertia of torsion cell K: torsion constant of the torsion Rod Change of rotational inertia, I, can be detected by increase (or decrease) of the resonant oscillation period,  o.

I(T)=I classical [1-f s (T)]

 We find evidence of superflow in bulk solid 4 He and solid 4 He in Vycor glass with pore diameter of 7nm and in porous gold with pore diameter of 490 nm.

Non-classical rotational inertia has been reproduced by  Non-classical rotational inertia has been reproduced by  Reppy group - Annealing Effect & Disorder effect (47% NCRIF)  Shirahama group - NCRI and weak annealing effect  Kubota group - Solid helium under rotation  Kojima group - Frequency dependence & hysteresis

 Non-Classical Rotational Inertia  Excess Heat Capacity Anomaly (Xi and Chan)  Ultrasound Anomaly (Goodkind)  Pressure driven DC Flow: No flow  Annealing Effect & confining effect  2 nd sound measurement ?  No anomaly in Pm  Superfluid flow in grain boundaries  Shear modulus at low temperatures Recent Experiments … and more questions to the nature of supersolid

Role of Defects? What kind of defect is responsible for the various NCRI values? What we can learn from 3 He impurity effect?

 -  *[ns]  *=971,000ns E. Kim & M.H.W. Chan Nature 427, 225 (2004) Data shifted vertically for easy comparison 4 He solid diluted with a low concentration of 3 He

Effect of 3 He impurities Supersolid fraction [%]

‘Bulk’ 4 He solid diluted with a low concentration of 3 He (85ppm) at 60 bar

Low f 0 Annular cell Open Cylinder TO1 Open cylinder TO2 Confining dimension 0.5cm0.7cm1 cm A/V (cm 2 /cc) Resonant Frequency 156Hz783Hz1298Hz Covered X 3 concentration 1ppb-47ppb47ppb - 30ppm1ppb-100ppb Three torsional oscillators

The effect of 3 He impurity Resonant frequency=156Hz T c ~85mK Supersolid fraction at 51 bars =10/11000 ~ 0.1% 3.25cm Channel width=0.5cm (ID=1.27cm OD=1.77cm) 3.0cm

47ppb 3 He in solid 4 He at 55bars Tc~105mK, Supersolid fraction 2.3ns/1100ns~0.2% Resonant frequency:783Hz, Q~1x10 6 Open cylinder (no annular channel) Torsion cell 0.76cm

Tc~105mK, Supersolid fraction 2.3ns/1100ns~0.2% Resonant frequency:783Hz, Q~1x10 6 Open cylinder (no annular channel)

Tc~140mK and Supersolid fraction 3.5ns/1110~0.3%

Tc~140mK and Supersolid fraction 4ns/1110~0.36% 150ppb 3 He in solid 4 He Resonant frequency:783Hz, Q~1x10 6 Open cylinder (no annular channel)

200ppb 3 He in solid 4 He at 61bars Tc~ 150mK and Supersolid fraction ~0.36% Supersolid fraction is smaller than that observed in annular channel.

200ppb 3 He in solid 4 He at 61bars Tc~ 150mK Supersolid fraction ~0.3% Supersolid fraction is smaller than that observed in annular channel.

Annular cell Vs. Open cell

3 He effect in solid 4 He Even though supersolid fraction is sensitive to the geometry and thermal history, The effect of 3 He on the onset temperature is robust.

Even though supersolid fraction is sensitive to the geometry and thermal history, The effect of 3 He on the onset temperature is robust. 3 He effect in solid 4 He

The effect of 3 He on the onset temperature is robust. 3 He effect in solid 4 He

10 and 30ppm 3 He in solid 4 He Effect of 3 He on supersolid transition

3.25cm Channel width=0.5cm (ID=1.27cm OD=1.77cm) 3.0cm Tc is too low? or Supersolid fraction is too small? Isotopically-pure 4 He?

Torsional oscillator f 0 = 1298Hz, Q~1x10 6 Total mass loading due to solid helium  He -  empty =3939ns Shift in the period  =1ns Supersolid fraction ~1ns/3939ns ~0.025% This work is done in the B/T facility of the high magnetic field lab. Dr. Xia (University of Florida) Torsion cell 1.0cm

Isotopically-pure* 4 He (*X 3 <1ppb) 1ppb Samples grown by CP or CT NCRIF 0 Be-Cu TO ( 0.3%) Ag TO (0.03%)

Isotopically-pure* 4 He (*X 3 <1ppb) 1ppb Samples grown by CP or CT NCRIF 0 Be-Cu TO ( 0.3%) Ag TO (0.03%)

Isotopically-pure* 4 He (*X 3 <1ppb) No extra temperature dependence down to 1mK. This work is done in the B/T facility of the high magnetic field lab. Dr. Xia (University of Florida)

Isotopically-pure* 4 He (*X 3 <1ppb) No extra temperature dependence down to 1mK. This work is done in the B/T facility of the high magnetic field lab. Dr. Xia (University of Florida)

The effect of 3 He impurity Tc~110mK Supersolid fraction ~0.11%

Effect of 3 He Addition of 3 He enhances T c NCRI marches up to higher temperature with increasing 3 He concentration.

Effect of 3 He Addition of 3 He enhances T c NCRI marches up to higher temperature with increasing 3 He concentration.

Temperature dependence

Effect of 3 He Phase separation ? regular solution theory

Common defect in crystals  dislocation line Ultrasound measurements:  Dislocation density in poor crystals ~ 10 9 per cm 2 (constant volume 1 )  Dislocation density in good crystals ~ per cm 2 (constant pressure 2 or temperature 3 above ~ 0.5K)  Dislocation density in best crystals ~ 0 to 100 (constant temperature 4 growth below ~ 0.2K) Dislocation 1. S.H. Castles & E.D. Adams, JLTP 19, 397 (1975). 2. I. Iwasa, K. Araki & H. Suzuki, J. Phys. Soc. Jap. 46, 1119 (1979). 3. V.L. Tsymbalenko, Low Temp. Phys. 21, 129 (1995). 4. J.P. Ruutu, P.J. Hakonen, A.V. Babkin, A.Ya. Parshin & G. Tvalashvili, JLTP 112, 117 (1998).

Dislocations intersect on a characteristic length scale of L N ( if  ~10 5 to10 7 cm -2 )  L N 2  0.19  L N ~ 1 to 10  m Dislocations can also be pinned by 3 He impurities L C ~ Distance between 3 He atoms Dislocation LcLc LNLN Dislocation density,  = 5 ~ cm -2 Solid helium grown by a constant volume method;  =10 5 to 10 7 cm -2

Dislocation slip Influence of an increasing external stress is shown in the fig. For small stress dislocation is pinned down by the impurity particles(A). Then for small stress the loops starts to deflects. At the break-away stress a large increase of the dislocation strain appears.

Torsion cell Torsional oscillator at 10  m/s:  ~ Pa Drive Detection Torsion rod Torsion cell In our torsional oscillator measurements, we gently oscillate a solid helium sample contained in a torsional cell. (stress applied < 0.1 dyne/cm~ Pa)

3 He and dislocation Actual 3 He concentration on dislocation line is thermally activated *Typical binding energy is very small, W 0, is 0.3K to 0.7K Pinning length due to 3 He impurity

3 He-dislocations interaction Line was drawn by considering W 0 =0.75K and average L 3He pinning length~ 0.15  m. Average length L Network ~ 0.15  m for  ~ 10 9 cm -2 (CV) Smaller lengths are expected for larger dislocation densities  cross-over from network pinning to 3 He pinning

3 He-dislocations interaction Much smaller lengths are expected in Vycor glass ( most of all dislocations are pinned) Why no difference in Vycor?

3.25cm Channel width=0.5cm (ID=1.27cm OD=1.77cm) 3.0cm Wall thickness of some cells very thick  It is highly unlikely that NCRI is due to stiffening Stiffening of solid helium in the cell?

Effect of 3 He Tc or onset temperature and supersolid fraction of superflow show strong dependence on concentration of 3 He.

Summary  Dramatic effect of 3 He impurities on supersolid 4 He. The addition of 3 He impurity broadens transition and enhances the onset temperatur e.  Not solely due to 3 He impurities  Not 3 He- 4 He phase separation of a solid mixture  The effect may be related with dislocation pinning by 3 He. After dislocation motion pinned by 3 He impurities supersolid phase appears  Pinning of dislocation increases shear modulus of solid helium?