Superfluidity in solid helium and solid hydrogen

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Superfluidity in solid helium and solid hydrogen

• E. Kim, A. Clark, X. Lin, J. West,
• M. H. W. Chan
• Penn State University

KAIST, Korea
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Outline

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

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Phase diagram of 4He
Fritz London is the first person to recognize
that superfluidity in liquid 4He is a BEC
phenomenon.
Solid
Condensation fraction was predicted and measured
to be 10 near T0. Superfluid fraction at T0,
however is 100.
Normal Liquid, (He I)
Superfluid (He II)
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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 T0.
  
• 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)

A.J.Leggett ,PRL 25, 1543 (1970)
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• Lindemann Parameter
• the ratio of the root mean square of the
  displacement of atoms to the interatomic distance
  (da)
• 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))

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• Superfluidity in solid
• not impossible!
• - If solid 4He 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)
• Phys. Rev. A 2,
  256 (1970)
• J. Sarfatt, Phys. Lett. 30A, 300 (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 Liftshitz, Zh.Eksp.Teor.Fiz. 56,
  205 (1969).

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• 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)

Quantum exchange of particles arranged in an
annulus under rotation leads to a measured moment
of inertia that is smaller than the classical
value
I(T)Iclassical1-fs(T)
fs(T) is the supersolid fraction Its upper limit
is estimated by different theorists to range from
10-6 to 0.4 Leggett 10-4
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No experimental evidence of superfluidity
in solid helium prior to 2004

• 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)
• PV(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

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Ultrasound velocity and dissipation measurements
in solid 4He with 27.5ppm of 3He
The results are interpreted by the authors as
showing BEC of thermally activated vacancies
above 200mK.
? 9.3 MHz x 28MHz ? 46MHz
P.C. Ho, I.P. Bindloss and J. M. Goodkind, J.
Low Temp. Phys. 109, 409 (1997)
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TEM of Vycor glass
Solid helium in a porous medium should have more
disorder and defects, which may facilitate the
appearance of superflow in solid?
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 4He 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.
Crystalline solid
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Torsional oscillator is ideal for the detection
of superfluidity
Resolution Resonant period (?o) 1
ms stability in ? is 0.1ns ??/?o 510-7
Mass sensitivity 10-7g
?f
Amp
f0
Qf0/?f 2106
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Torsional oscillator studies of superfluid films

• Vycor

??
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.
Berthold,Bishop, Reppy, PRL 39,348(1977)
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Solid helium in Vycor glass
f0 1024Hz Q 1106
0.38mm
2.2mm
Torsion Rod
Torsion Bob (vycor glass)
5cm
Drive
Detect
AA0sin?t vvmaxcos?t vmaxrA0?
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Solid 4He at 62 bars in Vycor glass
?966,000ns
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Supersolid response of helium in Vycor glass

• Period drops at 175mK
• ? appearance of NCRI
• size of period drop
• -?? 17ns

?971,000ns
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Superfluid response
Total mass loading 4260ns Measured
decoupling -??o17ns Apparent supersolid
fraction 0.4 (with tortuosity correction ?s/?
2 ) Weak pressure dependence
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Strong velocity dependence

• For liquid film adsorbed on Vycor glass
• vc gt 20cm/s
• Chan et. al. Phys. Rev. Lett. 32, 1347(1974).
• For superflow in solid 4He
• vc lt 30 µm/s

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Control experiment I Solid 3He?
Nature 427,225(2004)
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4He solid diluted with low concentration of 3He
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Effect of the addition of 3He impurities
At 0.3ppm, the separation of the 3He atoms is
about 450Å
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Search for the supersolid phase
in the bulk solid 4He.
Torsion cell with helium in annulus
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Torsional Oscillator (bulk solid helium-4)
Torsion rod
Torsion cell
3.5 cm
Detection
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Solid 4He at 51 bars
Porous media are not essential !
4µm/s corresponds to amplitude of oscillation of
7Å
NCRI appears below 0.25K Strong vmax
dependence (above 14µm/s) Amplitude minimum,
Tp
?0 1,096,465ns at 0 bar 1,099,477ns
at 51 bars
(total mass loading3012ns due to filling with
helium)
Science 305, 1941(2004)
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Non-Classical Rotational Inertia Fraction
vmax
?S/?
NCRIF
Total mass loading 3012ns at 51 bars
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Non-Classical Rotational Inertia Fraction
?S/?
vmax
Total mass loading 3012ns at 51 bars
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Control experiment II

• 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
Mg barrier
Al shell
Solid helium
Channel OD15mm Width1.5mm
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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.
?-?ns
Superflow viewed in the rotating frame
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With a block in the annulus, irrotational flow of
the supersolid fraction contributes about 1
(Erich Mueller) of the barrier-free
decoupling. ??1.5ns
?-?ns
Irrotational flow pattern in a blocked annular
channel (viewed in the rotating frame)
If no block, the expected ??90ns
A. L. Fetter, JLTP(1974)
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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 ??(T0) 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.
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Superflow persists up to at least 136 bars !
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Strong and universal velocity dependence in
all samples
vC 10µm/s 3.16µm/s for n1
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Pressure dependence

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

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Superfluidity in ultra-pure Solid Helium 1ppb 3He

• t0 0.77ms 1300Hz
• t4He - t0 3920ns
• NCRIF 1.25/3920 0.03

Exp. done at at U. of Florida
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Phase Diagram of 4He
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Heat Capacity signature?

• No reliable heat capacity measurement of solid
  4He below
• 200mK because of large background
• contribution due to the sample cell.

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Experimental cell of Xi Lin and Tony
ClarkSilicon!!
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Results pure 4He (0.3ppm 3He)
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Results pure 4He (0.3ppm 3He)
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Results pure 4He (0.3ppm 3He)
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Results pure 4He (0.3ppm 3He)
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Results pure 4He (0.3ppm 3He)
Heat capacity peak near the supersolid transition
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Is the supersolid phase unique with 4He?

• Apparently not!

Preliminary torsional oscillator data of Tony
Clark and Xi Lin indicate similar supersolid-like
decoupling in solid H2.
de Boer parameter

• 3He ? 3.09
• 4He ? 2.68
• H2 ? 1.73
• HD ? 1.41
• D2 ? 1.22

More quantum mechanical
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Hydrogen in a cylindrical cell
Inside Mg bob Hydrogen
space BeCu wall
Q 1.6million P0 560,400ns dP 0.05ns
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Hydrogen in a cylindrical cell
Inside Mg bob Hydrogen
space BeCu wall
DPHD 4014ns (93 filling)
HD
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Hydrogen in a cylindrical cell
Inside Mg bob Hydrogen
space BeCu wall
DPH2 1638ns (64 filling)
HD H2
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Hydrogen in a cylindrical cell
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
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Hydrogen in an annular cell
Samples contain lt 50ppm HD
Inside Mg bob Hydrogen
space (h3.5mm
w2.3mm)
Mg
X is the ortho conc,
BeCu wall
Q 350,000 P0 709,700ns dP lt0.1ns
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Hydrogen in an annular cell
Comparison of 50 and 200ppm HD
Inside Mg bob Hydrogen
space BeCu wall
Mg
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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.
• 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.
• Superflow is also seen in para-hydrogen.
• The supersolid fraction is on the order of
• 0.05

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