Superfluidity in solid helium and solid hydrogen E. Kim*, A. Clark, X. Lin, J. West, E. Kim*, A....

Superfluidity in solid helium and Superfluidity in solid helium and solid hydrogensolid hydrogen

E. Kim*,E. Kim*, A. Clark, X. Lin, J. West, A. Clark, X. Lin, J. West, M. H. W. ChanM. H. W. Chan

Penn State UniversityPenn State University

* KAIST, Korea

IntroductionIntroduction Theoretical background for supersolidTheoretical background for supersolid Experimental setup Experimental setup - Torsional oscillator technique- Torsional oscillator technique Supersolid in porous mediaSupersolid in porous media Supersolid in bulk Supersolid in bulk 44He He Heat Capacity of solid helium.Heat Capacity of solid helium. Results in para-hydrogenResults in para-hydrogen Summary Summary

OutlineOutline

Solid

Superfluid (He II)

Normal Liquid,(He I)

Fritz London is the first Fritz London is the first person to recognize that person to recognize that superfluidity in liquid superfluidity in liquid 44He He is a BEC phenomenon. is a BEC phenomenon.

Condensation fraction was predicted and measured to be 10% near T=0. Superfluid fraction at T=0, however is 100%.

Phase diagram of 4He

Can a solid be ‘superfluid’?*Can a solid be ‘superfluid’?*

- - In a perfect solid when each atom is localized at a specific In a perfect solid when each atom is localized at a specific lattice site and symmetry is ignored, then there is no BEC lattice site and symmetry is ignored, then there is no BEC at T=0. at T=0.

Penrose and Onsager, Penrose and Onsager, Phys. Rev.Phys. Rev. 104104, 576 (1956, 576 (1956))

- - Off Diagonal Long Range Order, or superfluidity, which is Off Diagonal Long Range Order, or superfluidity, which is directly related to Bose-Einstein Condensation, may occur directly related to Bose-Einstein Condensation, may occur in a solid phase if particles are not localized. in a solid phase if particles are not localized.

C. N. Yang,C. N. Yang, Rev. Mod. Phys.Rev. Mod. Phys. 3434, 694 (1962), 694 (1962)

*A.J.Leggett ,PRL 25, 1543 (1970)

Lindemann ParameterLindemann Parameter the ratio of the root mean square of the the ratio of the root mean square of the

displacement of atoms to the interatomic distance displacement of atoms to the interatomic distance (d(daa) )

A classical solid will melt if the Lindemann’s parameter A classical solid will melt if the Lindemann’s parameter

exceeds the critical value of ~0.1 .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))

26.02

a

L d

uZero-point Energy

Inter-atomic potential

total energy

zero-point energy

Superfluidity in solid: Superfluidity in solid: not impossible!not impossible!

- - If solid If solid 44He can be described by a Jastraw-type He can be described by a Jastraw-type

wavefunction that is commonly used to describe liquid wavefunction that is commonly used to describe liquid helium then crystalline order (with finite fraction of helium then crystalline order (with finite fraction of vacancies) and BEC can coexist.vacancies) and BEC can coexist.

G.V. Chester, G.V. Chester, Lectures in Theoretical PhysicsLectures in Theoretical Physics Vol XI-B(1969); Vol XI-B(1969);

Phys. Rev. APhys. Rev. A 22, 256 (1970), 256 (1970) J. Sarfatt, J. Sarfatt, Phys. Lett.Phys. Lett. 30A30A, 300 (1969), 300 (1969) L. Reatto, L. Reatto, Phys. Rev.Phys. Rev. 183183, 334 (1969), 334 (1969)

- Andreev and Liftshitz assume the specific scenario of - Andreev and Liftshitz assume the specific scenario of zero-point vacancies and other defects ( e.g. interstitial zero-point vacancies and other defects ( e.g. interstitial atoms) undergoing BEC and exhibit superfluidity. atoms) undergoing BEC and exhibit superfluidity.

Andreev & Liftshitz, Andreev & Liftshitz, Zh.Eksp.Teor.Fiz.Zh.Eksp.Teor.Fiz. 5656, 205 (1969)., 205 (1969).

The ideal method to detect superflow would be to The ideal method to detect superflow would be to subject solid helium to undergo dc or ac rotation to subject solid helium to undergo dc or ac rotation to look for evidence of look for evidence of ‘Non-Classical Rotational Inertia‘Non-Classical Rotational Inertia’. ’.

Leggett,Leggett, Phys. Rev. Lett. Phys. Rev. Lett. 2525, 1543 (1970), 1543 (1970)

fs(T) is the supersolid fractionIts upper limit is estimated by different theorists to range from 10-6 to 0.4; Leggett: 10-4

Solid Helium

R

I(T)=Iclassical[1-fs(T)]

Quantum exchange of particles arranged in an annulus under rotation leads to a measured moment of inertia that is smaller than the classical value

• 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 Ultrasound Measurements at UCSD. Goodkind Phys. Rev. Lett. 89,095301(2002) and references therein

No experimental evidence of superfluidity in solid helium prior to 2004

9.3 MHzx 28MHz 46MHz

P.C. Ho, I.P. Bindloss and J. M. Goodkind, J. Low Temp. Phys. 109, 409 (1997)

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.

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 4He2) 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.

Solid helium in a porous medium should Solid helium in a porous medium should have more disorder and defects, which have more disorder and defects, which may facilitate the appearance of may facilitate the appearance of superflow in solid?superflow in solid?

Crystalline solid

TEM of Vycor glass

Torsional oscillator is ideal for the detection of superfluidity

Be-Cu Torsion Rod

Torsion Bobcontaining helium

Drive

Detection

K

Io 2

Q=f0/f ~ 2×106

Resolution

Resonant period (o) ~ 1 ms

stability in is 0.1ns

/o = 5×10-7

Mass sensitivity ~10-7gf0

f

Am p

Torsional oscillator studies of Torsional oscillator studies of superfluid films superfluid films

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.

VycorVycor

Berthold,Bishop, Reppy, PRL 39,348(1977)

Δ

Solid helium in Vycor glassSolid helium in Vycor glass

5cm

Detect

Torsion Bob(vycor glass)

Torsion Rod

Drive

2.2mm

0.38mm

f0 = 1024HzQ ~ 1*106

A=A0sinωtv=|v|maxcosωt|v|max=rA0ω

Solid 4He at 62 bars in Vycor glass

Period shifted by 4260ns due to mass loading of solid helium

*=966,000ns

Supersolid response of helium in Vycor glassSupersolid response of helium in Vycor glass

• Period drops at 175mK appearance of NCRI

• size of period drop - ~17ns

*=971,000ns

Superfluid response

-

*[n

s]

*=971,000ns

Total mass loading =4260ns

Measured decoupling

-o=17ns

“ Apparent supersolid fraction”= 0.4%

(with tortuosity correction s/ =2% )

Weak pressure dependence

Δ

0[ns]

Strong velocity dependence

• For liquid film adsorbed on Vycor glass

vc > 20cm/s

Chan et. al. Phys. Rev. Lett. 32, 1347(1974).

• For superflow in solid 4He

vc < 30 µm/s

Control experiment I : Solid Control experiment I : Solid 33He?He?

Nature 427,225(2004)

4He solid diluted with low concentration of 3He

Effect of the addition of Effect of the addition of 33He impuritiesHe impurities

At 0.3ppm, the separation of the 3He atoms is about 450Å

Be-Cu Torsion Rod

OD=2.2mm

I D=0.4mm

Filling line

Detection

Drive

Torsion cell with helium in annulus

Mg disk

Filling line

Solid helium in annulus channel

Al shell

Channel OD=10mm

Width=0.63mm

Search for the supersolid phase Search for the supersolid phase in the bulk solid in the bulk solid 44He.He.

Torsional Oscillator (bulk solid helium-4) Torsional Oscillator (bulk solid helium-4)

Drive

Detection

3.5 cm

Torsion rod

Torsion cell

Solid 4He at 51 bars

NCRI appears below 0.25K

Strong |v|max dependence(above 14µm/s)

Amplitude minimum, Tp 0= 1,096,465ns at 0 bar

1,099,477ns at 51 bars(total mass loading=3012ns

due to filling with helium)

Science 305, 1941(2004)

4µm/s corresponds to amplitude of oscillation of 7Å

Porous media are not essential ! Porous media are not essential !

Non-Classical Rotational Inertia FractionNon-Classical Rotational Inertia Fraction

loading mass total

NCRIF

Total mass loading=3012ns at 51 bars

NC

RIF

ρS/ρ|v|max

loading mass total

NCRIF

Total mass loading=3012ns at 51 bars

ρS/ρ |v|max

Non-Classical Rotational Inertia FractionNon-Classical Rotational Inertia Fraction

Control experiment Control experiment IIII With a barrier in the annulus, With a barrier in the annulus, there should be there should be NONO simple simple

superflow and the measured superfluid decoupling should superflow and the measured superfluid decoupling should be vastly reducedbe vastly reduced

Torsion cell with blocked annulus

Solid helium

Mg barrier

Al shell

Mg Disk

Mg disk

Filling line

Solid helium in annulus channel

Al shell

Mg barrier

Channel OD=15mmWidth=1.5mm

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.

Superflow viewed in the rotating frame

-

*[ns

]

With a block in the annulus, irrotational flow of the supersolid fraction contributes about 1% (Erich Mueller) of the barrier-free decoupling.Δ~1.5ns

Irrotational flow patternin a blocked annular channel (viewed in the rotating frame)

-

*[ns

]

A. L. Fetter, JLTP(1974) * If no block, the expected Δ=90ns

Similar reduction in superfluidSimilar reduction in superfluid response is seen in response is seen in liquid helium at 19 bars in the same blocked cellliquid helium at 19 bars in the same blocked cell

measured superfluid decoupling in the blocked cell

Δ(T=0)≈ 93ns.

While the expected decoupling in unblocked cell is 5270ns.

Hence the ratio is 1.7% similar to that for solid.

[n

s]

Conclusion : superflow in solid as in superfluid is irrotational.

Superflow persists up to at least 136 bars !Superflow persists up to at least 136 bars !

ρs/ρ

136bar

ρs/ρ

108bar

Strong and ‘universal’ velocity dependence Strong and ‘universal’ velocity dependence in all samplesin all samples

vC~ 10µm/s

=3.16µm/s for n=1

nRm

hv

nm

hdlv

s

s

2

ω

R

Pressure dependencePressure dependence As a function of pressure the supersolid fraction shows a As a function of pressure the supersolid fraction shows a

maximum near 55bars. The supersolid fraction extrapolates maximum near 55bars. The supersolid fraction extrapolates to zero near 170 bars.to zero near 170 bars.

Superfluidity in ultra-pure Solid Helium: 1ppb Superfluidity in ultra-pure Solid Helium: 1ppb 33HeHe

00 ~ 0.77ms [1300Hz] ~ 0.77ms [1300Hz] 4He4He - - 00 = 3920ns = 3920ns NCRIF ~ 1.25/3920 = 0.03%NCRIF ~ 1.25/3920 = 0.03%

0 50 100 150 200 250

4722.0

4722.5

4723.0

4723.5

4724.0

* = 770,000ns

-

* [n

s]

Temperature [mK]

Exp. done atat U. of Florida

Phase Phase Diagram Diagram of of 44HeHe

Heat Capacity signature?Heat Capacity signature?

No reliable heat capacity No reliable heat capacity measurement of solid measurement of solid 44He below He below

200mK because of large background200mK because of large background

contribution due to the sample cell.contribution due to the sample cell.

Experimental cell of Xi Lin and Tony ClarkExperimental cell of Xi Lin and Tony ClarkSilicon!!Silicon!!

Results: pure Results: pure 44He (He (0.3ppm 0.3ppm 33HeHe) )

Results: pure Results: pure 44He (He (0.3ppm 0.3ppm 33HeHe) )

Results: pure Results: pure 44He (He (0.3ppm 0.3ppm 33HeHe))

Results: pure Results: pure 44He (He (0.3ppm 0.3ppm 33HeHe))

Results: pure Results: pure 44He (He (0.3ppm 0.3ppm 33HeHe) )

Heat capacity peak near the supersolid transition

Is the supersolid phase unique with Is the supersolid phase unique with 44He?He?

Apparently not!Apparently not!

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

3He 3.09

4He 2.68

H2 1.73

HD 1.41

D2 1.22

de Boer parameter

More quantum mechanical

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

-0.5

0.0

0.5

1.0

1.5

2.0

Oscillation Period vs. Temperature

(PO = 560,400ns)

Pe

rio

d C

ha

ng

e [

ns]

Temperature [K]

Empty Cell

Q = 1.6millionP0 = 560,400nsP ~0.05ns

InsideMg bob:

Hydrogen space

BeCu wall

Hydrogen in a cylindrical cell

InsideMg bob:

Hydrogen space

BeCu wall

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

-0.5

0.0

0.5

1.0

1.5

2.0

Oscillation Period vs. Temperature

(PO = 560,400ns)

Per

iod

Cha

nge

[ns]

Temperature [K]

Empty Cell Cell Full of HDHD

PHD = 4014ns(93% filling)

Hydrogen in a cylindrical cell

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

-0.5

0.0

0.5

1.0

1.5

2.0

Oscillation Period vs. Temperature

(PO = 560,400ns)

Per

iod

Cha

nge

[ns]

Temperature [K]

Empty Cell Cell Full of HD Cell Full of H2HDH2

PH2 = 1638ns(64% filling)

InsideMg bob:

Hydrogen space

BeCu wall

Hydrogen in a cylindrical cell

Hydrogen in a cylindrical cell

0.00 0.05 0.10 0.15 0.20 0.25 0.30-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5Oscillation Period vs. Temperature

(PO = 560,400ns)

Per

iod

Cha

nge

[ns]

Temperature [K]

Empty Cell Cell Full of HD Cell Full of H2HDH2

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%

0.0 0.1 0.2 0.3 0.4 0.5

0.00

0.01

0.02

0.03

0.04

0.05

NC

RIF

[%]

Temperature [K]

83% filling, x1~2.0%

68% filling, x1<0.5%

88% filling, x1<0.5%

InsideMg bob:

Hydrogen space (h=3.5mm w=2.3mm)

Mg

Q = 350,000P0 = 709,700nsP <0.1ns

Hydrogen in an annular cell

Samples contain < 50ppm HD

BeCu wall

X is the ortho conc,

InsideMg bob:

Hydrogen space

BeCu wall

Mg

Hydrogen in an annular cell

Comparison of 50 and 200ppm HD

0.0 0.1 0.2 0.3 0.4 0.5

0.00

0.01

0.02

0.03

0.04

0.05

NC

RIF

[%

]

Temperature [K]

88% filling, x1<0.5%

68% filling, x1<0.5%

94% filling, x1<1.0%**

83% filling, x1~2.0%

**200ppm HD

SummarySummary Superflow is seen in solid helium confined in Vycor glass Superflow is seen in solid helium confined in Vycor glass

with pores diameter of 7nm and also in bulk. Results in with pores diameter of 7nm and also in bulk. Results in bulk have been replicated in three other labs.bulk have been replicated in three other labs.

Supersolid fraction is on the order of 1% for He-4 sample Supersolid fraction is on the order of 1% for He-4 sample with 0.3ppm of He-3 impurities. For ultra-high purity with 0.3ppm of He-3 impurities. For ultra-high purity sample (1ppb He-3) the supersolid fraction is on the sample (1ppb He-3) the supersolid fraction is on the order of 0.03% and the transition temp. is depressed.order of 0.03% and the transition temp. is depressed.

There is preliminary evidence of a heat capacity peak at There is preliminary evidence of a heat capacity peak at the transition.the transition.

Superflow is also seen in para-hydrogen.Superflow is also seen in para-hydrogen. The supersolid fraction is on the order of The supersolid fraction is on the order of 0.05%0.05%

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

Xi, Tony, Eunseong, Josh