Upload
patrick-combs
View
216
Download
0
Tags:
Embed Size (px)
Citation preview
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