Superfluid Density of 3He in aerogel

1
Superfluid Density of 3He in aerogel
Jeevak Parpia, LASSP, Cornell University
Support NSF DMR 0202113 NSF INT-0128811 NATO-SA
(PST.CLG.979379)6993/FP
Thanks to E. Nazaretski, D. M. Lee
2
Overview Outline of Talk
Experiments Sound Cell TO A phase, B phase
superfluid density Hysteresis Results in field
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Bulk A phase ?s/? Results
In the bulk, A phase superfluid density can be
greater or less than that of the B phase,
(depends on texture), but ratio ?s/ ?s?is gt 0.5.
Without a field, textural alignment is unlikely.
H//
(?s?)
H?
(?s//)
H?
(?s//)
H//
(?s?)
Berthold, Giannetta, Smith, Reppy, PRL 37, 1138
(1976).
4
Modification of Phase Diagram by Disorder
Tcaerogel (P)
TA?B
Metastable A
Equilibrium A phase
Tcbulk (P)
Equilibrium B phase
Nazaretski, Mulders, and Parpia. JETP Lett. 79,
470 (2004).
5
Original ?s/? measurements
Bulk behavior
29
5
25
20.2
0
20.5
15
10
15
12.9
10
8
6.9
6.1
5
3.9
3.5
Superfluid fraction shows a different power law,
and is much reduced (compared to bulk)
Porto, Ph. D. thesis (Cornell).
6
Onset of superfluid is sharp
Question How sharp is the superfluid transition?
Heat capacity shows a width of 60 µK.
Superfluid density shows a much narrower
transition.
Period shift from torsion oscillator at 3.4bar
and 15 bar
Porto, Ph. D. thesis (Cornell).
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Simultaneous Torsion Pendulum Heat Capacity
with bulk - like contribution removed
Non-BCS-like behavior
Torsional oscillator dissipation
Tc (agel)
Tc (bulk)
J. He, A. D. Corwin, J. M. Parpia, and J. D.
Reppy Phys. Rev. Lett. 89, 115301 (2002)
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?s/? (base catalyzed aerogel) scales well with Tc0
Left plot shows ?s/? (with Fermi factors removed)
for 98, 99.5 open aerogels and bulk Right plot
shows how superfluid fraction scales with Tc
reduction.
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Early example of ?s/? A?B Transition

• Hybrid wire viscometer in magnetic field

A phase ?s/? much less than B phase result. A
phase ?s/? seen on warming is same as seen while
cooling
P. Brussaard et al Phys. Rev. Lett. 86, 4580,
2001
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Signature of the A-B transition
TA-B(bulk)
Tc(agel)
TA-B(agel)
Temperature (mK)
Transverse sound Northwestern
Tc(bulk)
Gervais,Haard,Nomura,Mulders,Halperin. PRL 87
35701 (2001)
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Systematic investigation of the phase diagram
200uK offset between TA?B, TB?A No TB?A on
warming for less than 1.4kG fields.
Gervais et al Phys. Rev. Lett. 87, 035701 (2001)
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Low frequency sound modes in aerogel
Caero 50m/s ltlt CHe, First sound ? fast
mode Fourth sound ? slow mode
A. I. Golov et al, PRL, 82 3492 (1999).
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Sound in 3He - Filled Aerogel
The slow mode shows the onset of superfluidity
and the A?B transition.
Helmholtz Mode
Slow Mode
Nazaretski, Mulders, Parpia JETP Lett. 79, 470
(2004)
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3He A, B phase Superfluid density in Aerogel
No sign of A phase on warming? Finite width of
TA?B
Nazaretski, Mulders, Parpia JETP Lett. 79, 470
(2004)
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Making mixtures of A and B
Main figure Mixture made by cooling into
TA?B. Inset Mixture made by warming into TB?N or
TB?A band.
Nazaretski, Mulders, Parpia JETP Lett. 79, 470
(2004)
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Superfluid density ratio
Superfluid density in A phase is ½ that of B
phase Results at 3 different pressures at right.
Nazaretski, Mulders, Parpia JETP Lett. 79, 470
(2004)
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Polycritical point
Polycritical point (bulk)
For 3He in aerogel, the polycritical point is
eliminated
Gervais, Yawata, Mulders and Halperin, PRB 66
054528 (2002)
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Ratio of rs/r A and B phase, hysteresis does not
change with field.No B ? A transition seen on
warming? Evidence for superheating? Is the A
phase the stable phase between normal and the B
phase?
Range of expected B?A transition
Nazaretski, Lee, Parpia to be published.
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B?A transition only seen in higher field
Nazaretski, Lee, Parpia to be published.
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Single power law near Tc

• Power law does not show any anomalies unlikely
  that there is a hidden B?A transition.

Plt15 bar
Pgt15 bar
Porto, Ph. D Thesis
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Temperature development of ?s /?
3.4 -15 bar
A. I. Golov et al, PRL, 82 3492 (1999).
20.5, 25, 29 bar
Porto, Ph. D Thesis
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Data from Florida
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Low pressure, low temperature behavior
Dashed lines data at 3.4, 4 bar Solid line
anomalous run at 2.73bar Note lower Tc higher rs.
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89 4He in aerogel - Path to study of 0D 3He
superfluid
High temp slow mode
Helmholtz Mode
Tc(bulk 3He)
No evidence of 3He slow mode (below percolation
threshold), but onset of 3He superfluidity
visible at Tc in aerogel. Implies isolated 3He
regions are superfluid.
Tc (3He in aerogel)
Lawes, Golov, Nazaretski, Mulders, Parpia, Phys.
Rev. Lett., 90, 195301, (2003).
Onset of shift of high temp slow mode
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Schematic Phase Transformations
Warming in field
A-like Phase
B Phase
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Conclusions

• 1. Aerogel introduces disorder into the purest
  material -- 3He.
• 2. So called A-B phase interface strongly pinned.
• 3. Why is the ?s/? in the A phase so much lower
  than B phase?
• 3. Significant alteration of phase diagram by
  aerogel.
• Puzzles Some Future experiments
• Is the A phase in aerogel the same as bulk?
• Why is it so reliably nucleated on cooling? Why
  not on warming?
• Region between the Tcs? Is there meta
  superfluidity?
• Opportunity to study effects of fractally
  correlated disorder.

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Surface Tension

• ?s/? ? ?0.5?bulk
• sABFs?(T) where Fs is the difference between
  normal and superfluid free energies at TAB,
• Setting , we get
• Also Rcaerogel? 5 Rcbulk strong pinning of
  interface by aerogel strands.

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Data from Osheroffs group
NMR data on 99.3 open aerogel in 28.4mT show
hysteresis in warming and cooling lineshape,
average frequency shift. Osheroff and
Baumgardner identify onset of A-like
characteristics at 2.225mK while warming. Tc is
2.362mK Above that point, they can make (and
stabilize) arbitrary mixture of A and B phases.
Baumgardner, Lee, Osheroff, Hrubesh Poco, PRL 93
055301-1, 2004
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Stanford strong pinning data.
By warming above TB?A, they make arbitrary
admixtures of A and B phase. Apparently never
recover pure A phase unless they warm above Tc.
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Stanford Phase diagram
Onset of A-like phase on warming shows positive
dP/dT (compared to) bulk. Max frequency shift in
A phase is 64 of bulk value.
Phase diagram for 99.3 open aerogel
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Planar phase?
Rmax related to maximum frequency shift, S
related to slope of TAB
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Reconcile rs to NMR data

• 1 The B phase superheats and so the A phase does
  not appear on warming unless a field is applied.
• 2 The texture of the A phase is different when
  it warms compared to when it coolsthus the A
  phase superfluid density is close to that of the
  B phase while warming.
• 3 In low and zero fields, the A like phase is
  restored on warming only in a region very close
  to Tc 20 µK wide.

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Dirty Helium in Rotation

• Rotation shows shift in spectrum while
  accelerating to above 3.3rad/sec. On
  deceleration, shifted signal appears even at
  0rad/sec ? vortices trap persistent current

M. Yamashita etal, J. Low Temp. Phys., 134, 749
(2004).
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Boundary Conditions for Bulk Superfluid 3He
At a diffuse surface, ?(max gap) is suppressed
over a length of order ?(T). On the left, the gap
suppression for diffuse boundary
conditions. Below, the superfluid fraction
expected for cylindrical and slab geometries as a
function of size.
D//
D-
T/Tc0.8
Fetter , Ullah, Jap. J. of App. Phys., 26, supp
26-3, 149 (1987). Zhang, Kurkijarvi and
Thuneberg, PRB, 36, 1987 (1987).
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Structure of 98 open silica aerogel
15nm thick slice of 98 open aerogel
Correlations of silica aerogel
Porto Parpia, PRB 59 14583 (1999)
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Information on Surface to Volume
Model of aerogel chains of clusters, radius r,
on a rectangular lattice of side l.
For 0.02 volume fraction ? ?r/l .05 and r
1.25nm ? 600m2/gm area. If we take ??015 nm, all
open regions are within a coherence length of the
aerogel.
l
2r
This is consistent with the diffusion limited
aggregation model of the structure of aerogel.
If aerogel acted as a diffuse scattering surface,
superfluidity of 3He would be suppressed to T?0
at all pressures.
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Superfluidity of 3He survives in the presence of
disorder
? 98 aerogel (new series) (cell C) 98
aerogel (original) (cell A) O 99.5 aerogel __
Bulk Tc vs Pressure
Tc reduction as a function of coherence length
G. Lawes, S. Kingsley, N. Mulders, J. M. Parpia,
Phys. Rev. Lett. 84, 4148 (2000)
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Compare suppression to model of point magnetic
scatterers in s-wave superconductors
Abrikosov-Gorkov homogenous scattering model
Thuneberg,Yip,Fogelstrom,Sauls, PRL 80
2861(1998), Hanninen, Setala, Thuneberg, Physica
B, 255 11 (1999),
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Modified HSM Model (Sharma Sauls)
When x3He xaltltl (mfp), Tc set by most dense
regions dTc/Tco-(x3He/xa)2 high pressure When
x3He gtgt xaltltl (mfp), dTc/Tco-(x3He /l). Within
this heuristic model, Sauls and Sharma find good
agreement between Tc, with a fixed mean free path
xa502Å, l1400Å.
Sharma Sauls, PRB 68 224500 (2003).
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Inhomogenous Impurity Scattering Model (IISM)
Void D
ClusterD
Cluster Profile
IISM
HSM
Hanninen and Thuneberg, PRB 67 214507-1, (2003).
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Heat Capacity Density of states
Non-zero intercept implies gapless superfluidity,
non-zero density of states at eF, Na(0)
Choi,Yawata,Haard, Davis, Gervais, Mulders,
Sharma, Sauls, Halperin (Northwestern) to be
published.
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Gapless superfluid?
Compare to rs/r
98 aerogel
99.5 aerogel
Compare to magnetization
Sharma, Sauls JLTP 125 115 (2001)
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Thermal Conductivity
Results show no superfluidity below
6bar. Extrapolation shows finite conductivity in
A phase _at_ T0, Implies gapless behavior.
Fisher, Guenault, Mulders, Pickett PRL 91,
105303-1 (2003).
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Magnetization, NMR frequency shift of 3He in
aerogel show A-like and B-like signatures
B phase
A phase
Barker,Lee,Polukhina,Osheroff,Hrubesh,Poco PRL
85, 2148 (2000), Barker, Thesis Stanford Univ,
2000.
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A1 Phase of 3He in aerogel
A1, A2 splitting for both bulk liquid and liquid
3He in 98 aerogel at 33.5 bars.
Yoonseok Lee et al, this conference, PRL
submitted J. A. Sauls and P. SharmaPhys. Rev. B
68, 224502 (2003)
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Other experiments

• Baumgartner et al saw evidence for pinning in
  magnetic field (Proc of LT23).
• Dmitriev et al saw time, temperature dependent
  behavior of the A -B conversion (Proc LT23).

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Region between Tc(aerogel) Tc Bulk
Tca
Tcbulk
Magnetization of solid continues to increase, yet
line-width stays the same below Tc bulk.
Possible signature of spin-superfluidity? See
also Volovik, JETP Lett.,
2
4
3
T (mK)
Bunkov et al (unpublished)
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Transport in disordered normal fluid.
Dilute aerogel in channel, 3He should exhibit
transition from Drude limit to Poiseuille flow.
Should be able to alter scattering from elastic
to inelastic by magnetic fields, surface 4He.
Einzel, Parpia, PRL 81, 3896 (1998). See also
Higashitani et al PRL, 89, 215301 (2002).
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Model of Aerogel
Consists of silica clusters, of mean diameter
2.5nm. Image is a 300 nm cube of computer
generated 98.5 open aerogel.
Porto Parpia, PRB 59 14583 (1999), A. Hasmy et
al, PRB, 50 6006 (1994), R. Vacher et al, PRB, 37
6500 (1988)
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Structure Correlations
homogenous regime

• Aerogels exhibit fractal correlations.
• 99.5 open base catalysed aerogel (Larry Luria)
• ? 96 open base catalysed aerogel
• ? 91 open base catalysed aerogel
• ?95.6 neutrally catalysed aerogel
• Cell A, C 98 open aerogel

Volume fractal regime
cellA
cellC
Surface fractal regime
J. V. Porto, PhD. Thesis, Cornell (1996)
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Length scales of 3He and aerogel
Below 3He coherence length vs pressure.
Mean free path vs concentration
J. V. Porto and J. M.Parpia, Czech. J. of
Phys.,46 S-6 2981, (1996)