Could a quantum solid flow like a superfluid

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Could a quantum solid flow like a superfluid ?
S. Sasaki, R. Ishiguro , F. Caupin, H.J. Maris
and S. Balibar Laboratoire de Physique
Statistique (ENS-Paris) Brown University,
Providence (RI, USA)
A reference Science 313, 1098 (25 aug. 2006)
Oxford, 25 jan 2007
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Evangelista Torricelli (1608-1647)
vacuum
1 atm 760 mmHg
Galileos friend invented the first barometer
liquid Hg
two communicating vessels (inside and outside the
tube) hydrostatic equilibrium the weight of the
liquid column is compensated by the atmospheric
pressure
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under vacuum same level
when Torricelli pumped through E liquid-gas
equilibrium in A and B same temperature same
vapor pressure same levels because a liquid
allows the mass flow which is necessary to
achieve hydrostatic equilibrium
we did the same experiment with solid 4He in eq.
with liquid 4He
E. Torricelli, Florence 1644
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Motivation is solid 4He  supersolid ?
E. Kim and M. Chan (Penn. State U. 2004)
a torsional oscillator (1 kHz) a change in the
period of oscillation below 200 mK 1 of the
solid mass decouples from the oscillating walls ?
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1 superfluid density in solid 4He ?
NCRI (non classical rotational inertia) 1 at
51 bar no effect in 3He
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early theoretical ideas
Penrose and Onsager 1956 BEC is impossible in a
solid (but they used non-symetrized wave
fonctions) Andreev and Lifshitz 1969
delocalized defects (vacancies) could exist at
T0 ( the crystal would be  incommensurate )
BEC gt superplasticity at low velocity or long
times Reatto, Chester and Leggett 1969-70 NCRI
is possible if atoms are delocalized (if there
are free vacancies ?) Imry and Schwartz (1975)
no supersolidity in a true crystal without free
vacancies (a lattice gas is different) ...
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recent theoretical ideas
Prokofev and Svistunov 2005 no BEC in crystals
without free vacancies (commensurate crystal,
vacancy-interstitial pairs) BEC in a 4He glass
(Boninsegni et al. PRL 2006)
Galli and Reatto 2006 superfluidity in
simulations with trial functions ( SWF )
which reproduce the properties of solid 4He
Clark and Ceperley (2006) superfluidity
depends on the trial functions not found in
quantum Monte Carlo simulations the crystal is
commensurate, no vacancies at T 0

• Anderson Brinkman and Huse 2005 a new analysis
  of the T variation of the
• lattice spacing (old experiments by Simmons)
• and the specific heat Cv(T) AT3 BT7
• a low density of zero-point vacancies (lt 10-3
  ?) TBEC a few mK ?s ?

PG de Gennes (CR-Physique 2006) quantum
dislocations are mobile at low T ...
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puzzling experimental results
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annealing the crystals, adding 3He
Rittner and Reppy (Cornell, 2006) annealing
destroys supersolid behavior
Kim and Chan (Penn State, 2006) annealing
enhances supersolid behavior !
Shirahama et al. (Tokyo, 2006) no effect of
annealing but the supersolid density ?s 0.1,
not 1 ...
Kim and Chan (Penn State, 2006) 3He impurities
increase Tc but decrease ?s but ultrapure 4He
shows very small ?s
thermodynamic quantities very small change in
the specific heat (Kim and Chan) no singularity
in the melting curve (Todoshchenko et al.
Helsinki 2006)
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two previous experiments on superflow
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ENS 2006 experimental setup
Fill a test tube (1 cm ??) at 1.3 K lower T down
to 50 mK melt the outside follow the level
inside any change in the level inside requires a
mass flow through the solid (?C 1.1
?L) melting velocity V 3 mm/h if critical
velocity 10 ?m/s and superfluid density ?s / ?C
10-2
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Ishiguros tube
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the ENS fridge with optical access
large optical access through sets of windows
down to 30 mK
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filling the tube with solid 4He makes defects
liquid
liquid
liquid
the inside crystallizes only if a substantial
stress is applied. For example if the outside is
warmed up to 1.4K for a few seconds while the
inside is at 1.3K
solid
Pm( 1.4 K) - Pm( 1.3 K) 0.3 bar fast growth
under inhomogeneous stress creates defects
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cusps and grain boundaries
mechanical equilibrium of surface tensions at
the liquid-solid interface each cusp signals
the existence of an emerging grain boundary
(GB) most cusps move away in a few
hours (melting-crystallization pinning) some
GBs stay pinned
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no flow in good quality crystals
for 10 crystals with no or very few cusps the
tube we could see no flow no mass leak along the
glass wall if supersolidity were due to a 1
superfluid density in the bulk with a critical
velocity vc 10 ?m/s the interface should relax
at V ?s/(?C - ?L)vc 1 ?m/s that is 3.6 mm
in 1 hour Instead, we see no flow within 50 ?m
in 4 hours, meaning 300 times less
gt supersolidity is not due to the superfluidity
of a 1 equilibrium density of vacancies
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mass flow in crystals with enough grain boudaries
for 3 crystals with some cusps inside the tube we
observed a mass flow If the cusps disappear, the
mass flow stops (see crystal 1) Mass flows along
grain boudaries
Solids with grain boudaries may be
supersolid (polycrystals) but not single crystals
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crystal 1 relaxed 1 mm down and stopped
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crystal 1
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crystal 2 had many defects
Many grain boundaries more in the lower
part faster flow down to equilibrium at h 0
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crystal 2 relaxed down to eq. (h 0)
time x 250 5 s 20 min
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crystal 2relaxation at 50 mK
relaxation is not exponential but linear with two
successive regimes, constant velocity 6 ?m/s
for 0 lt t lt 500 s 11 ?m/s for 500 lt t lt 1000
s more defects in the lower part of crystal
2 typical of superfluid flow at a critical
velocity
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crystal 1 a single grain boundary
The relaxation at V 0.6 ?m/s stops when the
cusp disappears (the grain boundary moves away,
unpinning from the wall somewhere)
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grain boundaries at Pm are comparable to liquid
films with atomic thickness
If we assume the existence of a single grain
boundary with thickness e , width w , the
critical velocity inside is vcGB
(?D2/4ew?s)(?C-?L)V 1.5 (a/e)(D/w)(?C /?s)
m/s comparable to 2 m/s measured by Telschow et
al. (1974) on free adsorbed films of liquid
He agreement with the prediction by Burovski,
Prokofev and Svistunov (PRL 2005) in a general
model. simulations of GBs in solid helium 4 are
in progress in their group (U. Mass. Amherst)
and at Urbana (Ceperley and Clark)
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Numerical simulation of grain boundaries
Nature 21 octobre 2006
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crystal 4 at 1.13 K
a highly distorted crystal final relaxation
at 0.9 ?m/s grain boundaries are superfluid up
to 1.13 K at least consistent with e 2a and ?s
?C at P Pm
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have we seen the same effect as Kim and Chan ?
the effect of annealing Rittner and Reppy
(2006) vs Kim and Chan (2004) large scatter of
data evidence for the importance of quenched
disorder not an intrinsic property of He
crystals most natural defect grain boundaries
increase of ?s (P) more grain boundaries ?
decrease of at large P superfluidity disappears
at high density
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Tc and vc are different
at P Pm, equilibrium with the liquid Partial
wetting of grain boundaries by the liquid phase
(long range van der Waals forces) The thickness
is microscopic (a few times a) Out of
equilibrium at high P prewetting near Pm ,
e(P) should decrease, Tc et vc as well below
one layer
P
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1 superfluid density is large
In torsional oscillator experiments,
crystallization at constant V from the normal
liquid At variable T and P gt
polycrystals grain boundaries every 100 à 200
a , about 50nm ??
1 vacancies would be very large too
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crystals grown from the normal liquid at 1.9 K
dendritic growth strong light scattering by a
high density of defects
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work in progress
The research is now focusing on the effect of
disorder, especially grain boundaires
(GB) calculate the thickness e and superfluid
transition temperature Tc of GBs measure the Tc
of GBs with variable misorientation measure vc in
fixed GBs, find a model for it measure GBs at P gt
Pm thinner ? lower Tc ? lower vc ? measure the
adsorption of 3He on GBs characterize the density
of GBs in crystals grown at cst V X rays, light
scattering study the pinning of GBs on different
walls torsional oscillator experiments in good
quality crystals grown at cst T and
P supersolidity under rotation reproduce the
measurement of the vacaqncy density vs T change
the frequency of torsional oscillator
measurements ...
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1 superfluid density is large
In torsional oscillator experiments, all crystals
have been grown at constant V from the normal
liquid phase variable T and P gt
polycrystals grain boundaries every 100 to 200 a
50 nm ? a very high density
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facets block the growth
no growth if the crystal level is raised again
outside except if a large ?P is applied facets
are easily pinned to wall defects facets
disappear during melting ( a geometrical effect)
gt no pinning
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