Pierre-Gilles de Gennes and the puzzle of supersolidity

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Pierre-Gilles de Gennes and the puzzle of
supersolidity
Sébastien Balibar, Frédéric Caupin and Satoshi
Sasaki Laboratoire de Physique Statistique
(ENS-Paris)
for references, articles and movies, see
http//www.lps.ens.fr/balibar/
De Gennes Days, 16 May 2008
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PG de Gennes 9 / 02 / 1995
 Le Palais de la Découverte est l'un des grands
centres européens d'initiation à la science.
Installé avenue Franklin-Roosevelt, depuis sa
fondation par Jean Perrin en 1937, il a marqué
des générations de lycéens. Nous sommes nombreux
à y avoir découvert notre passion pour la
recherche grâce à des expériences simples et bien
expliquées. L'expulsion du Palais de son bâtiment
serait un désastre.  le Palais est en danger, à
nouveau. Appel sur http//www.sauvonslepalaisdelad
ecouverte.fr/
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Trieste, May 2006
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Trieste, May 2006
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Trieste, May 2006
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Trieste, May 2006
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Trieste, May 2006
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Trieste, May 2006
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what was Pierre-Gilles talking about ?
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a  supersolid  is a solid ... ... which is
also superfluid !
a paradoxical idea
a solid transverse elasticity non zero shear
modulus a consequence of atom localization cryst
als - glasses
a superfluid a quantum fluid with zero
viscosity a consequence of   Bose-Einstein
condensation  atoms are undistinguishable and
delocalized
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Could a solid flow like a superfluid ?
E. Kim and M. Chan (Penn. State U. 2004)
a torsional oscillator (1 kHz) a change in the
period of oscillation below 100 mK 1 of the
solid mass decouples from the oscillating walls ?
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some early theoretical ideas
Penrose and Onsager 1956 generalize Bose
Einstein Condensation (BEC) to condensed matter
systems Off diagonal long range order in the
density matrix BEC is impossible in a solid (but
they used non-symmetrized wave fonctions)
Reatto and Chester 1969 some models of Q-solids
show BEC symmetry of the wave function ? overlap
is necessary (Imry and Schwartz 1975) a large
class of Q-solids do NOT show BEC Leggett 1970
non-classical rotation inertia (NCRI) if atoms
are delocalized (if there are free vacancies ?)
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some recent theoretical ideas
Prokofev , Svistunov, Boninsegni, et al. 2005-6
(MC calc.) no BEC in crystals without free
vacancies 4He crystals are commensurate (Evac
13K) BEC is possible in a 4He glass
(Boninsegni et al. PRL 2006)
controversies with Galli and Reatto 2006 , Clark
and Ceperley, Cazorla and Boronat, etc.
possible analogies with the Hubbard model and
cold atoms in optical lattices see I. Bloch, J.
Dalibard and W. Zwerger, Rev. Mod. Phys. 2008

• Anderson Brinkman and Huse (Science 2005) 4He
  crystals are incommensurate !
• a new analysis of the lattice parameter ?a/a (T)
  and specific heat Cv(T)
• not confirmed by new neutron scattering
  measurements (Blackburn et al. PRB 2007)
• criticized by H.J. Maris and S. Balibar (J. Low
  Temp. Phys. 147, 539, 2007)
• Anderson has now switched to a  vortex liquid 
  model (Nature Physics 2007)

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new experiments evidence for the importance of
disorder
Rittner and Reppy (Cornell, 2006-7) annealing
destroys supersolid behavior quenched cooled
crystals very large  superfluid fraction  ?s
up to 20 more experiments (Aoki and Kojima,
Clark and Chan, Shirahama...) ?s varies from
0.03 to 20 depending on sample preparation
Sasaki, Ishiguro, Caupin, Maris et Balibar (ENS,
Science 2006) two communicating vessels filled
with solid helium superfluid mass transport only
in the presence of grain boundaries
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PGG (CR Physique 7, 561, 2006) quantum
plasticity in a quantum crystal

• a model at T 0 large quantum tunneling of
  kinks
• weak pairing of kink and antikinks
• large mobility of dislocations
• large mobility of grain boundaries (
   dislocation ladders  )
• quantum plasticity at T 0
• a change in mechanical properties at some
  finite T ??

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Pollet et al. PRL 98, 135301, 2007
Grain boundaries are 3 atoms thick superfluid
for large misorientation not superfluid for small
misorientation edge dislocations are not
superfluid Tc 0.2 to 1 K depending on
orientation critical velocity ?
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Boninsegni et al. PRL 99, 035301, 2007
superfluidity of screw dislocation cores
a Monte Carlo calculation
phase coherence along the core of screw
dislocations on a distance 1/T a true 1D-
supersolid a network of dislocations with density
ns 3D- superfluidity below Tc 1/l ns1/2 in
their model, a very large dislocation density
would be needed to build a superfluid density of
order 0.1
in blue local superfluid density
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G. Biroli and J.P. Bouchaud preprint 2007
the free energy for the creation of kink-antikink
pairs should vanish at Tk proliferation of
kinks very large transverse fluctuations of
dislocations trigger atom exchange in the bulk
solid supersolidity below some temperature Tc lt
Tk
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S. Sasaki et al. _at_ENS Science 313, 1098, 2006
liquid helium
window
a glass tube (1 cm ??) grow a crystal from the
superfluid at 1.3 K lower T down to 50 mK melt
the outside gt height difference follow the level
inside
1 cm
solid helium
any change in the level inside requires a mass
flow through the solid since ?C 1.1 ?L
if critical velocity vc 10 ?m/s and superfluid
density ?s 10-2 ?C gt melting velocity V 3
mm/h
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filling the tube with solid 4He makes defects

• the liquid inside crystallizes if a substantial
  stress is applied.
• grain boundaries
• grooves at the liquid-solid interface

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cusps and grain boundaries (GBs)
mechanical equilibrium of surface tensions at
the liquid-solid interface ?GB ????LS
cos? each cusp signals the existence of an
emerging grain boundary
at Pm, most cusps move away in a few hours
pinning very fast dynamics of grain
boundaries some GBs stay pinned on walls
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without grain boundaries, no flow
If supersolidity was due to a 1 superfluid
density in the bulk with a critical velocity vc
10 ?m/s the interface should relax at V 1
?m/s, that is 3.6 mm in 1 hour Instead, we see
no flow within 50 ?m in 4 hours, meaning at
least 300 times less

• supersolidity is not due to the superfluidity of
  a 1 (even 0.03) equilibrium density of
  vacancies moving at 10?m/s.

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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 crystal 1 when the cusp
disappears, the mass flow stops
superflow of mass through solid 4He is associated
with the existence of grain boundaries
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crystal 1 relaxed 1 mm down and stopped
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crystal 2 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 its 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)
Assume 1 grain boundary (thickness e a 0.3 nm
, width w D 1cm) 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 liquid
films of atomic thickness
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1 superfluid density is large ! (Rittner and
Reppy 2007 20 in thin quenched cooled samples !)

• 1 matter with grain boundaries
• 1 atomic layer of superfluid matter
• grain size 100 nm
• 3 ?m for 0.03
• Is this possible ? may be
• We used to grow single crystals at constant P
  from the superfluid,
• but
• crystals grown at constant V from the normal
  liquid are usually polycrystals with much more
  disorder

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a high pressure cell to grow He crystals at
constant V
two cubic cells 11 x 11 x 10 mm3 or 11
x 11 x 3 mm3 thermal contact via 10 mm thick
copper walls 2 glass windows (4 mm
thick) indium rings stands 65 bar at
300K Straty-Adams pressure gauge (0 to 37 bar)
connection through a 3 cm long CuNi capillary
(0.6 mm ID)
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at T gt 1.8 K from the normal liquidgrowth is
dendritic if fast
T 1.87 K
fast mass injection through the fill line in the
normal liquid (here at 1.87 K) leads to dendritic
growth but not slow growth at constant V in a
T-gradient
11 mm
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more helium snowflakes
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slow growth at constant volume
slow growth (3 hours) in a temperature
gradient (Twalls lt Tcenter)
the solid is transparent but polycrystalline
liquid 2.56K
hcp solid 1.95 K
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melting a crystal grown at constant volume
0.04 K
liquid channels appear at the contact line of
each grain boundary with the windows grain size
?m ripening
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melting a crystal after fast growth from the
superfluid

• a the fast grown solid
• is transparent
• but polycrystalline
• b to f in 11 seconds
• some bulk liquid
• appears in f
• small size crystal grains
• ripening of the solid foam in a few seconds at
  the melting pressure

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further melting gt 2 crystals 1 grain boundary

• the cusp angle is non-zero gt the gain boundary
  energy ?GB is strictly lt 2 ?LS
• gt partial wetting of the GB by the liquid, the
  thickness of grain boundaries is microscopic as
  calculated by Pollet et al. (2007).
• complete wetting would imply ?GB ?????LS (2
  liq-sol interfaces with bulk liquid in between)

the contact of the GB with each window is a
liquid channel
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angle measurements gt the grain boundary energy

• here, the GB is parallel to the optical axis
• a fit with Laplace equation near the cusp leads
  to
• ? 14.5 4
• ??GB (1.93 0.04) ?LS
• other crystals
• ? 11 3
• ? 16 3

S.Sasaki et al. PRL 99, 205302 (2007)
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wetting of grain boundaries near a wall
GB
grain 2
grain 1
liquid
grain 1
grain 2
wall
wall
S. Sasaki, F. Caupin, and S. Balibar, PRL 2007
If ?GB?is large enough, more precisely if???
?c lt ?/2 the liquid wets the contact of the GB
with the wall. wetting and premelting of grain
boundaries an important problem in materials
science (see for ex. JG Dash Rep. Prog. Phys. 58,
115, 1995) this effect is responsible for the
apparent wetting of GBs observed with fcc
crystals by Franck et al. (Edmonton, 1983-5)
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hysteresis of the contact angle
advancing angle 22 6 (copper) 26 7
(glass) receding angle 55 6 (copper) 51
5 (glass) more hysteresis on copper rough
walls than on smooth glass walls, as expected
from E. Rolley and C. Guthmann (ENS-Paris) PRL
98, 166105 (2007)
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the contact line on the window is a liquid
channel whose width w (P-Pm)-1
the width w of the triangular liquid channel
decreases as 1/ z (the inverse of the departure
from the equilibrium melting pressure
Pm) consistent with the direct measurement but ?c
is hysteretic the channel should disappear
around Pm 10 bar (where 2w 1 nm)
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the grain boundary energy depends on orientation
no liquid channel along the wall if the GB has a
low energy (small misorientation)
a stacking fault ?
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two possible interpretations of Sasaki et al.
(Science 2006)
liquid
liquid

• the flow could be
• either along the GBs (then vc 1 m/s)
• or at the GB-wall contact (then vc 1 cm/s).
  This would explain why we saw mass flow up to
  1.1K at least.
• to be checked by changing the shape of the cell
• or by gluing a piece of graphite on the wall

solid
solid
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next experiment measure Tc inside a grain
boundaries
Pollet et al. (PRL 98, 135301, 2007) Tc 0.5 K
with three layers 3 times less than the bulk T?
at the solid density (1.5K) a possible
measurement squeeze the liquid channels with
an electric field make a height
difference measure the mass flow as a function of
T
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Day and Beamish (Nature 2007) a measurement of
the shear modulus of crystals grown at constant V
similar anomalies
the shear modulus increases by 15 below 100
mK dislocation pinning by 3He impurity adsorption
? relation to torsional oscillator experiments
? less inertia for a stiffer crystal ?? a new
theoretical challenge
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Clark and Chan an increase in stiffness ?
??????? (I/G)1/2 could the decrease in the period
???be due to an increase in the shear modulus ,
consequently the quantity G ? ?c/c 30 for
NCRIF 0.4
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conclusion

• solid helium 4 shows many anomalies at low T
  but their interpretation is not yet clear
• see S. Balibar and F. Caupin,  topical review 
• J. Phys. Cond. Mat. 20, 173201 (2008)
• superfluidity of solid helium 4 is not
  established
• check phase coherence
• superfluidity of grain boundaries and
  dislocation cores is predicted but not yet proved
  experimentally. New original quantum systems 1D
  or 2D supersolids.
• dynamics of dislocations and grain boundaries in
  quantum crystals
• solid He is stiffer at low T, apparently not
  superplastic