In the vicinity of In the vicinity of Pierre-Gilles, Pierre-Gilles, from superfluidity to from superfluidity to supersolidity supersolidity

(1)

In the vicinity of In the vicinity of

Pierre-Gilles, Pierre-Gilles,

from superfluidity to from superfluidity to

supersolidity supersolidity

Sébastien Balibar Sébastien Balibar

Laboratoire de Physique Statistique Laboratoire de Physique Statistique

Ecole Normale Supérieure (Paris) Ecole Normale Supérieure (Paris) associé au CNRS et aux Universités associé au CNRS et aux Universités

Paris 6 & 7 Paris 6 & 7

Trieste Trieste

20062006

for references and files :

for references and files : http://www.lps.ens.fr/~balibar/ http://www.lps.ens.fr/~balibar/

(2)

from june 1968 to may from june 1968 to may

2006 2006

At the Ecole Polytechnique in june At the Ecole Polytechnique in june 68, 68,

a series of lectures by PGG on a series of lectures by PGG on superfluidity

superfluidity February 2006, PGG writes a paper on February 2006, PGG writes a paper on supersolidity, a paradoxical phenomenon supersolidity, a paradoxical phenomenon on which I start experiments

on which I start experiments I never worked with PGG,

I never worked with PGG,

but certainly on the statics and but certainly on the statics and dynamics of interfaces,

dynamics of interfaces,

and often under his indirect influence and often under his indirect influence Short survey of a few examples

Short survey of a few examples

(3)

No boiling

QuickTime™ et un

décompresseur miroMotion JPEG A sont requis pour visionner cette image.

(4)

1972 : Jack Allen’s movie 1972 : Jack Allen’s movie

Jack Allen had discovered superfluidity in Jack Allen had discovered superfluidity in Cambridge (dec. 1937)

Cambridge (dec. 1937)

remembering PGG’s lectures ? remembering PGG’s lectures ?

I start working on superfluidity I start working on superfluidity

I was looking for a research subject : I was looking for a research subject : swimming in Haifa, drawing at Les Houches swimming in Haifa, drawing at Les Houches

1975: first experimental evidence for 1975: first experimental evidence for

« quantum evaporation »

(5)

P.W. Anderson 1966:

analogy with the photoelectric analogy with the photoelectric effect

effect

1 photon hv ejects 1 electron 1 photon hv ejects 1 electron with a kinetic energy

with a kinetic energy

EE_kin_kin = hv - E = hv - E₀₀(E(E₀₀ : binding energy) : binding energy) 1 roton with a energy E >

1 roton with a energy E >  = ₌ 8.65 K evaporates 1 atom with a 8.65 K evaporates 1 atom with a kinetic energy

kinetic energy

EE_kin_kin  - 7.15 = 1.5 K - 7.15 = 1.5 K

 

v > 79 v > 79 m/sm/s

Quantum evaporation

R R

^-^-

R R

⁺⁺

rotons (E > 8.65K) rotons (E > 8.65K) evaporated atoms evaporated atoms

E E

_kin_kin

> 1.5K > 1.5K

gas gas liquid liquid

S. Balibar et al. (PhD thesis 1976 and Phys. Rev. B18, 3096, 1978) : S. Balibar et al. (PhD thesis 1976 and Phys. Rev. B18, 3096, 1978) :

heat pulses at T < 100 mK

heat pulses at T < 100 mK  ballistic rotons and phonons ballistic rotons and phonons

atoms evaporated by rotons travel with a minimum velocity 79 m/s atoms evaporated by rotons travel with a minimum velocity 79 m/s

direct evidence for the existence of rotons and the quantization of heat at low T direct evidence for the existence of rotons and the quantization of heat at low T

For a quantitative study and the evidence for R

⁺⁺

and R and R

^-^-

rotons, see rotons, see M.A.H. Tucker, G.M. Wyborn et A.F.G. Wyatt , Exeter (1990-99)

M.A.H. Tucker, G.M. Wyborn et A.F.G. Wyatt , Exeter (1990-99)

(6)

Lev D. Landau Moscow 1941 - 47 Lev D. Landau Moscow 1941 - 47

1939: Landau comes out of prison thanks 1939: Landau comes out of prison thanks to Kapitza

to Kapitza

1941: in view of Kapitza’s results on 1941: in view of Kapitza’s results on thermomechanical effects, Landau thermomechanical effects, Landau introduces a more rigorous version of introduces a more rigorous version of Tisza’s two fluid model, but ignores

Tisza’s two fluid model, but ignores Fritz Fritz London and BEC :

London and BEC :

« the explanation advanced by Tisza (!) not only has no foundations in his suggestions but is in direct contradiction with them » The normal fluid is made of quantum The normal fluid is made of quantum elementary excitations (

elementary excitations (quasiparticlesquasiparticles): ):

phonons et

phonons et rotonsrotons ( elementary vortices ??) ( elementary vortices ??) Calculates the thermodynamic properties Calculates the thermodynamic properties prédicts the existence of a critical velocity prédicts the existence of a critical velocity and thermal waves (« second sound » and thermal waves (« second sound » in in agreement with Kapitza’s results

agreement with Kapitza’s results

(7)

neutron scattering: rotons exist

R+ and R- rotons have opposite group velocities The roton gap decreases with pressure

0 2 4 6 8 10 12 14

0 5 10 15 20 25

Energy (K)

Wavenumber (nm^-1) 20 bar

svp

phonons

rotons

R R

⁺⁺

R R

^-^-

(8)

rotons : a consequence of local order

F. London, LT0, Cambridge (1946) : F. London, LT0, Cambridge (1946) :

Fritz London criticizes Landau‘s « theory based on the shaky grounds of Fritz London criticizes Landau‘s « theory based on the shaky grounds of imaginary rotons »

imaginary rotons »

« …there has to be some short range order in liquid

« …there has to be some short range order in liquid helium. »

helium. »

A liquid-solid instability (Schneider and Enz 1971):

As the roton minimum

As the roton minimum decreases, order extends to decreases, order extends to larger and larger distances and the liquid structure larger and larger distances and the liquid structure gets closer to that of a crystal.

gets closer to that of a crystal.

An instability when

An instability when  =0 ; some information from =0 ; some information from acoustic crystallization ?

acoustic crystallization ?

R. Feynman, Prog. in LT Phys. 1955 :

R. Feynman, Prog. in LT Phys. 1955 : a vortex ring ? a vortex ring ? the dispersion relation of elementary excitations is:

the dispersion relation of elementary excitations is:

h h  

_q_q

= h _{= h}

²²

q q

²²

/ 2mS(q) / 2mS(q)

P. Nozières J. Low Temp. Phys. 137, 45, 2004:

« rotons are ghosts of a Bragg peak »

The roton minimum is a consequence of a maximum in the The roton minimum is a consequence of a maximum in the struture factor S(q), i.e. a large probability to find struture factor S(q), i.e. a large probability to find atoms at the average interatomic distance from their atoms at the average interatomic distance from their neighbors.

neighbors.

(9)

The The

metastability metastability

of liquids of liquids

liquid-gas or liquid-solid:

first order phase transitions first order phase transitions

  metastability is possible metastability is possible energy barriers

energy barriers

against the nucleation of the stable phase against the nucleation of the stable phase

liquid water to - 40 °C or + 200°C at 1 bar, or liquid water to - 40 °C or + 200°C at 1 bar, or - 1400 bar at +35 °C

- 1400 bar at +35 °C

What are the limits of metastability ? What are the limits of metastability ? Acoustics in liquid helium, now in water Acoustics in liquid helium, now in water Cavitation down to -9.5 bar, but

Cavitation down to -9.5 bar, but crystallization ?

crystallization ?

temperature

p r e s s u r e p r e s s u r e

crystallization

solid

solid liquid liquid

gas gas

boiling cavitation

(10)

the metastability

limits of liquid He Liquid-gas and liquid-solid : 1st order transitions

suppress impurities and walls

liquid helium can be observed in a metastable state for a finite time following J. Nissen (Oregon) and H.J. Maris (Brown Univ.),

we use high amplitude, focused acoustic waves

the tensile strength of liquid He:

how much can one stress liquid He without bubble nucleation ? a similar question: how far can one pressurize liquid He without crystal nucleation ?

a 1.3 MHz transducer a 1.3 MHz transducer

spherical geometry spherical geometry

(11)

high amplitude high amplitude

acoustic waves acoustic waves

At the focal point:

large pressure

oscillations away from any wall

(here : ± 35 bar) f ~ 100 kHz to 1 MHz during ~ T/10 ~ 100 ns to 1 s

in a volume

(/10)³ ~ 10^-8 to 10^-5 mm³

-50 0 50

0 5 10 15 20 25 30 35

Time (microseconds) cavitation at P

m = 25.3 bar

flight time (22 μs)

G.Beaume, S. Nascimbene, A.

Hobeika, F. Werner, Hobeika, F. Werner,

F. Caupin and S. Balibar (2002 - F. Caupin and S. Balibar (2002 -

2003) 2003)

(12)

acoustic acoustic

crystallization on crystallization on a clean glass plate a clean glass plate

X. Chavanne, S. Balibar and F.

Caupin Caupin

Phys. Rev. Lett. 86, 5506 (2001) Phys. Rev. Lett. 86, 5506 (2001)

acoustic bursts : 6

oscillations, rep. rate ~ 2Hz, P_stat= P_m = 25.3 bar) The crystallization

The crystallization threshold is at :

threshold is at :



 3.1 103.1 10^-3^-3 g/cm g/cm³³ (~2% of (~2% of

_m_m),_),

i.e. i.e. P = 4.3 barP = 4.3 bar

=> heterogeneous nucleation

=> heterogeneous nucleation on 1 defect

on 1 defect

0.170 0.175 0.180 0.185

20 25 30 35 40

11.0 V excitation densité statique 10.4 V excitation

Temps (microsecondes)

0.170 0.172 0.174 0.176 0.178 0.180 0.182 0.184

28.5 29 29.5 30 30.5

densité statique 10.4 Volt 11.0 Volt

temps (microsecondes)

(13)

search for homogeneous search for homogeneous

nucleation of solid helium with nucleation of solid helium with

acoustic waves acoustic waves

F.Werner, G. Beaume, C.Herrmann, A. Hobeika, S.

Nascimbene, Nascimbene,

F. Caupin and S. Balibar (J. Low Temp. Phys. 136, F. Caupin and S. Balibar (J. Low Temp. Phys. 136,

93, 2004) 93, 2004)

remove the glass plate remove the glass plate

increase the amplitude of the acoustic wave increase the amplitude of the acoustic wave

ArAr⁺⁺ laser laser

lenslens

transducer (1 transducer (1

MHz)MHz)

2 cm2 cm

(14)

nucleation nucleation

at high at high pressure:

pressure:

bubbles or bubbles or

crystals ? crystals ?

-50 0 50

0 5 10 15 20 25 30 35

Time (microseconds) cavitation at P

m = 25.3 bar

flight time (22 μs)

18 19 20 21 22 23 24 25 26

540 560 580 600 620 640 660 680

P

stat = - 9.45 + 0.051 ρ_LV_c

cavitationtheshodρ

LV_c(V.kg. ^-3)

according to previous according to previous measurements (Werner et measurements (Werner et al. 2004):

al. 2004):

 the cavitation threshold the cavitation threshold voltage V

voltage V_c_c (more precisely (more precisely the product

the product _L_LV_V_c_c) ) varies linearly varies linearly

with the pressure in the with the pressure in the cell P

cell P_stat_stat

 extrapolation => extrapolation =>

cavitation occurs at cavitation occurs at

-9.45 bar, in excellent -9.45 bar, in excellent agreement with theory (0.2 agreement with theory (0.2 bar above the spinodal

bar above the spinodal limit at - 9.65 bar) limit at - 9.65 bar)

bubbles,bubbles,

a calibration method for a calibration method for the wave

the wave

no crystallization up to no crystallization up to 160 +/- bar

160 +/- bar

(15)

the extended the extended phase diagram phase diagram

of He4 of He4

the standard theory the standard theory predicts homogeneous predicts homogeneous nucleation of

nucleation of

crystals at 65 bar.

Schneider and Enz Schneider and Enz (1971):

(1971):

an instability when an instability when

rot = 0 ?rot = 0 ?

at 200 bar (Maris)?

300 bar (Vranjes, 300 bar (Vranjes, Boronat) ?

Boronat) ?

The 4 data points (

The 4 data points (  ) assume ) assume linear sound focusing in a

linear sound focusing in a hemispherical geometry ,

hemispherical geometry , but ....

but ....

Superfluidity at high density ? Superfluidity at high density ?

see Nozieres 2004-2006 see Nozieres 2004-2006

Vranjes et al. 2006 Vranjes et al. 2006

Moroni and Boninsegni 2004 Moroni and Boninsegni 2004

(16)

an instability at an instability at

200 bar ? 200 bar ?

0 2 4 6 8 10 12 14

0 5 10 15 20 25

Energy (K)

Wavenumber (nm^-1) 20 bar

svp

phonons

rotons

H.J. Maris H.J. Maris noticed that, noticed that, according to the according to the

density density

functional form functional form of Dalfovo et al.

of Dalfovo et al.

,,

the roton gap the roton gap vanishes around vanishes around 200 bar where the 200 bar where the

density reaches density reaches

0.237 g/cm 0.237 g/cm³³ If true, this If true, this

"soft mode" at

"soft mode" at finite wave finite wave vector could vector could

imply

imply an an instability instability

towards a towards a periodic (i.e.

periodic (i.e.

crystalline ?) crystalline ?)

phase phase

(Schneider and Enz (Schneider and Enz PRL 27, 1186, 1971) PRL 27, 1186, 1971)

Vranjes, Boronat et al. (PRL 2005): the roton gap is Vranjes, Boronat et al. (PRL 2005): the roton gap is

3K at 250 bar 3K at 250 bar

instability at higher P (> 300 bar ?) instability at higher P (> 300 bar ?)

(17)

The condensate fraction vanishes

According to According to

Moroni and Moroni and

Boninsegni (JLTP Boninsegni (JLTP

2004), the 2004), the condesnate condesnate

fraction vanishes fraction vanishes exponentially as exponentially as

the density the density

increases.

Same numerical Same numerical results by Vranjes results by Vranjes

etal.

(18)

a new experiment : spherical geometry a new experiment : spherical geometry

at 140 kHz at 140 kHz

R. Ishiguro, F. Caupin and S. Balibar R. Ishiguro, F. Caupin and S. Balibar

submitted to Europhysics Letters, march 2006 submitted to Europhysics Letters, march 2006

2 2 transduce transduce

rsrs

3 cycles 3 cycles

at 140 at 140

kHzkHz Laser beam

Laser beam

lens outside lens outside (f = 20 cm) (f = 20 cm)

Experimental cell Experimental cell

(19)

bubbles or crystals?

nucleation times nucleation times

15 20 25

crystallization at 25.3 bar cavitation at 2 bar

time t - t

f (microseconds)

17.5 21.1

At 25.3 bar, At 25.3 bar, nucleation at nucleation at t -t t -t

_f_f

= 21.1 = 21.1   s _s

i.e. 2 + 3/4 i.e. 2 + 3/4 periods, where periods, where

P P

_max_max

is reached is reached 3.6 3.6   s , i.e. _{s , i.e.}

half a period half a period

later than later than nucleation at nucleation at low pressure low pressure (cavitation in (cavitation in

the negative the negative

swing) swing)

crystals ! crystals !

tt_f_f = flight time to the acoustic focus = flight time to the acoustic focus

(20)

What is the pressure at which What is the pressure at which

crystals nucleate ? crystals nucleate ?

P > 160 bar if Werner et al. were right but P > 160 bar if Werner et al. were right but their interpretation assumed linear focusing their interpretation assumed linear focusing non-linear effects make the measurement of non-linear effects make the measurement of P difficult

P difficult

Brillouin scattering (in progress):

Measure the local instantaneous pressure Measure the local instantaneous pressure

Calculate P from the sound velocity and the Calculate P from the sound velocity and the

known equation of state P(

known equation of state P(   ) ₎

a possible relation with the predicted instability a possible relation with the predicted instability

where rotons become soft collective modes ? Raman scattering where rotons become soft collective modes ? Raman scattering

superfluidity at high density?

a Brillouin line corresponding to second sound ?

(21)

the roughening transitions the roughening transitions

As T decreases, the surface is covered As T decreases, the surface is covered with more and more facets.

with more and more facets.

Successive roughening transitions in high Successive roughening transitions in high symmetry directions:

symmetry directions:

rough above T

rough above T_R_R  smooth below T smooth below T_R_R large scale fluctuations disappear large scale fluctuations disappear (no difference at the atomic scale) (no difference at the atomic scale) detailed study of critical behaviors detailed study of critical behaviors

step energy, step width, growth rate, curvature…

as a function of T and orientation as a function of T and orientation quantitative comparison with

quantitative comparison with renormalization renormalization group theory (P. Nozières 1987-92)

group theory (P. Nozières 1987-92) a Kosterlitz-Thouless transition a Kosterlitz-Thouless transition

1.4 K 1.4 K

1 K1 K

0.4 K 0.4 K

0.1 K 0.1 K Classical statics and quantum dynamics of

Classical statics and quantum dynamics of liquid-solid interfaces

liquid-solid interfaces

(22)

nucleation and growth of He

⁴

crystals from the superfluid

(23)

the universal the universal

relation relation

D.S. Fisher and J.D. Weeks, PRL 1983 D.S. Fisher and J.D. Weeks, PRL 1983

C. Jayaprakash, W.F. Saam and S. Teitel, PRL 1983 : C. Jayaprakash, W.F. Saam and S. Teitel, PRL 1983 :

k k

_B_B

T T

_R_R

= (2/ = (2/   ) ) g g

_R_R

  d d

²²

T T

_R_R

: roughening transition temperature : roughening transition temperature g g = = a a + ∂ + ∂

²²

a a /∂ /∂  

²²

: surface stiffness : surface stiffness

( ( a a : surface tension, : surface tension,   : angle) : angle) g g

_R_R

= = g g ( T ( T

_R_R

) )

(0001) or « c » facets in

⁴⁴

He: the universal relation is He: the universal relation is precisely satisfied with precisely satisfied with g g

_R_R

= 0.315 cgs and T = 0.315 cgs and T

_R_R

= 1.30K = 1.30K

other facets in

⁴⁴

He are anisotropic : checking the universal He are anisotropic : checking the universal relation is more difficult since k

relation is more difficult since k

_B_B

T T

_R_R

= (2/ = (2/   ) ( ) ( g g

₁₁

g g

₂₂

) )

^1/2^1/2

  d d

²²

The roughening temperature is proportional to the surface The roughening temperature is proportional to the surface

stiffness, not to the latent heat

(24)

up to 60 different facets up to 60 different facets

in liquid crystals in liquid crystals

shear modulus << surface tension shear modulus << surface tension : : a << a << gg

steps penetrate as edge steps penetrate as edge

dislocations below the crystal dislocations below the crystal surface

surface

-> the step energy

-> the step energy  ~ ~ aa²²/4/4 is is very small

very small

steps are very broad but

steps are very broad but their their interaction

interaction

d d ~ (~ (gga)a)²² /  / ll²² is large is large

 and and dd compensate each other compensate each other the roughening temperature for the roughening temperature for (1,n,0) surfaces is

(1,n,0) surfaces is

in the end, many facets because in the end, many facets because the unit cell

the unit cell

a ~ 50 Angström is large a ~ 50 Angström is large for (1,1,2) surfaces T

for (1,1,2) surfaces T_R_R ~ 27000 K ~ 27000 K

!!

for (9,8,15) surfaces T

for (9,8,15) surfaces T_R_R ~ 360 K ~ 360 K



€

T

_Rn

= 2

π γ

_⊥

γ

_//

a

_n²

= 2 π

6βδ

a

²

a

_n²

≈ γa

²

n

²

experiments: Pieranski et al.

PRL 84, PRL 84,

2409 (2000); Eur. Phys. J.

E5, 317 (2001) E5, 317 (2001)

theory: P. Nozières, F.

Pistolesi and Pistolesi and

S. Balibar Eur. Phys. J.

B24, 387 (2001) B24, 387 (2001)

(25)

Supersolidity:

mass flow through solid mass flow through solid

helium helium

R. Ishiguro , S. Sasaki, F. Caupin, R. Ishiguro , S. Sasaki, F. Caupin,

H.J. Maris*

and S. Balibar and S. Balibar

work in progress at work in progress at

Laboratoire de Pysique Statistique Laboratoire de Pysique Statistique

(ENS-Paris) (ENS-Paris)

* Brown University, Providence (RI,

USA) USA)

(26)

Order in real space and in Order in real space and in

momentum space momentum space

Lifhitz and Andreev and Lifhitz and Andreev and Lifshitz (1969), Leggett Lifshitz (1969), Leggett (1970), Chester (1970):

(1970), Chester (1970):

A lattice with vacancies A lattice with vacancies if delocalized

if delocalized by by

tunneling from site to tunneling from site to site,

site, and sufficiently and sufficiently numerous

numerous, , vacancies could vacancies could condense and become

condense and become superfluid

superfluid , provide , provide

superflow of mass through superflow of mass through the crystal

the crystal

Many attemps till the Many attemps till the

series of experiments by series of experiments by Kim and Chan (2004-5)

Kim and Chan (2004-5)

(27)

a torsional oscillator a torsional oscillator

The ideal method to detect superflow The ideal method to detect superflow would be to subject solid helium to would be to subject solid helium to

undergo dc or ac rotation to look for undergo dc or ac rotation to look for evidence of ‘Non-Classical Rotational evidence of ‘Non-Classical Rotational Inertia’. (A.J. Leggett, Phys. Rev.

Inertia’. (A.J. Leggett, Phys. Rev.

Lett. 25, 1543, 1970) Lett. 25, 1543, 1970)

Solid Helium

R

Kim and Chan (Nature Kim and Chan (Nature 2004 and Science

2004 and Science 2005) observe a 2005) observe a

decoupling of some decoupling of some

mass, a change in the mass, a change in the

angular momentum angular momentum

below a temperature below a temperature

of order of order

50 to 200 mK

(28)

a supersolid transition ? a supersolid transition ?

t

-

t

*[ns]

t*=971,000ns

Kim and Chan (2004- Kim and Chan (2004- 05): 05):

1% of the mass 1% of the mass

decouples below 100 - decouples below 100 - 200 mK

200 mK

depending on He3 depending on He3 impurity content impurity content

Similar effects in H Similar effects in H

₂₂

but not in He

³³

nor in nor in HD HD

Chan 2006: the effect Chan 2006: the effect nearly disappears in nearly disappears in ultrapure He

ultrapure He

⁴⁴

(29)

Kim and Chan add a barrier

With a barrier in the annulus,

With a barrier in the annulus, the decoupling should the decoupling should be reduced by 99% according to the geometry.

be reduced by 99% according to the geometry.

With a block in With a block in the annulus,

the annulus,

irrotational flow irrotational flow of the supersolid of the supersolid fraction

fraction

contributes about contributes about 1% (Erich Mueller) 1% (Erich Mueller) of the barrier-

of the barrier- free decoupling.

free decoupling.

Kim and Chan Kim and Chan observe a observe a

reduction by 99%

of the mass of the mass decoupling ! decoupling !

Irrotational flow pattern

in a blocked annular channel

(viewed in the rotating frame)

A. L. Fetter, JLTP(1974)

(30)

A surprising pressure dependence : defects ?

Crystals are Crystals are

grown at grown at constant constant

volume volume

more defects more defects when grown at when grown at

higher P ? higher P ?

Superfluidity Superfluidity

of grain of grain boundaries boundaries up to

up to ~200 bar ~200 bar

? ?

(31)

Pierre Gilles invokes Pierre Gilles invokes

dislocations dislocations

if dislocations are sufficiently mobile at if dislocations are sufficiently mobile at low T

low T

(due to quantum kinks), (due to quantum kinks),

some of the mass should be decoupled from some of the mass should be decoupled from the oscillator

the oscillator

(below a critical temperature ?) (below a critical temperature ?)

PG de Gennes, Comptes rendus Ac. Sc. 2006 PG de Gennes, Comptes rendus Ac. Sc. 2006 John Reppy et al. 2006: the effect

John Reppy et al. 2006: the effect

disappear after annealing the crystal (two disappear after annealing the crystal (two cycles near 2K)

cycles near 2K)

(32)

2 tentatives to observe mass supeflow

Unlikely but possible critics on 2 previous flow experiments:

. . . . . .

cryst cryst

alal liqui liqui

dd Day, Herman and Beamish (PRL

Day, Herman and Beamish (PRL 2005)

2005)

flow in Vycor glass flow in Vycor glass

the lattice is probably pinned at the lattice is probably pinned at low T,

low T,

mass flow requires motion of the mass flow requires motion of the lattice

lattice

But probably not in the new expt But probably not in the new expt through capillaries (condmat jan through capillaries (condmat jan 06)06)

Bonfait, Godfrin and Castaing (J.

Physique 1989) Physique 1989)

growth inside a thin capacitor growth inside a thin capacitor at T < 20 mK

at T < 20 mK

blocked by a facet at the blocked by a facet at the entrance ?

entrance ?

(33)

Our experimental setup

Fill a test tube (1 cm Fill a test tube (1 cm

) at 1.3 K_{) at 1.3 K}

lower T down to 50 mK lower T down to 50 mK

melt the outside melt the outside follow the level follow the level

inside inside

P = _{P =}gh = 2.10_{gh = 2.10}^-5^-5 bar bar According to Kim and According to Kim and Chan, melting velocity Chan, melting velocity

V = 1 cm/h V = 1 cm/h

if critical velocity if critical velocity 30 30 m/s and superfluid m/s and superfluid

density

density _s_s / _/_c_c = 10_{= 10}^-2^-2

V V

liquid liquid

solid solid

(34)

solid

⁴⁴

He He

does not flow does not flow

at 50 mK at 50 mK

with a mass flow with a mass flow at the critical at the critical velocity

velocity v v_c_c ~ 30 ~ 30

m/s m/s , and , and _s_s / _/

_c_c = 10_{= 10}^-2^-2 the the

interface should interface should move by 1 cm in 1 move by 1 cm in 1 hourhour

=> (

=> (_s_s / _/_c_c)₎ vv_c_c is is at least 4000

at least 4000 times smaller times smaller

liquid liquid

solid solid Inside a test

Inside a test tube

tube (1 cm

(1 cm ) : no _{) : no} measurable flow measurable flow over 4 hours at over 4 hours at 50 mK

50 mK

ENS-Paris, march-april 2006 ENS-Paris, march-april 2006 ::

one needs to apply a heat pulse to push the crystal one needs to apply a heat pulse to push the crystal

inside the tube at 1.3 K => a few defects inside the tube at 1.3 K => a few defects

No flow at the glass / He interface either No flow at the glass / He interface either

(35)

No growth either

(36)

no growth with a better

quality crystal

(37)

a bad quality crystal grown from the normal liquid phase at high T (

2 K)

Ryosuke Ishiguro, ENS-Paris, 13 march 2006 Ryosuke Ishiguro, ENS-Paris, 13 march 2006

(38)

would a bad quality He ⁴ crystal flow ?

Ryosuke Ishiguro, ENS-Paris, 13 march 2006 Ryosuke Ishiguro, ENS-Paris, 13 march 2006

Could grain Could grain boundaries be boundaries be superfluid and superfluid and sufficiently sufficiently numerous in numerous in such bad

such bad

crystals to crystals to

represent 1% of represent 1% of the mass ?

the mass ?

How to measure How to measure their density their density from light

from light scattering?

scattering?

(39)

a recent mail a recent mail

De: pgg@curie.fr

Date: 27 janvier 2006 15:17:07 GMT+01:00 À: balibar@lps.ens.fr

Cher Sebastien,

Je crains de t'ennuyer par mes messages successifs, mais tout de même...

a) Merci pour ta remarque: frequence = 1 kilocycle (j'avais mal lu le texte de Chan). A cette basse frequence le mecanisme de lag inertiel est

completement negligeable.

b) Dis-moi (si ce n'est pas secret) le principe de ta manip sur le solide.

c) Je soupconne (comme toi) que la superfluidite prend place sur des defauts comme les joints de

grains : mouvement de lacunes, ou superfluidite de surface. Ceci m'amene a une question. A-t-on jamais observe du prewetting sur la surface de He4 solide ? En tous cas, tous mes voeux pour ta manip.

Cordialement, Pierre-Gilles

(40)

(41)

Pressure dependence (Kim and Chan)

• As a function of pressure the supersolid fraction shows a

maximum near 55bars. The supersolid fraction extrapolates

to zero near 170 bars.

(42)

The pressure dependence of the The pressure dependence of the

« supersolidity »:

superfluidity of grain superfluidity of grain

boundaries or mobile boundaries or mobile

dislocations (PGG)?

In the range 25 to 55 bar, the number In the range 25 to 55 bar, the number

of defects (grain boundaries) increases of defects (grain boundaries) increases

due to the crystal preparation method due to the crystal preparation method

(constant volume) (constant volume)

The grain boundaries could be liquid The grain boundaries could be liquid

and have a superfluid transition in the and have a superfluid transition in the

range 50 to 200 mK range 50 to 200 mK

Superfluidity in the liquid grain Superfluidity in the liquid grain

boundaries disappears around 200 bar boundaries disappears around 200 bar

Another possibility: dislocations are Another possibility: dislocations are mobile at low T and adsorb vacancies, mobile at low T and adsorb vacancies,

so that some mass decouples.

(43)

the phase coherence the phase coherence

test the phase coherence with a barrier inside the oscillator test the phase coherence with a barrier inside the oscillator

According to Kim and Chan, there is phase coherence, According to Kim and Chan, there is phase coherence,

that is macroscopic mass flow without dissipation

But a single test a one frequency in one geometry

(44)

mass flow inside

³

He crystals near 0.32K where E

_vac

< 1K

the latent heat L is negligible, T is highly homogeneous the latent heat L is negligible, T is highly homogeneous

local growth and melting according to gravity, surface tension, and curvature, no facets local growth and melting according to gravity, surface tension, and curvature, no facets

the crystal seems to flow down in less than 1 minute but the lattice is immobilethe crystal seems to flow down in less than 1 minute but the lattice is immobile there must be an inverse flow of vacancies

there must be an inverse flow of vacancies

dripping ( c, g ...) + coalescence ( f, j ...) dripping ( c, g ...) + coalescence ( f, j ...) of single crystals with identical orientation of single crystals with identical orientation except for the last drop (k,l)

except for the last drop (k,l)

Graner et al.

Graner et al. J. Low Temp. Phys. 75, 69 (1989)J. Low Temp. Phys. 75, 69 (1989) Ishiguro et al. PRL 93, 235301 (2004) Ishiguro et al. PRL 93, 235301 (2004)

(45)

Echoes in a spherical Echoes in a spherical

geometry geometry

0 20 40 60 80 100 120 140

time t (microseconds)

Accurate measurement of Accurate measurement of

the flight time the flight time

tt_f_f = R/c = R/c

and the radius and the radius R = 9.42 +/- 0.02 mm R = 9.42 +/- 0.02 mm

Excitation : 3 cycles at 1.39 MHz Excitation : 3 cycles at 1.39 MHz

(46)

Non-linear sound Non-linear sound

focusing focusing

focusing with a focusing with a non-linear eq. of non-linear eq. of

state state

leads to sharp leads to sharp positive peaks positive peaks (Appert et al.

(Appert et al.

2003) 2003)

0 10 20 30 40 50 60 70

time t - t

f (microseconds)

22.3 bar

0 bar 2 bar 3.9 bar 10.3 bar excitation voltage V(t)

synchronization synchronization confirms R = 9.42 confirms R = 9.42 mmmm

period : 7.6

period : 7.6 s s corresponding to corresponding to 132 kHz

132 kHz

QuickTime™ et un décompresseur TIFF (LZW) sont requis pour visionner cette image.

(47)

non-linear non-linear

effects effects

0.154 0.156 0.158 0.160 0.162 0.164 0.166 0.168

32 32.5 33 33.5 34

TIME (microseconds)

At large amplitude, positive pressure peaks At large amplitude, positive pressure peaks

appear, due to the curvature of the appear, due to the curvature of the

equation of state equation of state

C. Appert, C. Tenaud, X. Chavanne, S.

Balibar, F. Caupin and D. d’Humières, Eur.

Phys. J. B35, 531 (2003) Phys. J. B35, 531 (2003)

QuickTime™ et un décompresseur TIFF (LZW) sont requis pour visionner cette image.

A fit with a measurement at 9.8 bar A fit with a measurement at 9.8 bar

in a quasi-spherical geometry

in a quasi-spherical geometryCalculation at larger amplitudeCalculation at larger amplitude

In the vicinity of In the vicinity of Pierre-Gilles, Pierre-Gilles, from superfluidity to from superfluidity to supersolidity supersolidity