Rotons, superfluidity, and He crystals

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Rotons, superfluidity, and He crystals
Sébastien Balibar Laboratoire de physique
statistique Ecole Normale Supérieure, Paris
(France)
LT 24, Orlando, aug. 2005
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Laszlo Tisza, june 17, 2005
From tisza_at_MIT.EDU Date 17 juin 2005 175540
GMT0200 ?o balibar_at_lps.ens.fr Dear
Sebastien, I am delighted to read in Physics
Today that you are to receive the Fritz London
Prize. This is wonderful! Please receive my
warmest congratulations. Yesterday I was leafing
through old correspondence and I found a letter
in which I nominated Landau for the Prize. I am
sure I was not alone. I was actually at LT-7 in
Toronto when the Prize was announced. It is
actually unconscionable of Landau not to have
taken note of the remarkable Simon - London work
on helium All he said that London was not a
good physicist. I am looking forward to your
book to straighten out matters. With warmest
regards, Laszlo
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Outline
BEC and rotons the London-Tisza-Landau
controversy
Quantum evaporation
The surface of He crystals
The metastability limits of liquid helium
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Looking back to the history of superfluidity
1928-38 discovery of superfluidity at Leiden,
Toronto, Cambridge, Moscow
J.F. Allen and A.D. Misener (Cambridge, jan
1938) flow rate Q in a capillary (radius
R) instead of Poiseuilles law Q p R4 DP / (8
h l) Q is nearly independent of DP and of R (10
to 500 ?m)  the observed type of flow cannot be
treated as laminar nor turbulent  The
hydrodynamics of helium II is non classical
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P. Kapitza rediscovers superleaks and introduces
the word  superfluid , in analogy with
 superconductor 
P. Kapitza (Moscow, dec. 1937) below Tl , the
viscosity of helium is very small ...   it is
perhaps sufficient to suggest, by analogy with
superconductors, that the helium below the
l-point enters a special state which might be
called a superfluid  this had already been
observed by Keesom and van den Ende, Proc. Roy.
Acad. Amsterdam 33, 243, 1930)
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5 march 1938, Institut Henri Poincaré (Paris)
Fritz Londonsuperfluidity has to be connected
with Bose-Einstein condensation
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Paris 1938 Laszlo Tisza introduces the
 two-fluid model
two parts a superfluid with zero entropy and
viscosity a  normal fluid  with non zero
entropy and non zero viscosity
two independent velocity fields vs and vn

• predicts thermomechanic effects
• the fountain effect observed by Allen and Jones,
  and the reverse effect
• thermal waves (second sound)

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Lev D. Landau Moscow 1941 - 47
1938 Landau comes out of prison thanks to
Kapitza 1941 in view of Kapitzas results on
thermal waves, Landau introduces a more rigorous
version of Tiszas two fluid model, but ignores
Fritz 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
elementary excitations (quasiparticles) phonons
et rotons ( elementary vortices ??) Calculates
the thermodynamic properties prédicts the
existence of a critical velocity and thermal
waves ( second sound  in agreement with
Kaptizas results
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The London-Tisza-Landau controversy
LT0 at Cambridge (1946), opening talk Fritz
London criticizes Landaus  theory based on the
shaky grounds of imaginary rotons  The
quantization of hydrodynamics by Landau is a
very interesting attempt however quite
unconvincing as far as it is based on a
representation of the states of the liquid by
phonons and what he calls  rotons . There is
unfortunately no indication that there exists
anything like a  roton  at least one searches
in vain for a definition of this word nor any
reason given why one of these two fluids should
have a zero entropy (inevitably taken by Landau
from Tisza) Despite their rather strong
disagreement, Landau was awarded the London prize
in 1960, six years after London's death
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BEC in 4He
London and Landau died too early to realize that
they both had found part of the truth
BEC takes place the condensate has been
measured and calculated at 0 bar from 7 to
9 at 25 bar from 2 to 4 3He behaves
differently
Moroni and Boninsegni (J. Low Temp. Phys. 136,
129, 2004)
and rotons exist they are not elementary quantum
vortices, but a consequence of local order in the
liquid
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neutron scattering rotons exist
R and R- rotons have opposite group
velocities The roton gap decreases with pressure
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rotons a consequence of local order
F. London, LT0, Cambridge (1946)    there has
to be some short range order in liquid helium. 
A liquid-solid instability (Schneider and Enz
1971) As the roton minimum ??decreases, order
extends to larger and larger distances and the
liquid structure gets closer to that of a
crystal. An instability when ? 0 some
information from acoustic crystallization ?
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Quantum evaporation
P.W. Anderson 1966 analogy with the
photoelectric effect 1 photon hv ejects 1
electron with a kinetic energy Ekin hv - E0
(E0 binding energy) 1 roton with a energy E gt
D 8.65 K evaporates 1 atom with a kinetic
energy Ekin gt D - 7.15 1.5 K ? v gt 79 m/s
S. Balibar et al. (PhD thesis 1976 and Phys.
Rev. B18, 3096, 1978) heat pulses at T lt 100 mK
? ballistic rotons and phonons 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 For a quantitative study and the evidence for
R and R - rotons, see M.A.H. Tucker, G.M.
Wyborn et A.F.G. Wyatt , Exeter (1990-99)
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The surface of helium crystals
For a detailed review, see S. Balibar, H. Alles,
and A. Ya. Parshin, Rev. Mod. Phys. 77, 317
(2005)
The roughening transitions. Helium crystals are
model systems whose static properties can be
generalized to all classical crystals
Crystallization waves and dynamic
properties. Helium crystals are also exceptional
systems whose dynamic properties are quantum and
surprising at 100 mK 4He crystals grow 1011
times faster than 3He crystals
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the roughening transitions
As T decreases, the surface is covered with more
and more facets. Successive roughening
transitions in high symmetry directions rough
above TR ? smooth below TR large scale
fluctuations disappear (no difference at the
atomic scale)
detailed study of critical behaviors step energy,
step width, growth rate, curvature as a
function of T and orientation quantitative
comparison with RG theory (P. Nozières 1987-92) a
Kosterlitz-Thouless transition
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roughening transitions in He 4
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the universal relation
D.S. Fisher and J.D. Weeks, PRL 1983 C.
Jayaprakash, W.F. Saam and S. Teitel, PRL 1983
kBTR (2/?) ?R d2 TR roughening transition
temperature ?? ? ?2? /? ?2 surface
stiffness (? surface tension, ? angle) ?R
??( TR)
(0001) or  c  facets in 4He the universal
relation is precisely satisfied with ?R 0.315
cgs and TR 1.30K
other facets in 4He are anisotropic checking
the universal relation is more difficult since
kBTR (2/?) (?1 ?2)1/2 d2
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up to 11 different facets on helium 3 crystals
0.55 mK
2.2 mK
(100)
(110)
(110)
(110)
(100)
Wagner et al., Leiden 1996 (100) and (211)
facets
Alles et al. , Helsinki 2001 up to 11 different
facets
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quantum fluctuations and coupling strength in 3He
growth shapes below 100 mK
(110) facets can be seen only below 100 mK E.
Rolley , S. Balibar, and F. Gallet, EuroPhys.
Lett. 1986 and 1989 due to a very weak coupling
of the crystal surface to the lattice, facets are
too small to be seen near TR 260 mK (known from
? 0.06 erg/cm2)
eq. shape at 320 mK ??? 0.06 erg/cm2
I. Todoshchenko et al. Phys. Rev. Lett. 93,
175301 (2004) and LT24 quantum fluctuations are
responsible for the weak coupling at high T but
damped at low T where the coupling is strong and
many facets visible.
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up to 60 different facets in liquid crystals
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3He crystals at 320 mK coalescence without
viscosity
no facets H.J. Maris a purely geometrical
problem dR/dt k/R2 neck radius R t 1/3 (as
for superfluid drops) inertia t1/2 viscosity
t ln(?t)
R. Ishiguro, F. Graner, E. Rolley and S.
Balibar, PRL 93, 235301 (2004)
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Crystallization waves
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melting and freezing
helium 4 crystals grow from a superfluid (no
viscosity, large thermal conductivity) the latent
heat is very small (see phase diagram) the
crystals are very pure wih a high thermal
conductivity ? no bulk resistance to the growth,
the growth velocity is limited by surface
effects smooth surfaces step motion rough
surfaces collisisions with phonons (no thermal
rotons below 0.6K) (cf. electron mobility in
metals) v k Dm with k T -4 the growth rate
diverges at low T helium crystals can grow and
melt so fast that crystallization waves propagate
at their surfaces as if they were liquids.

• 2 restoring forces
• surface tension g
• (more precisely the "surface stiffness" g )
• - gravity g
• inertia mass flow in the liquid ( rC gt rL)

? experimental measurement of the surface
stiffness g
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surface stiffness measurements

• the surface tension a is anisotropic
• the anisotropy of the surface stiffness
• a ? 2a/?q2 is even larger, especially for
  stepped surfaces close to facets.
• ?? ? ?/d?
• ?// ? 6???d?
• ? step width, energy ?, interactions ?

E. Rolley, S. Balibar and C. Guthmann PRL 72,
872, 1994 and J. Low Temp. Phys. 99, 851, 1995
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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
spherical geometry
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high amplitude acoustic waves

• At the focal point
• P Pstat dP cos (2p ?.t)
• f 1 MHz
• large pressure oscillations away from any wall
• (here 35 bar)
• during T/10 100 ns
• in a volume (l/10)3 15 mm3

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The tensile strength of liquid helium F. Caupin
, S. Balibar et al.see Phys. Rev. B 64, 064507
(2001) and J. Low Temp. Phys. 129, 363 (2002)
A singularity at 2.2K and -7 bar in agreement
with predictions of T? at negative pressure
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acoustic cristallization on a glass wallX.
Chavanne, S. Balibar and F. CaupinPhys. Rev.
Lett. 86, 5506 (2001)
amplitude of the acoustic wave at the nucleation
threshold 4.3 bar
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the extended phase diagram of liquid 4He
no homogeneous nucleation solid 4He up to 160
bar superfluidity at high P ? Nozieres JLTP 137,
45 (2004). an instability where ? 0 ? L.
Vranjes, J.Boronat et al. (preprint 2005) P gt
200 bar ?
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R. Ishiguro, F. Caupin and S. Balibar, LT24
a spherical transducer larger amplitude larger
non-linear effects
spherical transducer
HeNe laser
experimental cell
calibration of the acoustic pressure Brillouin
scattering inside the acoustic wave (in progress)
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Possible observation of homogeneous
crystallization
no nucleation
crystallization ?
We observe 2 nucleation regimes at high P
crystallization ? at low P cavitation
cavitation
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Intensity and time delay
R. Ishiguro, F. Caupin, and S. Balibar, this
conference

• The signal intensity increases when approaching
  Pm 25.3 bar
• nucleation at high P is delayed by 1/2 period
  compared to low P
• crystallization at high P ?
• calibration of the nucleation pressure
• Brillouin scattering inside the wave

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with many thanks to the co-authors of my papers
students, postdocs, visitors, hosts and
collaborators (chronological order)
B. Perrin, A. Libchaber, D. Lhuillier, J.
Buechner, B. Castaing, C. Laroche, D.O. Edwards,
P.E. Wolf, F. Gallet, E. Rolley, P. Nozières, C.
Guthmann, F. Graner, R.M.Bowley, W.F. Saam, J.P.
Bouchaud, M. Thiel, A. Willibald, P. Evers, A.
Levchenko, P. Leiderer, R.H. Torii, H.J.Maris,
S.C.Hall, M.S.Pettersen, C. Naud, E.Chevalier,
J.C.Sutra Fourcade, H. Lambaré, P. Roche,
O.A.Andreeva, K.O.  Keshishev, D. Lacoste, J.
Dupont-Roc, F. Caupin, S. Marchand, T. Mizusaki,
Y. Sasaki, F. Pistolesi, X. Chavanne, T. Ueno,
M. Fechner, C. Appert, C. Tenaud, D. d'Humières,
F. Werner,  G. Beaume, A. Hobeika, S.
Nascimbene, C. Herrmann, R. Ishiguro, H. Alles
and A.Ya. Parshin
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Dripping of helium 3 crystals