Transcript T c (Superfluidity) - CIMNE Congress Bureau

Phonon-roton excitations
and quantum phase
transitions in liquid 4He in
nanoporus media
Henry R. Glyde
Department of Physics & Astronomy
University of Delaware
Recent Progress in Many Body
Theories
Barcelona, 16-20 July, 2007
Excitations, BEC, and Superfluidity
Collaborators:
Jonathan Pearce
University of Delaware, ILL
National Physical Laboratory
Teddington, UK
Jacques Bossy
Centre de Recherche sur Les
Très Basses Temperature
CNRS, Grenoble, France
Francesco Albergamo
-ESRF, Grenoble, France
Bjorn Fåk
- Commissariat à l’Energie
Atomique, Grenoble, France
Norbert Mulders
-University of Delaware
Richard T. Azuah - NIST Center for Neutron
Research, Gaithersburg,
Maryland, USA
Excitations, BEC, and Superfluidity
Collaborators (Con’t):
Oliver Plantevin
-Université de Paris Sud
Helmut Schober - Institut Laue Langevin,
Grenoble, France
Excitations, BEC, and Superfluidity
Goals:
Explore the interdependence of BoseEinstein Condensation (BEC), phononroton excitations, and superfluidity.
Reveal origin of superfluidity in disorder
and confinement.
-BEC or well defined excitations.
Neutron scattering studies of excitations
of liquid 4He in confinement and disorder.
Compare with measurements of
superfluid density.
Excitations, BEC, and Superfluidity
Landau Theory:
Superfluidity follows from
existence of well defined phonon-roton
modes. The P-R mode is the only mode in
superfluid 4He.
Bose-Einstein Condensation:
Superfluidity follows from BEC. An
extended condensate has a well defined
magnitude and phase, <ψ> = √n0eιφ ;
vs ~ grad φ
Bose-Einstein Condensation (BEC):
Well defined phonon-roton modes
follow from BEC. Single particle and P-R
modes have the same energy when there
is BEC. No low energy single particle
modes.
Bosons in Disorder
Liquid 4He in aerogel, Vycor, gelsil (Geltech)
Bose gases in traps with disordered potentials
Josephson Junction Arrays
Granular Metal Films
Cooper Pairs in High Tc Superconductors
Flux Lines in High Tc Superconductors
Specific Present Goals:
Impact of finite size (confinement) and disorder on
excitations and Bose-Einstein condensation.
Localization of Bose-Einstein Condensation by disorder
Search for a Quantum Phase Transition
Explore liquid helium at higher pressure
Helium at negative pressure and on nanotubes (1D)
Excitations, BEC, and Superfluidity
Organization of Talk
1. Bulk liquid 4He --review
Superfluid density, ρS
BEC condensate fraction, n0
Phonon-roton excitations.
2. Porous media – p ~ 0, T dependence
Review ρS , TC
Present phonon-roton data.
Evidence for localized BEC at
temperatures above TC
3. Porous media –high pressures, low T
Phonon-roton modes disappear at 37
bars and T ~ 0 K, evidence for a
superfluid-normal transition at T ~ 0
K, a quantum phase transiton? Or
just solidification.
BULK HELIUM: Phase Diagram
SUPERFLUIDITY
1908 – 4He first liquified in Leiden
by Kamerlingh Onnes
1925 – Specific heat anomaly
observed at Tλ = 2.17 K by Keesom.
Denoted the λ transiton to He II.
--------------------
1938 – Superfluidity observed in He
II by Kaptiza and by Allen and
Misener.
1938 – Superfluidity interpreted as
manifestation of BEC by London
vS = grad φ (r)
Kamerlingh Onnes
London
Superfluid Density s(T)
Bulk Liquid 4He
Superfluid Density
ρS (T) = 0 at T = Tλ
Phase Diagram of Bulk Helium
BOSE-EINSTEIN CONDENSATION
Atoms in Traps
Bose-Einstein Condensation:
Atoms in Traps
Bose-Einstein Condensation
Glyde, Azuah, and Stirling
Phys. Rev. B62, 14337 (2000)
Bose-Einstein Condensation
Expt: Glyde et al. PRB (2000)
Condensate fraction bulk 4He
L. Vranjes and J. Boronat et al.
PRL (2005)
Condensate fraction bulk 4He
Moroni and Boninsegni JLTP (2004)
50 bars
Bose-Einstein Condensation
Solid Helium p = 41 bars
Diallo et al. PRL 98, 205301 (2007)
PHONONS AND ROTONS
 Donnelly et al., J. Low Temp. Phys. (1981)
 Glyde et al., Euro Phys. Lett. (1998)
Roton Energy versus Pressure
Roton energy at Q ~ 2.1 Å-1 as a function
of pressure.
Vranjes et al. PRL (2005)
Liquid 4He at Negative Pressure
Liquid 4He at Negative Pressure
Dispersion curve at SVP and - 5 bar
Liquid 4He at Negative Pressure
MCM-41
Adsorption isotherm
Pores are full with 4He at negative
pressure at fillings C to H. C = -5.5 bar.
Maxon Energy versus Pressure
Maxon energy at Q = 1.1 Å-1 as a function
of pressure.
Phonon-roton mode of 4He
under pressure, 24.7 bars
Phonon-roton mode of 4He
under pressure, 31.2 bars
Temperature dependence of mode
intensity: Maxon, bulk liquid 4He
Talbot et al., PRB, 38, 11229 (1988)
Roton in Bulk Liquid 4He
Talbot et al., PRB, 38, 11229 (1988)
Beyond the Roton in Bulk 4He
Data: Pearce et al. J Phys Conds Matter (2001)
Phonons and Rotons (sharply
defined modes) arise From BoseEinstein Condensation
Bogoliubov (1947) showed:
Bose gas with BEC -- quasiparticles
have energy:
  cQ
Q
- phonon (sound) form
Quasiparticle mode coincides with
sound mode.
Only one excitation when have BEC.
Phonons and Rotons Arise From
Bose-Einstein Condensation
Gavoret and Nozières (1964) showed:
Dense liquid with BEC
– only one excitation: density and
quasiparticle modes have the same
energy, as in Bose gas.   cQ
Q
-- no other excitations at low energy
(could have vortices).
Ma and Woo (1967), Griffin and
Cheung (1973), and others showed:
Only a single mode at all Q with BEC -the phonon-roton mode.
Excitations in a Bose Fluid
ρ+
Excitations, BEC, and Superfluidity
Bulk Liquid 4He
BEC, well-defined phonon-roton modes at
Q > 0.8 Å-1 and superfluidity coincide.
e.g., all have some “critical” temperature,
Tλ = 2.17 K
SVP
Tλ = 1.76 K
25 bar
Phase Diagram of Bulk Helium
Superfluidity
Landau Theory
Superfluidity follows from the nature of
the excitations:
that there are phonon-roton
excitations only and no other low
energy excitations to which superfluid
can decay
have a critical velocity and an energy
gap (roton gap ).
Via P-R excitations, superflow arises
from BEC.
BEC and Phase Coherence, Ø (r)
Superfluidity follows directly from BEC,
phase conherence   (r ).
s
Landau
POROUS MEDIA
AEROGEL
Open
95% porous
87% porous
A
87% porous
B
-- grown with deuterated
materials or flushed with D2
VYCOR
30% porous
70 Å pore Diameter -- grown with B11 isotope
GELSIL (GELTECH) 50% porous
44 Å pore Diameter
34 Å pore Diameter
25 Å pore Diameter
MCM-41
47 Å pores
30% porous
Superfluid Properties in
Confinement/Disorder
Confinement reduces Tc below Tλ  2.17K .
Confinement modifies  s (T ) (T dependence).
Confinement reduces  s (T ) (magnitude).
Porous media is a “laboratory” to investigate the
relation between superfluidity, excitations, and
BEC.
Measure corresponding excitations and
condensate fraction, no(T). (new, 1995)
Tc in Porous Media
Superfluid Density in Porous Media
Chan et al. (1988)
Miyamoto and Takeno (1996)
Geltech
(25 Å pores)
Superfluid Density in gelsil
(Geltech) – 25 A diameter
- Yamamoto et al.
Phys. Rev. Lett. 93, 075302 (2004)
Schematic Phase Diagram of
Helium Confined to Nanoscales
e.g. 2 - 4 nm
Phase Diagram of gelsil:
25 Å pore diameter
- Yamamoto et al,
Phys. Rev. Lett. 93, 075302 (2004)
Bose-Einstein Condensation
Liquid 4He in Vycor
Tc (Superfluidity) = 2.05 K
Azuah et al., JLTP (2003)
Bose-Einstein Condensation
Vycor
Azuah et al., JLTP (2003)
Phonons, Rotons, and Layer Modes
in Vycor and Aerogel
Temperature Dependence
of Roton Energy
Fåk et al., PRL, 85 (2000)
Excitations of Liquid 4He in
Confinement
Conclusions:
• Liquid helium in porous media supports
well defined phonon-roton excitations – up
to wave vectors Q ≈ 2.8 Å.
• Energies and widths (within precision) are
the same as in bulk 4He at all T.
• Liquid also supports “layer modes” at
roton wave vectors.
• At partial fillings, can also see ripplons on
4He liquid surfaces. (Lauter et al. Appl.
Phys. A 74, S1547 (2002))
Intensity in P-R Mode vs. T
Glyde et al., PRL, 84 (2000)
Mode Intensity in Vycor:
T = 1.95 K
Mode Intensity in Vycor
T = 2.05 K
Mode Intensity in Vycor:
T = 2.15 K
Mode Intensity in Vycor:
T = 2.25 K
Fraction, fs(T), of Total Intensity
in Phonon-Roton Mode
Vycor Tc = 2.05 K
Albergamo et al.
Phys. Rev. B69, 014514 (2004)
Mode Intensity in 44A Gelsil:
versus T. Tc = 1.92 K
Albergamo et al. PRB (2007)
Fraction, fs(T), of total scattering
intensity in Phonon-Roton Mode
- gelsil 44 A pore diameter
Liquid 4He in 25 A gelsil (Geltech)
Tc (Superfluidity) ~ 1.3 K
Localization of Bose-Einstein
Condensation in disorder
Conclusions:
• Observe phonon-roton modes up to
T = Tλ = 2.17 K in porous media, i.e.
above Tc for superfluidity
• Well defined phonon-roton modes exist
because there is a condensate. Thus have
BEC above Tc in porous media.
Vycor
Tc = 2.05 K
gelsil (44 Å)
Tc = 1.92 K
gelsil (25 Å)
Tc = 1.3 K
• At temperatures Tc < T < Tλ
- BEC is localized by disorder
- No extended phase coherence
across the sample
- No superflow
Liquid 4He in Disorder and Boson
Localization
Conclusions:
• Extended BEC at temperature below Tc
in superfluid phase.
• Superfluid - Normal liquid transition
associated with an extended to
localized BEC cross over at SVP.
Schematic Phase Diagram
of BEC in Nanoporous media
PRESSURE DEPENDENCE
Phonon-Roton modes, Low T
Liquid 4He up 57 bars in gelsil
• gelsil 44 Å mean pore diameter,
– Pearce et al. PRL (2004)
• gelsil 34 Å mean pore diameter
- Pearce et al. Preprint (2006)
• gelsil 25 Å mean pore diameter
- being analysed (2006)
- Compare with Yamamoto et
al. PRL (2004) , superfluid
density in 25 Å gelsil.
Quantum Phase Transition in
25 A pore diameter gelsil ?
- Yamamoto et al,
Phys. Rev. Lett. 93, 075302 (2004)
Phonon-roton mode of 4He
under pressure, 31.2 bars
Pressure dependence:
44 Å gelsil
phonon (Q = 0.7 Ǻ-1) roton (Q=2.1Å-1)
Pressure dependence of
S(Q,ω) at the roton (Q=2.1Å-1)
34 A gelsil
Pressure dependence of
S(Q,ω) at the roton (Q=2.1Å-1)
25 A gelsil
Roton energy and intensity
in roton peak vs pressure
gelsil 34 Å
Pearce et al. (2006)
Phase diagram of modes of
liquid 4He in 34 Å pore diameter
gelsil
4He
remains liquid in 34 A gelsil
up to what pressure?
Δp = pL – pS = 2α / Rc
pS = 25.3 bars
Rc = 14 Å
(a) α = 0.17 erg/cm2 -- constant
pL = 50 bars
(b) α = -increases with pressure
(Maris and Caupin, JLTP 131, 145 (2003))
pL = 70 bars
Vycor,
pL = 45 bars
Rc = 35 Å
Quantum Phase Transition in
25 A pore diameter gelsil ?
- Yamamoto et al,
Phys. Rev. Lett. 93, 075302 (2004)
Schematic Phase Diagram
QPT in Nanoporous media
Net Scattering intensity
gelsil 34 Å
Pearce et al. PRL ( rejected 2006-7)
Compare with L. Vranjes, J. Boronat et al.
PRL,95, 145302 (2005)
Net Scattering intensity, gelsil 34 Å
and bulk liquid simulation compared.
← 60 bars
Bulk liquid
Pearce et al. (in progress)
Scattering intensity, gelsil 70 Å
and p = 70 bars
Wallacher et al. JLTP 138, 1013 (2005)
Schematic Phase Diagram
QPT in Nanoporous media
Liquid 4He in Disorder and Boson
Localization
Conclusions:
• Extended BEC at temperature below Tc
in superfluid phase at SVP.
• Superfluid - Normal liquid transition
associated with an extended to
localized BEC cross over at SVP.
• Quantum Phase Transition at p ~ 35 bars
Only localized BEC at p > 35 bars.
Liquid 4He in Disorder and Boson
Localization
Conclusions (QPT):
• At T ~ 0 K and higher pressure, ( p > 25
bars) BEC condensate fraction is small.
(n0 ~ 1 % at p = 70 bars, bulk 4He)
. Speculation:
At T ~ 0 K and pressures p > pc
- BEC is localized by disorder
- No extended phase coherence
across the sample
- No superflow
Quantum Phase Transition at 35 bars
. Phonon – roton modes disappear, p ~ 38
bars
- Have liquid up to 38 bars and liquidsolid co-existence above 38 bars,
probably up to 45-50 bars.
Excitations of superfluid 4He at
pressures up to 40 bars
Phase diagran and excitations of
superfluid 4He in 44 Å gelsil
Pearce et al., PRL (2004)
Bose-Einstein Condensation
PHONONS AND ROTONS
 Donnelly et al., J. Low Temp. Phys. (1981)
 Glyde et al., Euro Phys. Lett. (1998)
Superfluid Properties in
Confinement/Disorder
Confinement reduces Tc below Tλ  2.17K .
Confinement modifies  s (T ) (T dependence).
Confinement reduces  s (T ) (magnitude).
Porous media is a “laboratory” to investigate the
relation between superfluidity, excitations, and
BEC.
Measure corresponding excitations and
condensate fraction, no(T). (new, 1995)
Excitations of liquid 4He in 34 Å
pore diameter gelsil
Pearce et al.,(2006) (in progress)
BEC, Excitations, and Superfluidity
BEC in 2D
Boninsegni et al. PRL 96, 070601 (2006)
Condensate fraction bulk 4He
L. Vranjes and J. Boronat et al.
PRL (2005)
Condensate fraction bulk 4He
Moroni and Boninsegni JLTP (2004)
50 bars
Sum rule for condensate component
of S(Q,ω)
HRG, PRL (1995)
Topic of Talk:
Tc
• Well defined p-r excitations (Q > 0.8 Å) exist
because there is Bose-Einstein condensation (BEC).
• Measure superfluid density ρs (T) and determine the
normal to superfluid transition temperature Tc in
Vycor (same sample). Find:
Tc = 2.05 K
(Vycor)
<
Tλ = 2.17 K
(Bulk)
- disorder suppresses Tc below Tλ
• Find well defined phonon–roton excitations in Vycor
at temperatures T > Tc, up to T = Tλ = 2.17 K
• Thus BEC in Vycor above Tc , at temperatures
Tc < T < Tλ .
- localized BEC.
Momentum distribution solid 4He
Layer Mode in Porous Media
Layer Mode in Vycor and Aerogel
Liquid 4He in Disorder and Boson
Localization
Conclusions:
• Observe phonon-roton modes up to
T = Tλ = 2.17 K in porous media, i.e.
above Tc for superfluidity
• Well defined phonon-roton modes exist
because there is a condensate. Thus have
BEC above Tc in porous media.
Vycor
Tc = 2.05 K
Geltech (44 Å)
Tc = 1.92 K
Geltech (25 Å)
Tc = 1.0 K
• At temperatures Tc < Tc < Tλ
- BEC is localized by disorder
- No extended phase coherence
across the sample
- No superflow
Quantum Liquids in Confinement
Lopatin and Vinokur (2002):
Same model as Huang & Meng
-- disorder arising from random impurities
Reduction of critical temperature for BEC by
disorder
0
2 3
kT
(
m
/

)
o
c
Tc (BEC)  Tc [1 
R0 ]
2
6 n
Reduction of critical temperature for
superfluidity by disorder.
32
T  T [1  ( R0 ) 2 ]
c
c
27
0
Quantum Liquids in Confinement
Giorgini et al. (1994):
Same model as Huang & Meng
-- disorder arising from random impurities
Sound velocity
5 NR
c  c [1 
]
3 N
2
2
0
Half width of phonons
Q4
(Q) 
R0
2 2 2
24 (m /  ) c
Quantum Liquids in Confinement
Huang and Meng (1992):
Dilute Bose gas in disorder (T = OK). Disorder
potential u (x) arises from hard sphere impurities
placed at random.
 u( x )  0
 u( x )u( y)  Ro ( x  y )
Condensate fraction
No
8
N
 1  3 (na 3 )1/ 2  R
N
N
n
Superfluid density
s

 1
4 NR
3 N
where
N R nR (m /  2 ) 2
1/ 2


(
n
a
)
R0
0
3/ 2
N
n
8 n
Astrakharchik et al (2002)
-- Monte Carlo extension to Bose fluid.
Beyond the Roton in Bulk Liquid
4He
Phase Diagram of gelsil:
25 A pore diameter
- Yamamoto et al,
Phys. Rev. Lett. 93, 075302 (2004)
Bose-Einstein Condensation
Liquid 4He in Vycor
Tc (Superfluidity) = 1.95-2.05 K
Azuah et al., JLTP (2003)
Phonon in Bulk Liquid 4He
Q= 0.4 Å-1
Stirling and Glyde, PRB, 41, 4224 (1990)
Excitations, BEC, and Superfluidity
Liquid 4He in confinement, disorder
BEC and well-defined phonon-roton
modes are separated from superfluidity.
Below Tc – have superfluidity, BEC and
well-defined phonon-roton modes. BEC is
extended. Have extended phase coherence.
Above Tc - have phonon-roton modes and
BEC but no superflow. BEC is localized
by disorder. No extended phase coherence.
Localized BEC at Tc < T < Tλ .
Localized BEC at p > pc
New Here
Measurements of phonon-roton
excitations and BEC in disorder
Quantum Phase Transition in
25 A pore diameter gelsil ?
- Yamamoto et al,
Phys. Rev. Lett. 93, 075302 (2004)
Physics &
Astronomy
Superfluid and Normal 4He
J(Q,s) = 1(s) R(Q,s)
J(Q,s) - Fourier transform of J(Q,y)
Shows difference arising from the
condensate
Excitations, BEC, and Superfluidity
Neutron scattering studies of excitations
of liquid 4He in confinement and disorder.
• phonons and rotons in helium at
nanoscale size, in disorder, near surfaces.
• identify new excitations.
• temperature and pressure
dependence.
Explore the interdependence of BoseEinstein Condensation (BEC), phononroton excitations, and superfluidity.
Reveal origin of superfluidity, BEC or
well defined excitations.
Phonon-roton mode of liquid 4He
in 34 Å pore diameter gelsil
Pearce et al. (2006)
Pressure dependence of
S(Q,ω) at the roton (Q=2.1Å-1)
Excitations, BEC, and Superfluidity
Conclusions
-- porous media
At SVP and lower p, have localized BEC
in “normal” liquid phase, i.e. for
temperatures Tc < T < Tλ .
Have order in the normal phase up to Tλ
At SVP, superfluid-normal transition in
porous media is associated with an
extended to localized BEC cross over.
At pressures, p > 35 bars, liquid 4He no
longer supports well- defined P-R modes.
No roton for p > 35 bars.
Loss of P-R modes coincides with a
superfluid –normal Quantum Phase
Transition at pc ~ 35 bars
Localized BEC at Tc < T < Tλ .
No phonon - roton mode at p > pc
Excitations, BEC, and Superfluidity
Future program:
* Observe BEC in solid helium.
* Observe P-R modes in 25 Å gelsil (same
sample as used by Yamamoto et al).
Compare directly with ρS (p, T), pc , Tc .
* Observe OBDM in 2D.
(peak in n(k) in 2D).
• 1D 4He on nanotubes,
observe vibrational density of states.
Carl Weyman and Eric Cornell