Localized Bose-Einstein Condensation
in Liquid 4He in Disorder
Henry R. Glyde
Department of Physics & Astronomy
University of Delaware
APS March Meeting
Denver, Co
3-7 March, 2014
BEC, Excitations, Superfluidity
Bose Einstein Condensation
(neutrons)
1968Collective Phonon-Roton modes (neutrons)
1958Superfluidity
(torsional oscillators)
`
1938He in porous media integral part
of historical superflow measurements.
BEC, Phonon-roton modes and Superfluidity
Scientific Goals:
• Observe BEC and Phonon-roton modes
in bulk liquid helium and in helium in porous media
(also layer modes in porous media)
• Explore the interdependence of BEC, well defined phononroton modes and superflow.
• BEC is the origin superflow.
Well defined p-r modes exist because there is BEC.
BEC, Superfluidity and Superfluidity
Organization of Talk
1. Bulk liquid 4He. Measurements of :
- superfluidity (historically first)
- phonon-roton modes
- BEC
BEC, P-R modes, superflow coincide.
2. Measurements in Porous Media (Bosons in
disorder)
-P-R modes
-BEC (just starting)
P-R modes and BEC exist at temperatures above
superfluid phase in PM. (TC < T < TC )
P-R modes exist where there is BEC.
BEC and n (k) (single particle excitations)
Collaborators: SNS and ISIS
Richard T. Azuah
Souleymane Omar Diallo
Norbert Mulders
Douglas Abernathy
- NIST Center for Neutron
Research, Gaithersburg, USA
- Spallation Neutron source,
ORNL, Oak Ridge, TN
- University of Delaware
Jon V. Taylor
- Spallation Neutron source,
ORNL, Oak Ridge, TN
- ISIS Facility, UK
Oleg Kirichek
- ISIS Facility, UK
Collective (Phonon-roton) Modes, Structure
Collaborators: (ILL)
JACQUES BOSSY Institut Néel, CNRS- UJF,
Grenoble, France
Helmut Schober
Institut Laue-Langevin
Grenoble, France
Jacques Ollivier
Institut Laue-Langevin
Grenoble, France
Norbert Mulders
University of Delaware
Phase Diagram of Bulk Helium
Phase Diagram Bulk helium
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)
London
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)
SUPERFLUID: Bulk Liquid SF Fraction s(T)
Critical Temperature Tλ = 2.17 K
Landau Theory of Superfluidity
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 ).
PHONON-ROTON MODE: Dispersion Curve
←Δ
 Donnelly et al., J. Low Temp. Phys. (1981)
 Glyde et al., Euro Phys. Lett. (1998)
BOSE-EINSTEIN CONDENSATION
1924
Bose gas : Φk = exp[ik.r] , Nk
k = 0 state is condensate state for uniform fluids.
Condensate fraction, n0 = N0/N = 100 % T = 0 K
Condensate wave function: ψ(r) = √n0 e iφ(r)
Bose-Einstein Condensation: Gases in Traps
Bose-Einstein Condensation, Bulk Liquid 4He
Glyde, Azuah, and Stirling
Phys. Rev., 62, 14337 (2000)
Bose-Einstein Condensation: Bulk Liquid
Expt: Glyde et al. PRB (2000)
Phase Diagram Bulk helium
BEC: Bulk Liquid
4He vs pressure
PR B83, 100507 (R)(2011)
Bose-Einstein Condensate Fraction
Liquid Helium versus Pressure
Glyde et al. PR B83, 100507 (R)(2011)
Bose-Einstein Condensate Fraction
Liquid Helium versus Pressure
Diallo et al. PRB 85, 140505 (R) (2012)
Phase Diagram Bulk helium
PHONON-ROTON MODE: Dispersion Curve
←Δ
 Donnelly et al., J. Low Temp. Phys. (1981)
 Glyde et al., Euro Phys. Lett. (1998)
Maxon in 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)
BEC, Excitations and Superfluidity
Bulk Liquid 4He
1. Bose-Einstein Condensation,
2. Well-defined phonon-roton modes, at Q > 0.8 Å-1
3. Superfluidity
All co-exist in same p and T range.
They have same “critical” temperature,
Tλ = 2.17 K
SVP
Tλ = 1.76 K
25 bar
Phase Diagram Bulk helium
Excitations, BEC, and Superfluidity
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 :
Well defined phonon-roton modes follow from BEC.
Single particle and P-R modes have the same energy when there
is BEC. When there is BEC there are no low energy single
particle modes.
Landau Theory:
Superfluidity follows from existence of well defined
phonon-roton modes. The P-R mode is the only mode in
superfluid 4He. Energy gap
B.
HELIUM IN POROUS MEDIA
AEROGEL*
Open
95% porous
87% porous
A
87% porous
B
- 95 % sample grown by John Beamish at U of A entirely with deuterated
materials
VYCOR (Corning)
70 Å pore Dia.
30% porous
-- grown with B11 isotope
GELSIL (Geltech, 4F)
25 Å pores
44 Å pores
34 Å pores
50% porous
MCM-41
30% porous
47 Å pores
NANOTUBES (Nanotechnologies Inc.)
Inter-tube spacing in bundles 1.4 nm
2.7 gm sample
* University of Delaware, University of Alberta
Bosons in Disorder
Liquid 4He in Porous Media
Flux Lines in High Tc Superconductors
Josephson Junction Arrays
Granular Metal Films
Cooper Pairs in High Tc Superconductors
Models of Disorder
excitation changes
new excitations at low energy
Helium in Porous Media: Superfluidity
Superfluid Density in Porous Media
Chan et al. (1988)
Phase Diagram in gelsil: 25 A pore diameter
- Yamamoto et al, Phys. Rev. Lett. 93, 075302 (2004)
Helium in MCM-41 (45 A) and in gelsil (25 A)
Bossy et al. PRB 84,1084507 (R) (2010)
Phonon-Roton Dispersion Curve
←Δ
 Donnelly et al., J. Low Temp. Phys. (1981)
 Glyde et al., Euro Phys. Lett. (1998)
S(Q,ω) of Helium in MCM-41 powder
Pressure dependence of S(Q,ω) at the roton
(Q=2.1Å-1): MCM-41
Net Liquid He at 34 bar in MCM-41
Bossy et al. EPL 88, 56005 (2012)
Liquid 4He in gelsil
25 A pore diameter
Tc ~ 1.3 K
Net Liquid He in MCM-41
Temperature dependence
Bossy et al. EPL 88, 56005 (2012)
Liquid He in MCM-41
Temperature dependence
Bossy et al. EPL 88, 56005 (2012)
Normal Liquid He Response vs Pressure
Helium in MCM-41 (45 A) and in gelsil (25 A)
Bossy et al. PRB 84,1084507 (R) (2010)
P-R modes and BEC: Conclusions
1. At 34 bar P-R modes exist up a specific
temperature only, T = 1.5 K, a temperature that is
identified as Tc (BEC), critical temperature for BEC.
2.
The intensity in the mode decreases with increasing
T without mode broadening and vanishes at Tc
(BEC), because Tc (BEC) is so low at 34 bars.
3.
At 34 bar the response of normal liquid is like that
of a classical fluid (the intensity peaks near ω = 0)
3.
Phonon-roton modes at higher wave vector exist at
temperatures and pressures where there is BEC.
BEC: Liquid 4He in MCM-41
Diallo, Azuah, Glyde et al. (2014)
Localization of Bose-Einstein Condensation in disorder
Conclusions:
• Observe phonon-roton modes and BEC up to T ~ Tλ
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,
in the temperature range Tc < T <Tλ = 2.17 K
Vycor
Tc = 2.05 K
gelsil (44 Å)
Tc = 1.92 K
gelsil (25 Å)
Tc = 1.3 K
• At temperatures above Tc
- BEC is localized by disorder
- No superflow
Localized Bose-Einstein Condensation
in Films of Liquid 4He in Disorder
Henry R. Glyde
Department of Physics & Astronomy
University of Delaware
APS March Meeting
Denver, Co
3-7 March, 2014
Phase Diagram in gelsil: 25 A pore diameter
- Yamamoto et al, Phys. Rev. Lett. 93, 075302 (2004)
Phase Diagram
in gelsil
Films in gelsil
Phase diagram of 4He films in gelsil: 25 A
Adsorption Isotherm of 4He in gelsil
25 A pore diameter
Phonon-Roton Dispersion Curve (in gelsil F = 86 %)
←Δ
Bossy et al. (in preparation)
Phonon-Roton Dispersion Curve (in gelsil F = 97 %)
←Δ
Bossy et al. (in preparation)
Phonon-roton and layer mode versus Filling
Phonon-roton and layer mode vs temperature
Phonon-roton mode at Filling F = 86 %
Phonon-roton and layer mode at Filling F = 86 %
Modes vs Filling F = 86-97 %
Modes vs Filling F = 86-97 %
Temperature Dependence
of modes
Mode Intensities vs Temperature
Phase diagram of 4He films in gelsil: 25 A
Liquid 4He in Disorder and Boson Localization
Conclusions:
• At partial fillings, we observe P-R modes (BEC)
at temperatures above Tc at temperatures
above the superfluid phase.
• Above Tc we have apparently localized BEC,
islands of BEC, as at full filling. It is not clear if
we have 2D or 3D liquid close to full filling.
• P-R modes and superflow start at about the
same filling, 20-25 μmol/m**2.
Helium in MCM-41 (45 A) and in gelsil (25 A)
Bossy et al. PRB 84,1084507 (R) (2010)
Schematic Phase Diagram He in Nanoporous media
Bossy et al., PRL 100, 025301 (2008)
Schematic Phase Diagram: He in
Nanoporous media
Kamerlingh Onnes
Cuprates Superconductors
Insulator
T
Pseudo-gap
Metal
Metal
AF Mott
Insulator
Superconductor
Doping Level
Schematic Phase Diagram High Tc
Superconductors
Alvarez et al. PRB (2005)
Patches of Antiferromagnetic and
Superconducting regions
Alvarez et al. PRB (2005)
Phase Diagram High Tc
Superconductor
Gomes et al. Nature (2007)
Patches of Energy gap, TC= 65K
Gomes et al. Nature (2005)
Helium in MCM-41 (45 A) and in gelsil (25 A)
Bossy et al. PRB 84,1084507 (R) (2010)
Liquid 4He in Disorder and Boson Localization
Conclusions:
• Tc for superfow is supressed below TBEC in porous
media. Tc < TBEC in confinement and disorder.
TBEC ~ Tλ .
• In the temperature range Tc < T < TBEC the BEC is
localized to patches, denoted the localized BEC region.
The localized BEC region lies between the superfluid
and normal phase.
• Superfluid – non superfluid liquid transition is associated
with an extended BEC to localized BEC cross over.
• Well defined Phonon-roton modes (Q > 0.8 A-1) exist
because there is BEC.