Phonon-roton Phonon-roton excitations and excitations and quantum phase quantum phase transitions in liquid transitions in liquid 4 4 He in nanoporus media He in nanoporus media Henry R. Glyde Department of Physics & Astronomy University of Delaware Recent Progress in Many Body Theories Barcelona, 16-20 July, 2007
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Phonon-roton excitations and quantum phase transitions in liquid 4 He in nanoporus media
Phonon-roton excitations and quantum phase transitions in liquid 4 He 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: - PowerPoint PPT Presentation
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Phonon-roton excitations Phonon-roton excitations and quantum phase and quantum phase
transitions in liquid transitions in liquid 44He in He in nanoporus mediananoporus media
Henry R. GlydeDepartment of Physics & Astronomy
University of Delaware
Recent Progress in Many Body Theories
Barcelona, 16-20 July, 2007
Excitations, BEC, and SuperfluidityExcitations, BEC, and Superfluidity
Collaborators:
Jonathan Pearce University of Delaware, ILLNational Physical Laboratory
Teddington, UK
Jacques Bossy Centre de Recherche sur LesTrès Basses TemperatureCNRS, 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
Helmut Schober Institut Laue-Langevin
Grenoble, France
Excitations, BEC, and SuperfluidityExcitations, BEC, and Superfluidity
Collaborators (Con’t):
Oliver Plantevin - Université de Paris Sud
Helmut Schober - Institut Laue Langevin, Grenoble, France
Excitations, BEC, and SuperfluidityExcitations, BEC, and Superfluidity
Goals:
Explore the interdependence of Bose-Einstein Condensation (BEC), phonon-roton 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 SuperfluidityExcitations, 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 DisorderBosons 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: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 SuperfluidityExcitations, BEC, and Superfluidity
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 TPhonon-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.
Moroni and Boninsegni JLTP (2004)Moroni and Boninsegni JLTP (2004)
50 bars
Bose-Einstein CondensationBose-Einstein CondensationSolid Helium p = 41 barsSolid Helium p = 41 bars
Diallo et al. PRL 98, 205301 (2007)
PHONONS AND ROTONSPHONONS AND ROTONS
Donnelly et al., J. Low Temp. Phys. (1981) Glyde et al., Euro Phys. Lett. (1998)
Roton Energy versus PressureRoton Energy versus Pressure
Roton energy at Q ~ 2.1 Å-1 as a function of pressure.
Vranjes et al. PRL (2005)
Liquid Liquid 44He at Negative PressureHe at Negative Pressure
Liquid Liquid 44He at Negative Pressure He at Negative Pressure
Dispersion curve at SVP and - 5 bar
Liquid Liquid 44He at Negative Pressure He at Negative Pressure MCM-41 MCM-41
Adsorption isotherm
Pores are full with 4He at negative pressure at fillings C to H. C = -5.5 bar.
Maxon Energy versus PressureMaxon Energy versus Pressure
Maxon energy at Q = 1.1 Å-1 as a function of pressure.
Phonon-roton mode of Phonon-roton mode of 44He He under pressure, 24.7 barsunder pressure, 24.7 bars
Phonon-roton mode of Phonon-roton mode of 44He He under pressure, 31.2 barsunder pressure, 31.2 bars
Temperature dependence of mode Temperature dependence of mode intensity: Maxon, bulk liquid intensity: Maxon, bulk liquid 44He He
Talbot et al., PRB, 38, 11229 (1988)
Roton in Bulk Liquid Roton in Bulk Liquid 44HeHe
Talbot et al., PRB, 38, 11229 (1988)
Beyond the Roton in Bulk Beyond the Roton in Bulk 44HeHe
Data: Pearce et al. J Phys Conds Matter (2001)
Phonons and Rotons (sharply Phonons and Rotons (sharply defined modes) arise From Bose-defined modes) arise From Bose-Einstein CondensationEinstein Condensation
Schematic Phase DiagramSchematic Phase Diagram QPT in Nanoporous media QPT in Nanoporous media
Conclusions:Conclusions:
Liquid 4He in Disorder and Boson Liquid 4He in Disorder and Boson LocalizationLocalization
• 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 Quantum Phase Transition at p ~ 35 bars Only localized BEC at p > 35 bars.Only localized BEC at p > 35 bars.
Conclusions (QPT):Conclusions (QPT):
Liquid 4He in Disorder and Boson Liquid 4He in Disorder and Boson LocalizationLocalization
• At T ~ 0 K and higher pressure, ( p > 25 At T ~ 0 K and higher pressure, ( p > 25 bars) BEC condensate fraction is small.bars) BEC condensate fraction is small.
(n(n00 ~ 1 % at p = 70 bars, bulk ~ 1 % at p = 70 bars, bulk 44He)He)
. 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 liquid-solid co-existence above 38 bars, probably up to 45-50 bars.
Excitations of superfluid Excitations of superfluid 44He at He at pressures up to 40 barspressures up to 40 bars
Phase diagran and excitations of Phase diagran and excitations of superfluid superfluid 44He in 44 He in 44 ÅÅ gelsil gelsil