Phonon-roton excitations and quantum phase transitions in liquid 4 He in nanoporus media

1. 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

2. Excitations, BEC, and Superfluidity Collaborators: Jonathan PearceUniversity 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 Helmut Schober Institut Laue-Langevin Grenoble, France

3. Excitations, BEC, and Superfluidity Collaborators (Con’t): Oliver Plantevin - Université de Paris Sud Helmut Schober - Institut Laue Langevin, Grenoble, France

4. Excitations, 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.

5. 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.

6. 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 TcSuperconductors 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)

7. Excitations, BEC, and Superfluidity • Organization of Talk • 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.

8. BULK HELIUM: Phase Diagram

9. 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)

10. Kamerlingh Onnes

11. London

12. Superfluid Density s(T) Bulk Liquid 4He Superfluid Density ρS (T) = 0 at T = Tλ

13. Phase Diagram of Bulk Helium

14. BOSE-EINSTEIN CONDENSATIONAtoms in Traps

15. Bose-Einstein Condensation: Atoms in Traps

16. Bose-Einstein Condensation Glyde, Azuah, and Stirling Phys. Rev. B62, 14337 (2000)

17. Bose-Einstein Condensation Expt: Glyde et al. PRB (2000)

18. Condensate fraction bulk 4HeL. Vranjes and J. Boronat et al. PRL (2005)

19. Condensate fraction bulk 4HeMoroni and Boninsegni JLTP (2004) 50 bars

20. Bose-Einstein CondensationSolid Helium p = 41 bars Diallo et al. PRL 98, 205301 (2007)

21. PHONONS AND ROTONS  Donnelly et al.,J. Low Temp. Phys. (1981)  Glyde et al.,Euro Phys. Lett. (1998)

22. Roton Energy versus Pressure Roton energy at Q ~ 2.1 Å-1 as a function of pressure. Vranjes et al. PRL (2005)

23. Liquid 4He at Negative Pressure

24. Liquid 4He at Negative Pressure Dispersion curve at SVP and - 5 bar

25. 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.

26. Maxon Energy versus Pressure Maxon energy at Q = 1.1 Å-1 as a function of pressure.

27. Phonon-roton mode of 4He under pressure, 24.7 bars

28. Phonon-roton mode of 4He under pressure, 31.2 bars

29. Temperature dependence of mode intensity: Maxon, bulk liquid 4He Talbot et al., PRB, 38, 11229 (1988)

30. Roton in Bulk Liquid 4He Talbot et al., PRB, 38, 11229 (1988)

31. Beyond the Roton in Bulk 4He Data: Pearce et al. J Phys Conds Matter (2001)

32. Phonons and Rotons (sharply defined modes) arise From Bose-Einstein Condensation Bogoliubov (1947) showed: Bose gas with BEC -- quasiparticles have energy: - phonon (sound) form Quasiparticle mode coincides with sound mode. Only one excitation when have BEC.

33. 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. -- 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.

34. Excitations in a Bose Fluid ρ+

35. 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

36. Phase Diagram of Bulk Helium

37. 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 .

38. Landau

39. POROUS MEDIA • AEROGEL 95% porous • Open 87% porous A • 87% porous B • -- grown with deuterated materials or flushed with D2 • VYCOR 30% porous • Å pore Diameter -- grown with B11 isotope • GELSIL (GELTECH) 50% porous • 44 Å pore Diameter • 34 Å pore Diameter • 25 Å pore Diameter • MCM-4130% porous • 47 Å pores

40. Superfluid Properties in Confinement/Disorder Confinement reduces Tc below . Confinement modifies (T dependence). Confinement reduces (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)

41. Tc in Porous Media

42. Superfluid Density in Porous Media Chan et al. (1988) Miyamoto and Takeno (1996) Geltech (25 Å pores)

43. Superfluid Density in gelsil (Geltech) – 25 A diameter - Yamamoto et al. Phys. Rev. Lett. 93, 075302 (2004)

44. Schematic Phase Diagram of Helium Confined to Nanoscalese.g. 2 - 4 nm

45. Phase Diagram of gelsil: 25 Å pore diameter - Yamamoto et al, Phys. Rev. Lett. 93, 075302 (2004)

46. Bose-Einstein CondensationLiquid 4He in Vycor Tc (Superfluidity) = 2.05 K Azuah et al., JLTP (2003)

47. Bose-Einstein Condensation Vycor Azuah et al., JLTP (2003)

48. Phonons, Rotons, and Layer Modes in Vycor and Aerogel

49. Temperature Dependenceof Roton Energy Fåket al., PRL, 85 (2000)

50. 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))