Giant coupling effects in confined 4 He ( What constitutes a weak link for 4 He?)

1. Giant coupling effects in confined 4He (What constitutes a weak link for 4He?) Francis M. Gasparini Department of Physics, University at Buffalo, The State University of New York, U.S.A Justin K. Perron Mark O. Kimball Kevin P. Mooney

2. Experimental cells for heat capacity and superfluid density h l Silicon 4He L SiO2 s Silicon

3. Statementsand questions • One may view the helium in the boxes and in • the film/channel as two phases of the same system • To what extent do these phases couple? • One may think, as in superconductors, that coupling • should take place on the scale of the correlation length. • This is not correct for 4He • How do the boxes-film system differ from a simpler, • homogeneous confinement? Perronet al. Nature Phys. 6, 499-502 (2010) http://enthalpy.physics.buffalo.edu/Publications

4. Specific heat for planar confinement Gaspariniet al. RMP, 80,1009 (2008)

5. Data collapse for planarconfinement Gaspariniet al. RMP, 80,1009 (2008)

6. Limited data collapse for planar confinement

7. Specific heat for 0D confinement

8. Lack of collapse, 0D confinement

9. Lack of collapse, 0D confinement Is there coupling among the boxes?

10. New cell design for 0D

11. Measurement of heat capacity

12. Heat capacity of film + boxes;;and, uniformfilm only Perronet al. Nature Physics, 2010

13. Specific heat after subtraction for a uniform film

14. AFR resonance and superfluid density Gaspariniet al,. JLTP (2001)

15. Example of resonance: temperature and phase

16. Superfluid density for two films bulk expected BKT jump

17. Superfluid density and heat capacity

18. Coupling in 1 micrometer boxes

19. Excess specific heat due to coupling

20. Summary • One may think of the boxes-film system as displaying both coupling (box-to-box) and proximity effects (box-to-film) • [helium; other critical systems] • These effects extend to much larger distances than the correlation length • [high-Tcsuperconductors] • It seems likely that this is due to the role of critical point fluctuations, below and above T • [other critical systems] • Overall, this behavior goes beyond Josephson coupling • [helium, superconductors]

21. Comment 1 Josephson effects in 4He Sukhatmeet al, Nature 2001: array of 24 slits Hoskinsonet al., Nature 2006: array of circular apertures Both experiments show superflow in region where the slits or apertures should be normal. However, l~ .

22. “Two-peaks” specific heat Comment 2 200 nm 5.5 nm T. P. Chen et al., JLTP, 1977

23. Comment 3 Giant proximity effects in cuprate superconductors Bozovic et al., Phys. Rev. Lett., 2004

24. Comment 4 2D “Layered Ising lattice” n = 4 M. E. Fisher, J. Phys. Soc. Jap. 1969; Nature Physics, News and Views, 2010

25. Mean field calculation Comment 5 After Mamaladze and Cheishvili, Sov. Phys. JETP,1966 (Ginzburg-Pitaevskiiequation) bulk slit x t t t bulk x Slit, 32 nm

26. Comment 6 Role of dimensionality on the specific heat Kimball et al. PRL, 2004

27. Comment 6 Corrected 0D data

28. Comment 7 Correlation length is renormalized

29. SEM micrograph of 2 micrometer boxes

30. Specific heat for planar confinement Gaspariniet al. RMP, 80,1009 (2008)

31. Superfluid density for two films bulk expected tc Perron et al. Nature Physics, 2010

32. How uniform is the oxide? Oxide thick. (nm) Y (mm) X (mm)

33. Lack of scaling for planar confinement near maximum

34. Cell staged on cryostat

35. Infrared picture of 0.3 micrometer cell

36. Surface of separation:1 micrometer boxes Gaspariniet al. RMP, 80,1009 (2008)