Confinement and collective behavior of 4 He near the superfluid transition Francis M. Gasparini

1. Confinement and collective behavior of 4He near the superfluid transition 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. Two regions of helium separated by a connecting channel D2 h L D1 Can regions be considered independently? If they couple (h, L) , how is their behavior modified? Superconductors connected with a weak link Critical systems with region of weaker interactions Is coupling on the scale of the correlation length? What is the role of critical fluctuations?

3. Schematic of cell geometry: 34 million boxes connected through a 32 nm film

4. Cell assembled from two patterned silicon wafers

5. Results from Perronet al. Nature Physics, 6, 499-502 (2010) The super fluid onset for the film was significantly enhanced by the presence of helium in the boxes The specific heat of the film was also enhanced and shifted to a higher temperature The helium in the boxes—except near the region where the film ordered—showed no signs of box-to-box coupling Using finite-size scaling , it was deduced that , in a previous cell for boxes, we must have had a substantial contribution from box-to-box coupling To do: Measure a uniform 32 nm film Move boxes closer to see if coupling among boxes is manifest

6. Superfluid fraction with correlation lengths Uniform film, 33.6 nm; Film, 31.7 nm, with boxes at h/S=0.008

7. bulk h bulk bulk weak link slit Mamaladze and Cheishvili, Sov. Phys. JETP, 23, 112 (1966)

8. uniformfilm weak link bulk bulk For our experiment h/S= 0.008

9. Heat capacity of boxes with film; and, just a film

10. Enhancement of 32 nm film’s specific heat due to presence of boxes 4000 nm apart

11. New cell boxes and film 32.5 nm SiO2 uniform film

12. Infrared image (1 µm wavelength) of new cell boxes and film bonded SiO2 border uniform film fill hole

13. Schematic of confinement for new cell Silicon wafer 375000 nm thick ~2-6 mm film 2000 nm film 33.6 nm 4 mm border, bonded SiO2 2000 nm boxes Silicon wafer 370,000 nm thick Three confinements: uniform film, film over boxes, boxes

14. Superfluid fraction D2 D1 The super fluid density persists one decade closer to Tl for the coupled region

15. Boxes specific heat for three arrangements D2 D1 There is substantial coupling at 2 micrometer separation

16. Summary and conclusions • Coupling in helium He-4 near Tl extends over distances orders • of magnitude larger than the correlation length • This cannot be understood in the context of mean field theory • and must be due to the role of fluctuations near the critical point • Helium in a heterogeneous confinement (powders and porous • glasses) is more complex than expected, i.e. there is no • ‘additivity’ in the thermodynamic response. There is a unique, • non-universal response near Tlfor each confined system. • Other critical systems, where fluctuations are important should • have similarly large coupling (superconductors, magnets, etc.) • What has been termed “giant proximity” effects in cuprate • superconductors may be a manifestation of the same physics we • have observed.

17. Boxes –channel arrangement 10 nm film

18. Coupling in 1 micrometer boxes

19. Excess specific heat due to coupling

20. Corrected 0D data

21. SEM micrograph of 2 micrometer boxes

22. After Mamaladze and Cheishvili, Sov. Phys. JETP,1966 bulk slit x t t bulk t x Slit, 32 nm

23. Normlized superfluid density for 32 nm slit and weak link 64 nm long bulk h bulk bulk weak link slit

24. bulk bulk Superfluid density for 32 nm weak link; 64 nm long

25. Measurement of heat capacity Mehta et al. JLTP 114, 467 (1999)

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

27. Superfluid density: Planar film, 33.6 nm Film, 31.7 nm, with boxes

28. Example of resonance: temperature and phase

29. Specific heat after subtraction for a uniform film non-universal

30. Role of dimensionality on the specific heat Kimball et al. PRL, 2004