Confinement and collective behavior of 4Henear the superfluid transition

  Francis M. Gasparini

Department of Physics, University at Buffalo, The State University of New York, U.S.A

Justin K. PerronMark O. KimballKevin P. Mooney

Two regions of helium separated by a connecting channel

1. Can regions be considered independently?2. If they couple (h, L) , how is their behavior modified?

3. Superconductors connected with a weak link4. Critical systems with region of weaker interactions5. Is coupling on the scale of the correlation length?6. What is the role of critical fluctuations?

D1 D2

hL

Schematic of cell geometry: 34 million boxesconnected through a 32 nm film

32 2 2 m

film 32nm

4 mS

Cell assembled from two patterned silicon wafers

Results from Perron et al. Nature Physics, 6, 499-502 (2010)

1. The super fluid onset for the film was significantly enhanced by the presence of helium in the boxes2. The specific heat of the film was also enhanced and shifted to a higher temperature3. The helium in the boxes—except near the region where the film ordered—showed no signs of box-to-box coupling4. 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

31 m

To do:1. Measure a uniform 32 nm film2. Move boxes closer to see if coupling among boxes is manifest

Superfluid fraction with correlation lengths

Uniform film, 33.6 nm;

Film, 31.7 nm, with boxes at h/S=0.008

2/3

2/3

22 3

1/ 2

2/30

Phenomenological -theory (Ginzburg Pitaevskii equation)

assume: 1 ; ln( )

0

where ; lengths

sP

s

b

Tk kt C A t B

T

f f f f

Lf

t

bulkslit

h

bulk bulkweaklink

Mamaladze and Cheishvili, Sov. Phys. JETP, 23, 112 (1966)

Results from theory: 32 nm film;

32 nm slit, 64 nm long, coupling bulk regions, 0 / .5h S

bulk bulk

weak

link

For our experiment h/S= 0.008

uniform film

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

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

New cell

Boxes are now at 2000nm edge-to-edge

boxes and film

32.5 nm SiO2

uniform film

Infrared image (1 µm wavelength) of new cell

bonded SiO2border

boxes and film

uniform film

fill hole

Schematic of confinement for new cell

Silicon wafer 375000 nm thick

4 mm border, bonded SiO2

~2-6 mm film

2000 nm boxes

2000 nm film

33.6 nm

Silicon wafer 370,000 nm thick

Three confinements: uniform film, film over boxes, boxes

Superfluid fraction

The super fluid density persists one decade closer to T for the coupled region

D1 D2

Boxes specific heat for three arrangements

There is substantial coupling at 2 micrometer separation

D1 D2

Summary and conclusions• Coupling in helium He-4 near T 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 T for 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.

Boxes –channel arrangement

32 2 2 m

2 mS

2SiO

2SiO

2SiO

2SiO

10 nm film

1/

scaling coupling

1/ 1/coupling 2micron 1micron

, ,C t C t l t Ct g tl

C C C

C g tl g tl t

Coupling in 1 micrometer boxes

T T

410 0.07,0.17 m

spacing of boxes 1 m edge to edge

connecting film has 0.02

bulk

c

t

t

Excess specific heat due to coupling

Corrected 0D data

SEM micrograph of 2 micrometer boxes

After Mamaladze and Cheishvili, Sov. Phys. JETP,1966

bulk

s

x t

Slit, 32 nm

bulk

slit

t

x

s

t

A

x

A

x

bulk bulk

bulkslit

h

Normlized superfluid density for 32 nm slit and weak link 64 nm long

weaklink

Superfluid density for 32 nm weak link; 64 nm long

bulk bulk

Measurement of heat capacity

0

2q fC

g

Mehta et al. JLTP 114, 467 (1999)

AFR resonance and superfluid density

Gasparini et al,. JLTP (2001)

sup e rfluid ve lo c ity

20

S

P T CVl K K

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

Example of resonance: temperature and phase

2 0.05 KT

Specific heat after subtraction for a uniform film

non-universal

Role of dimensionality on the specific heat

Kimball et al. PRL, 2004/ 1T T

L 1 m