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. PerronMark O. KimballKevin P. Mooney

Silicon

SiO2

Silicon

4He L

h

7 8

Si wafers: 5cm diameter, 375 m thick

Boxes: 1, 2 m; 10 10 per cellFilm or channel: 10 30 nmSeparation: 2 6 m

Lh

S

s

Experimental cells for heat capacity and superfluid density

l

• 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?

Statements and questions

Perron et al. Nature Phys. 6, 499-502 (2010)

http://enthalpy.physics.buffalo.edu/Publications

Specific heat for planar confinement

T T

/ 1t T T

Gasparini et al. RMP, 80,1009 (2008)

T T

Data collapse for planar confinement

Gasparini et al. RMP, 80,1009 (2008)

T T

Limited data collapse for planar confinement

T T

Specific heat for 0D confinement

T T

T T

Lack of collapse, 0D confinement

2 m boxes :

2 m 2

m

0.01 m1 m boxes :1 m 1 m 0.0 m

2

l w h

Lack of collapse, 0D confinement

Is there coupling among the boxes?

New cell design for 0D

Measurement of heat capacity

Heat capacity of film + boxes;;and, uniform film only

Perron et al. Nature Physics, 2010

Specific heat after subtraction for a uniform film

AFR resonance and superfluid density

Gasparini et al,. JLTP (2001)

sup e rfluid ve lo c ity

Example of resonance: temperature and phase

2 0.05 KT

3 0.002 0.024 m; boxes at 4 mD t l

Superfluid density for two films

bulk

expected BKT jump

Superfluid density and heat capacity

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

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-Tc superconductors]• 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]

Comment 1

Josephson effects in 4He

Sukhatme et al, Nature 2001: array of 24 slits

3 0.17 0.15 m m m w h l

Hoskinson et al., Nature 2006: array of circular apertures

0.04 0.05 m m diameter l

Both experiments show superflow in region where the slits or apertures should be normal. However, l~ .

200 nm

5.5 nm

T. P. Chen et al., JLTP, 1977

“Two-peaks” specific heatComment 2

Giant proximity effects in cuprate superconductors

Bozovic et al., Phys. Rev. Lett., 2004

LCOcT

0.6nmThickness of LCO: 1.3 to 20 nm

n

Comment 3

2D “Layered Ising lattice”

JJn = 4

M. E. Fisher, J. Phys. Soc. Jap. 1969; Nature Physics, News and Views, 2010

Comment 4

J J

After Mamaladze and Cheishvili, Sov. Phys. JETP,1966 (Ginzburg-Pitaevskii equation)

bulk

s

x t

Slit, 32 nm

bulk slit

t

x

s

t

Comment 5

AX

AX

Mean field calculation

Role of dimensionality on the specific heat

Kimball et al. PRL, 2004/ 1T T

Comment 6

Corrected 0D dataComment 6

t TT

1

C O RRELATIO N LENG TH

-1

-1c ro sso ve r re g io n

-1

0

Correlation length is renormalized

/ 1T T

Comment 7

SEM micrograph of 2 micrometer boxes

T T

Specific heat for planar confinement

Gasparini et al. RMP, 80,1009 (2008)

Superfluid density for two films

bulk

expected tc

3 0.024 mcD t

Perron et al. Nature Physics, 2010

How uniform is the oxide?

Oxi

de th

ick.

(nm

)

X (mm)Y (mm)

Lack of scaling for planar confinement near maximum

L T va lv e

In d ium O -r in g

Sta in less s tee lca p illa ry

G erm an iumth erm om ete r

E v ap or ate dfilm hea te r

S iliconp iece B on d ed w afe rs

K a p ton s le ev e

C o p p e r w ire

C o pp ersta ge s

S 1

S 2

Cell staged on cryostat

Infrared picture of 0.3 micrometer cell

Surface of separation:1 micrometer boxes

Gasparini et al. RMP, 80,1009 (2008)