confinement and collective behavior of 4 he near the superfluid transition francis m. gasparini
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Confinement and collective behavior of 4 He 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. - PowerPoint PPT PresentationTRANSCRIPT
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