vortex drag in a thin-film giaever transformer
DESCRIPTION
Vortex drag in a Thin-film Giaever transformer. Yue (Rick) Zou (Caltech) Gil Refael (Caltech) Jongsoo Yoon (UVA) Past collaboration: Victor Galitski (UMD) Matthew Fisher (Caltech) T. Senthil (MIT). $$$: Research corporation, Packard Foundation, Sloan Foundation. Outline. - PowerPoint PPT PresentationTRANSCRIPT
Vortex drag in a
Thin-film Giaever transformer
Yue (Rick) Zou (Caltech)
Gil Refael (Caltech)
Jongsoo Yoon (UVA)
Past collaboration:
Victor Galitski (UMD)
Matthew Fisher (Caltech)
T. Senthil (MIT)
$$$: Research corporation, Packard Foundation, Sloan Foundation
Outline
• Experimental Motivation – SC-metal-insulator in InO, TiN, Ta and MoGe.
• Two paradigms:
- Vortex condensation: Vortex metal theory.
- Percolation paradigm
• Thin film Giaever transformer – amorphous thin-film bilayer.
• Predictions for the no-tunneling regime of a thin-film bilayer
• Conclusions
SC-insulator transition• Thin films: B tunes a SC-Insulator transition.
(Hebard, Paalanen, PRL 1990)
InO
B
SC
Ins
Quantum vortex physics
B
V
I
Observation of Superconductor-insulator transition
• Thin amorphous films: B tunes a SC-Insulator transition.
InO:
• Saturation as T 0
(Steiner, Kapitulnik)(Sambandamurthy, Engel, Johansson, Shahar, PRL 2004)
• Insulating peak different from sample to sample, scaling different – log, activated.
Observation of a metallic phase
• MoGe:
(Mason, Kapitulnik, PRB 1999)
Observation of a metallic phase
• Ta:
(Qin, Vicente, Yoon, 2006)
• Saturation at ~100mK: New metalic phase? (or saturation of electrons temperature)
Vortex Paradigm
Correlated states in higher dimensions:
Superconductivity
kk cc• Pairs of electrons form Cooper pairs:
• Cooper pairs are bosons, and can Bose-Einstein condense:
(c’s are creation operatorsfor electrons)
]exp[~ iGSGS
H. K. Onnes, Commun. Phys. Lab.12,120, (1911)
http://dept.phy.bme.hu/research/sollab_nano.htmlGap in tunneling density of states
Meissner effectwww.egglescliffe.org.uk
V
• Vortex motion leads to a voltage drop:
• Vortices:
Free energy of a superconductor –Landau-Ginzburg theory
• Most interesting, phase dynamics . ]exp[~ i
~J
• Supercurrent:
)sin( JII (Josephson I)
e
V2
(Josephson II)
X-Y model for superconducting film: Cooper pairs as Bosons
)](exp[ 1 iiS i
Hopping:
in ],ˆ[
Chargingenergy:
2ˆ jnU
i
ij
ijs nUH 2ˆ)cos(
• Large U - Mott insulator (no charge fluctuations)
• Large - Superfluid (intense charge fluctuations, no phase fluctuations)
s
Us /
superfluidinsulator
• Standard model for bosonic SF-Ins transition – “Bose-Hubbard model”:
• When the superconducting order is strong – ignore electronic excitations.
Vortex description of the SF-insulator transition
)ˆcos( ijVt
• Vortex hopping: (result of charging effects)
• Vortex-vortex interactions:
ji
jijViVs xxnn,
||ln21
Us /superfluidinsulator
Cooper-pairs:
Vs t/V-superfluid V- insulator
Vortices:
inV ],ˆ[
Vortex:
Condensed vortices = insulating CP’s
(Fisher, 1990)
Universal (?) resistance at SF-insulator transition
Assume that vortices and Cooper-pairs
are self dual at transition point.
• EMF due to vortex hopping:
Ve
2
22e
V
• Current due to CP hopping:eI 2
2e
• Resistance: kehe
eIVR 5.6
42
22
2
I
In reality superconducting films are not self dual:
• vortices interact logarithmically, Cooper-pairs interact at most with power law.
• Samples are very disordered and the disorder is different for cooper-pairs and vortices.
Magnetically tuned Superconductor-insulator transition
• Net vortex density:
Bneh
V ˆ2
• Disorder pins vortices for small field – superconducting phase.• Large fields some free vortices appear and condense – insulating phase.
B
RDisorder
pins vortices:
Phase coherent SC
Free vortices:
Vortex SFinsulator Disorder localized
Electrons:Normal (unpaired)
• Larger fields superconductivity is destroyed – normal (unpaired) phase.
Magnetically tuned Superconductor-insulator transition
• Net vortex density:
Bneh
V ˆ2
B
R
Disorder localized Electrons:
Normal (unpaired)
Problems• Saturation of the resistance – ‘metallic phase’
• Non-universal insulating peak – completely different depending on disorder.
Metallic phase?
Two-fluid model for the SC-Metal-Insulator transition
CPJ
CPV Jz
ˆ
Finite conductivity:
VVV Fj
Uncondensed vortices: Cooper-pair channel
Disorder induced Gapless QP’s (electron channel)
(delocalized core states?)
EJ ee
EJV
CP
1
EJ Ve
)( 1
(Galitski, Refael, Fisher, Senthil, 2005)
Two channels in parallel:
VjzE
ˆ
eJ
Transport properties of the vortex-metal1 Veeff Effective conductivity:
• Assume: - grows from zero to . - grows from zero to infinity.Ve N
B
V
VB
e
BeB
N
VB
V
1e
eB
Vortexmetal
Normal (unpaired)
Weak insulators:Ta, MoGeWeak InO
B
effR
Ve BB
Transport properties of the vortex-metal1 Veeff Effective conductivity:
Chargless spinons contribute to conductivity!
Strong insulators:TiN, InO
• Assume: - grows from zero to . - grows from zero to infinity.Ve N
VB
V
1e
eB
Vortexmetal
Normal (unpaired)
B
effRInsulator
B
V
VB
e
BeB
N
Ve BB
More physical properties of the vortex metalCooper pair tunneling
CPe GGG 2
(Naaman, Tyzer, Dynes, 2001).
• A superconducting STM can tunnel Cooper pairs to the film:
More physical properties of the vortex metal
)lnexp(1~ 22 T
TG VCP
strongly T dependent
CPGG T
GG e
2
2
ln/1~
VB
V
1e
eB
Vortexmetal
Normal (unpaired)
B
effRInsulator
Cooper pair tunneling
CPe GGG 2• A superconducting STM can tunnel Cooper pairs to the film:
Vortex metal phase:
22 ~ eeG
Normal phase:
e e
CPCP
Percolation Paradigm(Trivedi, Dubi, Meir, Avishai, Spivak, Kivelson,et al.)
SC
Pardigm II: superconducting vs. Normal regions percolation
• Strong disorder breaks the film into superconducting and normal regions.
NOR
B
R
NOR
Pardigm II: superconducting vs. Normal regions percolation• Strong disorder breaks the film into superconducting and normal regions.
• Near percolation – thin channels of the disorder-localized normal phase.
B
R
NOR
SC
SC
SC
SC
SC
Pardigm II: superconducting vs. Normal regions percolation• Strong disorder breaks the film into superconducting and normal regions.
• Near percolation – thin channels of the disorder-localized normal phase.
B
R
NOR
• Far from percolation – normal electrons with disorder.
Magneto-resistance curves in the percolation picture
• Simulate film as a resistor network:
Normal links:kTeRR /|)||||(|
02121~
NOR island
SC islandNor-SC links:
TEGeRR /0~ SC-SC links:
TR ~
Reuslting MR:
(Dubi, Meir, Avishai, 2006)
Drag in a bilayer system
Giaever transformer – Vortex dragTwo type-II bulk superconductors:
1V
1
2
IVRD
Vortices tightly bound:
12 VV
2V
Di
BB
1I
(Giaever, 1965)
2DEG bilayers – Coulomb drag
1I
2V
Two thin electron gases:
1V
1
2
IVRD
• Coulomb force creates friction between the layers.
2
1
eD n
R
Di
• Opposite sign to Giaever’s vortex drag.
• Inversely proportional to density squared:
2DEG bilayers – Coulomb drag
1I
2V
Two thin electron gases:
1V
1
2
IVRD
Di
Example: 1T “Excitonic condensate”
(Kellogg, Eisenstein, Pfeiffer, West, 2002)
Thin film Giaever transformer
DV
1I
Amorphous (SC) thin films
Insulating layer,Josephson tunneling:
0J or 0J
nmdSC 20~
nmd Ins 5~
Percolation paradigm
• Drag is due to coulomb interaction.
• Electron density:320
2 10~ cmdn SCd
( QH bilayers: 210
2 105~ cmn d
214102 cm
)
Drag suppressed
Vortex condensation paradigm
• Drag is due to inductive current interactions, and Josephson coupling.
• Vortex density:2
][11
0
)10(~~ cmBBn TV
Significant Drag
?
$
?
Vortex drag in thin films bilayers: interlayer interaction
r
• Vortex current suppressed. e.g., Pearl penetration length:
SC
Leff d
22
• Vortex attraction=interlayer induction. Also suppressed due to thinness.
]/)[(2)(
22212
20
intereff
qaeff
qa
eff eqqeqU
effeff
rr
),ln(4
~2
0
arar
eff
,4
~2
2
20
2
SCd
Vortex drag in thin films within vortex metal theory
1I
2V
1
2
IVRD •
• Perturbatively:
],[~ 21 jjGR dragVD
• Expect:2
2
1
1
V
V
V
VdragV nn
G
2
2
1
1
V
V
V
VdragV nn
G
(Following von Oppen, Simon, Stern, PRL 2001)
• Answer:
)2/(sinhImIm||
8 2212321
4
20
2
TUqdqd
BR
BR
TeGR drag
VD
U – screened inter-layer potential. - Density response function (diffusive FL)
Drag genericallyproportional to MR slope.
1A1j 2j
eU
eU2A
BR
BR
21
(Kamenev, Oreg)
Vortex drag in thin films: Results
• Our best chance (with no J tunneling) is the highly insulating InO:
• maximum drag:
mRD 1.0~max
)2/(sinhImIm||
8 2212321
4
20
2
TUqdqd
BR
BR
TeGR drag
VD
Note: similar analysis for SC-metal ‘bilayer’ using a ground plane.
Experiment: Mason, Kapitulnik (2001) Theory: Michaeli, Finkel’stein, (2006)
Percolation picture: Coulomb drag
• Solve a 2-layer resistor network with drag.
0, D
NORSCD
SCSC RR
• Can neglect drag with the SC islands:
- Normal
- SC
• Normal-Normal drag – use results for disorder localized electron glass:
(Shimshoni, PRL 1987)0
22
2
221
2 21ln
)(/961
xdaneT
eRRR
filme
DNORNOR
Percolation picture: Results
• Drag resistances:
022
2
221
2 21ln
)(/961
xdaneT
eRRR
filme
DNORNOR
0,
DNORSC
DSCSC RR
• Solution of the random resistor network:
?
Compare to vortex drag:
Conclusions
• Vortex picture and the puddle picture: similar single layer predictions.
• Giaever transformer bilayer geometry may qualitatively distinguish: Large drag for vortices, small drag for electrons, with opposite signs.
• Drag in the limit of zero interlayer tunneling:
mR vortexD 1.0~ vs. 1110~npercolatio
DR
• Intelayer Josephson should increase both values, and enhance the effect. (future theoretical work)
• Amorphous thin-film bilayers will yield interesting complementary information about the SIT.
Conclusions
• Vortex picture and the puddle picture: similar single layer predictions.
• Giaever transformer bilayer geometry may qualitatively distinguish: Large drag for vortices, small drag for electrons.
• What induces the gigantic resistance and the SC-insulating transition?
• What is the nature of the insulating state? Exotic vortex physics?
Phenomenology:
Experimental suggestion: