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.html

Gap in tunneling density of states Meissner effect

www.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,

||ln2

1

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:e

I2

2e

• Resistance: kehe

eI

VR 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:

Bne

hV ˆ

2

• Disorder pins vortices for small field – superconducting phase.

• Large fields some free vortices appear and condense – insulating phase.

B

R

Disorder pins vortices:

Phase coherent

SC

Free vortices:

Vortex SF

insulator Disorder localized Electrons:

Normal (unpaired)

• Larger fields superconductivity is destroyed – normal (unpaired) phase.

Magnetically tuned Superconductor-insulator transition

• Net vortex density:

Bne

hV ˆ

2

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-metal

1 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-metal

1 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 metal

Cooper 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

TT

G 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

I

VRD

Vortices tightly bound:

12 VV

2V

Di

BB

1I

(Giaever, 1965)

2DEG bilayers – Coulomb drag

1I

2V

Two thin electron gases:

1V

1

2

I

VRD

• Coulomb force creates friction between the layers.

2

1

e

Dn

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

I

VRD

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:

3202 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(~~ cmBB

n 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

inter

effqa

eff

qa

eff eqq

eqU

effeff

rr

),ln(4

~2

0

ara

r

eff

,4

~2

2

20

2

SCd

Vortex drag in thin films within vortex metal theory

1I

2V

1

2

I

VRD •

• 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/(sinh

ImIm||

8 2212321

4

20

2

TUqdqd

B

R

B

R

T

eGR drag

VD

U – screened inter-layer potential. - Density response function (diffusive FL)

Drag genericallyproportional to MR slope.

1A

1j 2jeU

eU2A

B

R

B

R

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/(sinh

ImIm||

8 2212321

4

20

2

TUqdqd

B

R

B

R

T

eGR 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 2

1ln

)(/96

1

xdane

T

e

RRR

filme

DNORNOR

Percolation picture: Results

• Drag resistances:

022

2

221

2 2

1ln

)(/96

1

xdane

T

e

RRR

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: