heterogeneous vortex dynamics in high temperature … · introduction methods results discussions...

Introduction Methods Results Discussions Summary

Heterogeneous vortex dynamics in hightemperature superconductors

Feng YANG

Laboratoire des Solides Irradiés,Ecole Polytechnique,

91128 Palaiseau, France.

June 18, 2009/PhD thesis defense

Outline

1 IntroductionSuperconductivityModel NMR experimentsShear viscosity of the vortex liquid

2 MethodsExperimental proceduresVerification: bulk or surface properties?Magneto-optical imaging and transport measurements

3 ResultsComparison with 2D melting modelComparison with 3D Bose-glass model

4 Discussions

5 Summary

Superconductivity

Outline

4 Discussions

5 Summary

Superconductivity

Zero resistance and diamagnetism

85 90 95 100 105

T ( K )

Perfect conductivity.

Exclusion of magnetic field (known as the Meissner effect).

Superconductivity is a thermodynamic state.

Superconductivity

85 90 95 100 105

T ( K )

Superconductivity

85 90 95 100 105

T ( K )

Superconductivity

Superconducting materials

Many materials become superconducting at lowtemperatures or high pressures."New" discoveries:

cuprate family: YBCO (1987), BSCCO (1988), ...boron-doped group-IV semiconductors (diamond, silicon,...) (since 2001)FeAs-based superconductors (2006)SiH4 (2008, under high pressure)

Future: new forms of superconductivity?

Superconductivity

Two types of superconductors

superconducting state (Meissner state)

normal state

Hc (T)

Type-I

In general, type-II superconductors have much higher Hc , Jc

and also Tc than type-I superconductors. Here, we study type-IIsuperconductors.

Superconductivity

normal state

Hc (T)

Type-IT

Meissner state

normal state

Hc2(T)

Hc1(T)

mixed state

Type-II

Superconductivity

normal state

Hc (T)

Type-IT

Meissner state

normal state

Hc2(T)

Hc1(T)

mixed state

Type-II

Superconductivity

Magnetic flux quantization

Magnetic flux quantification in type-II superconductors ⇒ vortices

B = nφ0, φ0 = h2e = 2.07 × 10−7 G·cm2.

Vortex lattice observed in Bi2Sr2CaCu2Ox with micro Hallprobes, H//c = 12 Oe, T = 81 K.A. Grigorenko et al., Nature 414, 728 (2001).

Superconductivity

Vortex distribution in real superconductors

An ideal vortex lattice yields jc = 0, R 6= 0.jc is the critical current.

Vortex pinning by material defects (pinning centers) ⇒Vortex distribution is no longer uniform ⇒ jc > 0, R = 0.

Bean’s bulk pinning model (1962).

dBxdz − dBz

dx = µ0j ,where j = jc , -jc or 0.

Superconductivity

dBxdz − dBz

Superconductivity

dBxdz − dBz

Superconductivity

dBxdz − dBz

Superconductivity

dBxdz − dBz

Superconductivity

Nonuniform vortex distribution observed by MOI: bulkpinning

Magneto-optical imaging(MOI) measures the averagedflux density.

Image intensity gradient ∼ jc .

Superconductivity

100 Oe full penetration10 Oe

T = 11.6 K, Field increasing

Magneto-optical images of aNbN thin film (Tc = 14 K) with athickness of 76 nm (deposited ona 12 nm thick Pt-Co layer with Sias the substrate).

Magneto-optical image ofa YBa2Cu4O8 single crystal,acquired at T = 10 K andHa = 180 Oe.

Superconductivity

Nonuniform vortex distribution observed by MOI:surface barrier

Even in the absence of bulk pinning, there isstill a surface barrier.

Once vortices overcome the barrier, theyaccumulate in the center of the sample, yieldinga dome profile.

Weak surface pinning, strong bulk pinning ⇒ Bean’s profile.

Strong surface pinning, weak bulk pinning ⇒ Dome profile.

Superconductivity

Outline

4 Discussions

5 Summary

Influences of bulk pinning and surface barrier to othermeasurementsExample: Nuclear Magnetic Resonance (NMR)

Inhomogeneous field distribution!

Questions:

Is all the sample probed by NMR experiments?

Supercurrent affects the density of states and thus the NMR Knight shiftdata. Is this influence important?

Influences of bulk pinning and surface barrier to othermeasurementsExample: Nuclear Magnetic Resonance (NMR)

Inhomogeneous field distribution!

Questions:

Is all the sample probed by NMR experiments?

Supercurrent affects the density of states and thus the NMR Knight shiftdata. Is this influence important?

Method to obtain ac current distribution

250 Oe

x (axis b)z (axis c)

y (axis a) Hdc

Jac(x)

HacYBaCuOtime (s)

Hac(Oe)

averaged

0 10 20 30 605040 70

10 direct images

90 100 11080

averaged

Differential image acquisition procedure

NMR-like field configuration

ac current distribution in YBa2Cu4O8 (Tc = 82 K)

Three regimes

negligible screening current (T > 70 K)

surface barrier flow (20 K < T < 70 K)

bulk pinning flow (T < 20 K)

ac current distribution in YBa2Cu4O8 (Tc = 82 K)

-0.4 -0.2 0 0.2 0.4-0.8

x (mm)

40 K45 K50 K55 K

-0.2 -0.1 0 0.1 0.2-0.5

x (mm)

nt J y(x)

40 K45 K50 K55 K

-0.4 -0.2 0 0.2 0.4-0.4

x (mm)

55 K60 K65 K70 K

-0.2 -0.1 0 0.1 0.2-0.5

x (mm)

nt J y(x)

55 K60 K65 K70 K

Three regimes

negligible screening current (T > 70 K)

surface barrier flow (20 K < T < 70 K)

bulk pinning flow (T < 20 K)

Results: ac field penetration

Only the regions where the ac field penetratesare probed by NMR measurements.

Results: ac field penetration

Only the regions where the ac field penetratesare probed by NMR measurements.

-0.4 -0.2 0 0.2 0.4

0 T < 20 K

x (mm)

40 K55 K65 K35 K

Discussions

Questions:Is all the sample probed by NMR measurements?

Supercurrent affects the density of states and thus the NMRKnight shift data. Is this influence important?

Answers obtained from our NMR model experiment:

At low temperatures (bulk pinning regime), only the sampleedges are probed by NMR measurements.

For certain materials whose jc is large, the supercurrent mayaffect the NMR Knight shift data.

At intermediate temperatures (surface barrier regime), only thesample bulk is probed.

There may be a tiny Ks due to the current at the edges only.

Discussions

Questions:Is all the sample probed by NMR measurements?

Supercurrent affects the density of states and thus the NMRKnight shift data. Is this influence important?

Answers obtained from our NMR model experiment:

At low temperatures (bulk pinning regime), only the sampleedges are probed by NMR measurements.

For certain materials whose jc is large, the supercurrent mayaffect the NMR Knight shift data.

At intermediate temperatures (surface barrier regime), only thesample bulk is probed.

There may be a tiny Ks due to the current at the edges only.

Shear property

Outline

4 Discussions

5 Summary

Shear property

High temperature superconductors

New paradigm (∼ 1989): existence of a vortex liquid state.

Shear property

Meissner state

normal state

Hc2(T)

Hc1(T)

Abrikosovvortex lattice

Conventional

Shear property

Meissner state

normal state

Hc2(T)

Hc1(T)

Conventional High-Tc (YBCO, BSCCO, …)

Meissner state

normal state

Hc2(T)

glass or

liquid

Shear property

Vortex lattice melting in BSCCO

vortex lattice melting:

jump in vortex density.

R → 0.

However, pinning centers do not disappear!

Why R → 0 at the vortex liquid-lattice transition?

Shear property

R → 0.

Shear property

R → 0.

Shear property

R → 0.

Shear property

Resistance appears at vortex lattice melting

In 2D: by the appearance of free vortex lattice dislocations.Resistance is related to the free dislocation density(Nelson-Halperin theory).

In 3D: unclear. Is plastic motion of vortex lines important?

Answer:Measure the vortex shear properties.

Shear property

How to measure the shear viscosity?

Method

Introduce artificial shear flow in weak pinning channel between strongpinning walls.

Hydrodynamic description

−γv + η 2⊥

v + f = 0

Result

ρ = ρf [1 − 2δL tanh( L

2δ )]

when δ(T ) ≡√

η/γ >> L, onehas:

Relation between shearviscosity and resistivity:

ρ(T ) ∼ B2 L2

η(T )

Shear property

Method

−γv + η 2⊥

v + f = 0

Result

2δ )]

when δ(T ) ≡√

η/γ >> L, onehas:

ρ(T ) ∼ B2 L2

η(T )

Shear property

Method

−γv + η 2⊥

v + f = 0

Result

2δ )]

when δ(T ) ≡√

η/γ >> L, onehas:

ρ(T ) ∼ B2 L2

η(T )

Shear property

Method

−γv + η 2⊥

v + f = 0

Result

2δ )]

when δ(T ) ≡√

η/γ >> L, onehas:

ρ(T ) ∼ B2 L2

η(T )

Shear property

Previous workH. Pastoriza and P. H. Kes, Phys. Rev. Lett. 75, 3525 (1995)

Interpretation

c66 = 0 in the vortex liquid state while c66 > 0 inthe vortex solid state (c66: shear modulus).

But surface barrier problem ...

Shear property

Interpretation

Shear property

Interpretation

Shear property

Interpretation

Shear property

Signature of surface barrier in transportD. T. Fuchs et al., Phys. Rev. Lett. 81, 3944 (1998)

Signature of surface barrier

Nonlinear resistance in theliquid vortex state.

Normalized R(T) of thesquare and strip crystal in thevicinity of the first ordertransition at H//c = 300 Oe andwith 10 mA current.

Measurements performed on Bi2Sr2CaCu2O8 single crystals.

Shear property

Our approach

Objective

Bulk viscosity measurements without surface barrier.

Method

Contacts and channel structure are remote from the sampleedges. Furthermore, the contacts are heavily irradiated in orderto attract the current.

Shear property

Our approach

Objective

Method

Shear property

Our approach

Objective

Method

Sample preparation

Outline

4 Discussions

5 Summary

Sample preparation

Experimental procedures

Selection of BSCCO single crystals

Realization of channel structure through irradiation

Realization of electrical contacts for transport measurements

Sample preparation

Selection of BSCCO single crystals

The channels (weak pinning) should not contain anymacroscopic defects. ⇒ Necessary to select macroscopicdefect-free single crystals.

Sample preparation

Realization of channel structure through irradiation(GANIL)

Selective irradiation through nickel masksThickness of a nickel mask is 6 ∼ 10 µm. 4 to 5 masks were superposed toblock the Pb56+ ion beam of 1 GeV.

Definition of matching field Bφ

Bφ ≡ ndφ0, where nd is the density of columnar defects introduced by ionirradiation.

Sample preparation

Realization of electrical contacts

Plasma etching

Photolithography

bulk pinning vs. surface pinning

Outline

4 Discussions

5 Summary

Verification: bulk or surface properties?

Mapping of critical current.

Current path imaging.

Transport measurements.

Verification: bulk or surface properties?

Mapping of critical current.

Current path imaging.

Transport measurements.

Experimental results: MOI

Mapping of critical currentField modulated MOI acquired at T = 80.5 K with fieldmodulation of 0.5 Oe, base field = 25 Oe, on BSCCOcrystal "iv" (clean 20 µm wide channels).

Current path imagingCurrent modulated differentialimage acquired at T = 68 K,H//c = 100 Oe, with I = +30 mA,-30 mA, on BSCCO crystal "24-4"(channels + low density ofcolumnar defects (Bφ = 10 G) in thechannels).

Experimental results: MOI

Mapping of critical currentField modulated MOI acquired at T = 80.5 K with fieldmodulation of 0.5 Oe, base field = 25 Oe, on BSCCOcrystal "iv" (clean 20 µm wide channels).

Current path imagingCurrent modulated differentialimage acquired at T = 68 K,H//c = 100 Oe, with I = +30 mA,-30 mA, on BSCCO crystal "24-4"(channels + low density ofcolumnar defects (Bφ = 10 G) in thechannels).

Experimental results: transport measurements

7678808284868890

1 mA4 mA8 mA

= 116 Oe

BSCCO "iv"

20 µm wide channels only (no columnar defects in the channels)

Present work

Bulk flow.

Signature of shear flow.

7678808284868890

1 mA4 mA8 mA

= 116 Oe

BSCCO "iv"

Present work

Bulk flow.

7678808284868890

1 mA4 mA8 mA

= 116 Oe

BSCCO "iv"

Present work

Bulk flow.

7678808284868890

1 mA4 mA8 mA

= 116 Oe

BSCCO "iv"

Present work

Bulk flow.

Summary: bulk pinning vs. surface pinning

Experimental factsField modulated differential magneto-optical imaging ⇒ jc,walls > jsurface.

Current path imaging ⇒ current flows through the irradiated structure.

Transport measurements: no nonlinear resistance ⇒ no surface barriereffect in liquid vortex state.

Therefore we probe the bulk.

Summary: bulk pinning vs. surface pinning

Experimental factsField modulated differential magneto-optical imaging ⇒ jc,walls > jsurface.

Current path imaging ⇒ current flows through the irradiated structure.

Transport measurements: no nonlinear resistance ⇒ no surface barriereffect in liquid vortex state.

Therefore we probe the bulk.

Magneto-optical imaging and transport measurements

Outline

4 Discussions

5 Summary

Signature of shear flow in transport measurements

60 65 70 75 80 85 90

310 Oe155 Oe116 Oe77 Oe56 Oe35 Oe16 Oe11 Oezero-field

R ( Ω

BSCCO "iv"20 µm wide channels only

(no columnar defects in the channels)

TirrCD

Characteristic fields and temperatures

55 60 65 70 75 80 85 90

homogenous liquid vortex

region

surface pinning effective region

Only regions 1 and 2 are probed

by resistance measurements.

Bulk propertiesof vortex system

are probed by resistance

measurements.

shear flow

Comparison with 2D melting model

Outline

4 Discussions

5 Summary

D = 2: Nelson-Halperin model

scaling law of resistivity

ρ(T ) ≈ C1exp[−2C2(Tm

T−Tm)0.37],

where C1 ∼ ρflux−flow , C2 ∼ 1, and Tm isthe melting (freezing) temperature.

Remarkably, R(T ) of our 3D superconductor is well fittedwith 2D scaling law ...

60 65 70 75 80 85 90

310 Oe155 Oe116 Oe77 Oe56 Oe35 Oe16 Oe11 OeZero-fieldR

BSCCO "iv"

Fit with NH model: R = C1 exp ( - 2 C

m/(T-T

m)|0.37 ), C

2 = 1.25

T−Tm)0.37],

60 65 70 75 80 85 90

310 Oe155 Oe116 Oe77 Oe56 Oe35 Oe16 Oe11 OeZero-fieldR

BSCCO "iv"

Fit with NH model: R = C1 exp ( - 2 C

m/(T-T

m)|0.37 ), C

2 = 1.25

T−Tm)0.37],

I-V characterization

2D Nelson-Halperinmelting property

Power law: V = Ia, wherethe exponent a has auniversal jump from 1 to 3 atT = Tm (characteristic of 2Dmelting).

This jump is observed!

Measurements performed on a Bi2Sr2CaCu2O8 single crystal, containing

clean 20 µm wide channels.

I-V characterization

85.5 86 86.5 87 87.5 88 88.5

a (critical-exponent), V = I a.

1 1.5 2 2.5 3 3.5 4 4.5

86.88 K86.70 K86.50 K86.30 K86.13 K86.04 K85.93 K85.73 K85.55 K

Log 10

µV) Temperature

increasing

BSCCO "iv"H

// c = 35 Oe

I (µA)

2D Nelson-Halperinmelting property

Power law: V = Ia, wherethe exponent a has auniversal jump from 1 to 3 atT = Tm (characteristic of 2Dmelting).

This jump is observed!

Measurements performed on a Bi2Sr2CaCu2O8 single crystal, containing

clean 20 µm wide channels.

Possible explanations

Current flows only at the top layer. (B. Khaykovich et al., Phys.Rev. B 61, R9261 (2000))

A dimension cross-over takes place nearly simultaneously withthe liquid (2D) - solid (3D) transition.

Layered structure of Bi2Sr2CaCu2O8

Suggestion

Multi-terminal transportmeasurements withelectrical contacts on boththe top and bottom surfaces.

Possible explanations

Current flows only at the top layer. (B. Khaykovich et al., Phys.Rev. B 61, R9261 (2000))

A dimension cross-over takes place nearly simultaneously withthe liquid (2D) - solid (3D) transition.

Layered structure of Bi2Sr2CaCu2O8

Suggestion

Multi-terminal transportmeasurements withelectrical contacts on boththe top and bottom surfaces.

Comparison with 3D Bose-glass model

Outline

4 Discussions

5 Summary

D = 3 with columnar defects: Bose-glass model

Marchetti and Nelson’s proposal

Introduce a low density of columnar defects in the channels. A Bose liquidstate should be realized in the channels.

Prediction

Vortex liquid to Bose-glass transition at TBG.

Near TBG, ρ(T ) ∼ L2|T − TBG|v⊥z for channel confined

vortices.

v⊥ is the static critical exponent, z is the dynamic criticalexponent. Simulations: v⊥ ≈ 1,z ≈ 4.6.

Reference: non-confined Bose-liquid

Near TBG, ρ(T ) ∼ |T − TBG|v⊥(z−2)

Prediction

vortices.

Prediction

vortices.

Experimental data vs. 3D Bose-glass model

80 82 84 86 88 90

155 Oe116 Oe77 Oe35 OeZero-field

Fit with Bose-glass model: R = C(T-TBG

)s, s = 1.9

BSCCO "24-4"

BSCCO "24-4", containing lowdensity columnar defects (Bφ = 10 G)in the 20 µm wide channels. s = 1.9

70 75 80 85 90

310 Oe155 Oe116 Oe77 Oe56 Oe

T ( K )

Fit with Bose-glass model: R = C(T-TBG

BSCCO "10G"

BSCCO "10G", uniformly irradiatedwith a dose of Bφ = 10 G.1.2 < s < 1.8we find: s = 0.8 + 0.0032H.

Comparison of different types of confinement

101010101010 100.75 0.8 0.85 0.9 0.95 1 1.05

µ !"!#µ $ %

φ & ' ( !)*)!#+, - %φ & ' ( ,,.,/ !' (!#0 %12133/145 6#

R ( Ω

T / Tc

= 116 Oe

200 µm

Degree of confinement comparison:

20 µm wide channels + Bφ = 10 G≈ Bφ = 10 G > 20 µm wide clean channels > pristine.

Confinement realized in a uniformly irradiated sample

Magnetic decoration withB = 8Bφ, Bφ = 10 G.From: M. Menghini et al.,PRL 90, 087004 (2003)

Summary

Bulk vortex properties have been successfully probed.Both of the 2D and 3D models fit with the experimentalresistance data approaching zero-resistance. Why?

ρc → 0.Surface barrier contribution when it becomes effective.Defects in 3D vortex lattice yield similar contribution to ρ(T )as defects in 2D vortex lattice.Defects in vortex lattice in layered BSCCO resemble 2Ddefects (i.e., pancake vortices).

Field modulated differential magneto-optical imaging canserve as a tool for estimating transport current flowdistribution prior to the transport measurements.

OutlookVarying channel width: size effect.Establishing electrical contacts on both the top and bottomsurfaces: c-axis correlation.

Acknowledgment

Kees van der BeekMarcin KonczykowskiRozenn BernardJavier BriaticoPanayotis SpathisTatiana Taurines...

Thank you for your attention!

heterogeneous vortex dynamics in high temperature … · introduction methods results discussions...

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