Introduction Methods Results Discussions Summary Heterogeneous vortex dynamics in high temperature superconductors Feng YANG Laboratoire des Solides Irradiés, Ecole Polytechnique, 91128 Palaiseau, France. June 18, 2009/PhD thesis defense
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
Introduction Methods Results Discussions Summary
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
Introduction Methods Results Discussions Summary
Superconductivity
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
Introduction Methods Results Discussions Summary
Superconductivity
Zero resistance and diamagnetism
10-7
10-6
10-5
10-4
10-3
10-2
10-1
85 90 95 100 105
R (
Ω )
T ( K )
Perfect conductivity.
Exclusion of magnetic field (known as the Meissner effect).
Superconductivity is a thermodynamic state.
Introduction Methods Results Discussions Summary
Superconductivity
Zero resistance and diamagnetism
10-7
10-6
10-5
10-4
10-3
10-2
10-1
85 90 95 100 105
R (
Ω )
T ( K )
Perfect conductivity.
Exclusion of magnetic field (known as the Meissner effect).
Superconductivity is a thermodynamic state.
Introduction Methods Results Discussions Summary
Superconductivity
Zero resistance and diamagnetism
10-7
10-6
10-5
10-4
10-3
10-2
10-1
85 90 95 100 105
R (
Ω )
T ( K )
Perfect conductivity.
Exclusion of magnetic field (known as the Meissner effect).
Superconductivity is a thermodynamic state.
Introduction Methods Results Discussions Summary
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?
Introduction Methods Results Discussions Summary
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?
Introduction Methods Results Discussions Summary
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?
Introduction Methods Results Discussions Summary
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?
Introduction Methods Results Discussions Summary
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?
Introduction Methods Results Discussions Summary
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?
Introduction Methods Results Discussions Summary
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?
Introduction Methods Results Discussions Summary
Superconductivity
Two types of superconductors
superconducting state (Meissner state)
normal state
H
TTc
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.
Introduction Methods Results Discussions Summary
Superconductivity
Two types of superconductors
superconducting state (Meissner state)
normal state
H
TTc
Hc (T)
Type-IT
Meissner state
normal state
Hc2(T)
H
Tc
Hc1(T)
mixed state
Type-II
In general, type-II superconductors have much higher Hc , Jc
and also Tc than type-I superconductors. Here, we study type-IIsuperconductors.
Introduction Methods Results Discussions Summary
Superconductivity
Two types of superconductors
superconducting state (Meissner state)
normal state
H
TTc
Hc (T)
Type-IT
Meissner state
normal state
Hc2(T)
H
Tc
Hc1(T)
mixed state
Type-II
In general, type-II superconductors have much higher Hc , Jc
and also Tc than type-I superconductors. Here, we study type-IIsuperconductors.
Introduction Methods Results Discussions Summary
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).
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
Superconductivity
Nonuniform vortex distribution observed by MOI: bulkpinning
Magneto-optical imaging(MOI) measures the averagedflux density.
Image intensity gradient ∼ jc .
Introduction Methods Results Discussions Summary
Superconductivity
Nonuniform vortex distribution observed by MOI: bulkpinning
Magneto-optical imaging(MOI) measures the averagedflux density.
Image intensity gradient ∼ jc .
Introduction Methods Results Discussions Summary
Superconductivity
Nonuniform vortex distribution observed by MOI: bulkpinning
100 Oe full penetration10 Oe
1 mm
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.
Magneto-optical imaging(MOI) measures the averagedflux density.
Image intensity gradient ∼ jc .
Introduction Methods Results Discussions Summary
Superconductivity
Nonuniform vortex distribution observed by MOI: bulkpinning
100 Oe full penetration10 Oe
1 mm
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.
Magneto-optical imaging(MOI) measures the averagedflux density.
Image intensity gradient ∼ jc .
Introduction Methods Results Discussions Summary
Superconductivity
Nonuniform vortex distribution observed by MOI: bulkpinning
100 Oe full penetration10 Oe
1 mm
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.
Magneto-optical imaging(MOI) measures the averagedflux density.
Image intensity gradient ∼ jc .
Introduction Methods Results Discussions Summary
Superconductivity
Nonuniform vortex distribution observed by MOI:surface barrier
BSCCO
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.
Introduction Methods Results Discussions Summary
Superconductivity
Nonuniform vortex distribution observed by MOI:surface barrier
BSCCO
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.
Introduction Methods Results Discussions Summary
Superconductivity
Nonuniform vortex distribution observed by MOI:surface barrier
BSCCO
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.
Introduction Methods Results Discussions Summary
Superconductivity
Nonuniform vortex distribution observed by MOI:surface barrier
BSCCO
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.
Introduction Methods Results Discussions Summary
Superconductivity
Nonuniform vortex distribution observed by MOI:surface barrier
BSCCO
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.
Introduction Methods Results Discussions Summary
NMR
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
Introduction Methods Results Discussions Summary
NMR
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?
Introduction Methods Results Discussions Summary
NMR
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?
Introduction Methods Results Discussions Summary
NMR
Method to obtain ac current distribution
Introduction Methods Results Discussions Summary
NMR
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
10
0 10 20 30 605040 70
10 direct images
10 direct images
M1
M2
M1-M2
90 100 11080
averaged
Differential image acquisition procedure
NMR-like field configuration
Introduction Methods Results Discussions Summary
NMR
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)
Introduction Methods Results Discussions Summary
NMR
ac current distribution in YBa2Cu4O8 (Tc = 82 K)
-0.4 -0.2 0 0.2 0.4-0.8
-0.4
0.0
0.4
0.8
x (mm)
B z
40 K45 K50 K55 K
-0.2 -0.1 0 0.1 0.2-0.5
0.0
0.5
1.0
1.5
2.0
x (mm)
Sheet
curre
nt J y(x)
40 K45 K50 K55 K
-0.4 -0.2 0 0.2 0.4-0.4
-0.2
0.0
0.2
0.4
x (mm)
B z
55 K60 K65 K70 K
-0.2 -0.1 0 0.1 0.2-0.5
0.0
0.5
1.0
1.5
2.0
x (mm)
Sheet
curre
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)
Introduction Methods Results Discussions Summary
NMR
Results: ac field penetration
Only the regions where the ac field penetratesare probed by NMR measurements.
Introduction Methods Results Discussions Summary
NMR
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
Hx/H
ac
0 0
0 T < 20 K
1
x (mm)
40 K55 K65 K35 K
Introduction Methods Results Discussions Summary
NMR
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.
Introduction Methods Results Discussions Summary
NMR
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.
Introduction Methods Results Discussions Summary
Shear property
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
Introduction Methods Results Discussions Summary
Shear property
High temperature superconductors
New paradigm (∼ 1989): existence of a vortex liquid state.
Introduction Methods Results Discussions Summary
Shear property
High temperature superconductors
TTc
Meissner state
normal state
Hc2(T)
H
Hc1(T)
Abrikosovvortex lattice
Conventional
New paradigm (∼ 1989): existence of a vortex liquid state.
Introduction Methods Results Discussions Summary
Shear property
High temperature superconductors
TTc
Meissner state
normal state
Hc2(T)
H
Hc1(T)
Abrikosovvortex lattice
Conventional High-Tc (YBCO, BSCCO, …)
H
Meissner state
normal state
Hc2(T)
TTc
Abrikosovvortex lattice
glass or
liquid
New paradigm (∼ 1989): existence of a vortex liquid state.
Introduction Methods Results Discussions Summary
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?
Introduction Methods Results Discussions Summary
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?
Introduction Methods Results Discussions Summary
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?
Introduction Methods Results Discussions Summary
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?
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
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 )
Introduction Methods Results Discussions Summary
Shear property
How to measure the shear viscosity?
Method
Introduce artificial shear flow in weak pinning channel between strongpinning walls.
y
x
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 )
Introduction Methods Results Discussions Summary
Shear property
How to measure the shear viscosity?
Method
Introduce artificial shear flow in weak pinning channel between strongpinning walls.
y
x
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 )
Introduction Methods Results Discussions Summary
Shear property
How to measure the shear viscosity?
Method
Introduce artificial shear flow in weak pinning channel between strongpinning walls.
y
x
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 )
Introduction Methods Results Discussions Summary
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 ...
Introduction Methods Results Discussions Summary
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 ...
Introduction Methods Results Discussions Summary
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 ...
Introduction Methods Results Discussions Summary
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 ...
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
Sample preparation
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
Introduction Methods Results Discussions Summary
Sample preparation
Experimental procedures
Selection of BSCCO single crystals
⇓
Realization of channel structure through irradiation
⇓
Realization of electrical contacts for transport measurements
Introduction Methods Results Discussions Summary
Sample preparation
Selection of BSCCO single crystals
The channels (weak pinning) should not contain anymacroscopic defects. ⇒ Necessary to select macroscopicdefect-free single crystals.
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
Sample preparation
Realization of electrical contacts
Plasma etching
⇓
Photolithography
Introduction Methods Results Discussions Summary
bulk pinning vs. surface pinning
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
Introduction Methods Results Discussions Summary
bulk pinning vs. surface pinning
Verification: bulk or surface properties?
Mapping of critical current.
Current path imaging.
Transport measurements.
Introduction Methods Results Discussions Summary
bulk pinning vs. surface pinning
Verification: bulk or surface properties?
Mapping of critical current.
Current path imaging.
Transport measurements.
Introduction Methods Results Discussions Summary
bulk pinning vs. surface pinning
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).
Introduction Methods Results Discussions Summary
bulk pinning vs. surface pinning
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).
Introduction Methods Results Discussions Summary
bulk pinning vs. surface pinning
Experimental results: transport measurements
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
7678808284868890
1 mA4 mA8 mA
R (
Ω )
T (K)
H//c
= 116 Oe
BSCCO "iv"
20 µm wide channels only (no columnar defects in the channels)
Tirr
CD
Present work
Bulk flow.
Signature of shear flow.
Introduction Methods Results Discussions Summary
bulk pinning vs. surface pinning
Experimental results: transport measurements
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
7678808284868890
1 mA4 mA8 mA
R (
Ω )
T (K)
H//c
= 116 Oe
BSCCO "iv"
20 µm wide channels only (no columnar defects in the channels)
Tirr
CD
Present work
Bulk flow.
Signature of shear flow.
Introduction Methods Results Discussions Summary
bulk pinning vs. surface pinning
Experimental results: transport measurements
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
7678808284868890
1 mA4 mA8 mA
R (
Ω )
T (K)
H//c
= 116 Oe
BSCCO "iv"
20 µm wide channels only (no columnar defects in the channels)
Tirr
CD
Present work
Bulk flow.
Signature of shear flow.
Introduction Methods Results Discussions Summary
bulk pinning vs. surface pinning
Experimental results: transport measurements
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
7678808284868890
1 mA4 mA8 mA
R (
Ω )
T (K)
H//c
= 116 Oe
BSCCO "iv"
20 µm wide channels only (no columnar defects in the channels)
Tirr
CD
Present work
Bulk flow.
Signature of shear flow.
Introduction Methods Results Discussions Summary
bulk pinning vs. surface pinning
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.
Introduction Methods Results Discussions Summary
bulk pinning vs. surface pinning
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.
Introduction Methods Results Discussions Summary
Magneto-optical imaging and transport measurements
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
Introduction Methods Results Discussions Summary
Magneto-optical imaging and transport measurements
Signature of shear flow in transport measurements
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
60 65 70 75 80 85 90
310 Oe155 Oe116 Oe77 Oe56 Oe35 Oe16 Oe11 Oezero-field
R ( Ω
)
T (K)
BSCCO "iv"20 µm wide channels only
(no columnar defects in the channels)
TirrCD
TTirr
CD
Introduction Methods Results Discussions Summary
Magneto-optical imaging and transport measurements
Characteristic fields and temperatures
0
50
100
150
200
250
300
350
55 60 65 70 75 80 85 90
H (
Oe
)
T (K)
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.
32
1
shear flow
Introduction Methods Results Discussions Summary
Comparison with 2D melting model
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
Introduction Methods Results Discussions Summary
Comparison with 2D melting model
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 ...
Introduction Methods Results Discussions Summary
Comparison with 2D melting model
D = 2: Nelson-Halperin model
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
60 65 70 75 80 85 90
310 Oe155 Oe116 Oe77 Oe56 Oe35 Oe16 Oe11 OeZero-fieldR
( Ω
)
T (K)
BSCCO "iv"
Fit with NH model: R = C1 exp ( - 2 C
2 |T
m/(T-T
m)|0.37 ), C
2 = 1.25
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 ...
Introduction Methods Results Discussions Summary
Comparison with 2D melting model
D = 2: Nelson-Halperin model
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
60 65 70 75 80 85 90
310 Oe155 Oe116 Oe77 Oe56 Oe35 Oe16 Oe11 OeZero-fieldR
( Ω
)
T (K)
BSCCO "iv"
Fit with NH model: R = C1 exp ( - 2 C
2 |T
m/(T-T
m)|0.37 ), C
2 = 1.25
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 ...
Introduction Methods Results Discussions Summary
Comparison with 2D melting model
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.
Introduction Methods Results Discussions Summary
Comparison with 2D melting model
I-V characterization
0.5
1
1.5
2
2.5
3
3.5
4
4.5
85.5 86 86.5 87 87.5 88 88.5
a (critical-exponent), V = I a.
a (c
ritic
al-e
xpon
ent)
T (K)
-2
-1
0
1
2
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
V (
µV) Temperature
increasing
BSCCO "iv"H
// c = 35 Oe
Log10
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.
Introduction Methods Results Discussions Summary
Comparison with 2D melting model
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.
Introduction Methods Results Discussions Summary
Comparison with 2D melting model
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.
Introduction Methods Results Discussions Summary
Comparison with 3D Bose-glass model
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
Introduction Methods Results Discussions Summary
Comparison with 3D Bose-glass model
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)
Introduction Methods Results Discussions Summary
Comparison with 3D Bose-glass model
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)
Introduction Methods Results Discussions Summary
Comparison with 3D Bose-glass model
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)
Introduction Methods Results Discussions Summary
Comparison with 3D Bose-glass model
Experimental data vs. 3D Bose-glass model
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
80 82 84 86 88 90
155 Oe116 Oe77 Oe35 OeZero-field
R (
Ω )
T (K)
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
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
70 75 80 85 90
310 Oe155 Oe116 Oe77 Oe56 Oe
R (
Ω )
T ( K )
Fit with Bose-glass model: R = C(T-TBG
)s
BSCCO "10G"
BSCCO "10G", uniformly irradiatedwith a dose of Bφ = 10 G.1.2 < s < 1.8we find: s = 0.8 + 0.0032H.
Introduction Methods Results Discussions Summary
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
H// c
= 116 Oe
200 µm
Degree of confinement comparison:
20 µm wide channels + Bφ = 10 G≈ Bφ = 10 G > 20 µm wide clean channels > pristine.
Introduction Methods Results Discussions Summary
Confinement realized in a uniformly irradiated sample
Magnetic decoration withB = 8Bφ, Bφ = 10 G.From: M. Menghini et al.,PRL 90, 087004 (2003)
Introduction Methods Results Discussions Summary
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.
Introduction Methods Results Discussions Summary
Acknowledgment
Kees van der BeekMarcin KonczykowskiRozenn BernardJavier BriaticoPanayotis SpathisTatiana Taurines...
Thank you for your attention!