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Bardeen-Stephen flux flow law disobeyed in Bi 2 Sr 2 CaCu 2 O 8+δ

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Bardeen-Stephen flux flow law disobeyed in Bi2Sr2CaCu2O8+δ

G. Kriza,1,2 A. Pallinger1, B. Sas1, I. Pethes1, K. Vad3, F. I. B.Williams1,4

1Research Institute for Solid State Physics and Optics,Budapest, Hungary

2Institute of Physics, Budapest University of Technology and Economics,Budapest, Hungary

3Institute of Nuclear Research, Debrecen, Hungary

4Service de Physique de l’Etat Condensée,Direction Sciences de la Matière, Comissariat à l’Energie Atomique,

Gif-sur-Yvette, France and

B ab

Transport current JT

Abrikosov vortex

Bardeen–Stephen law (BS)

- No clear experimental evidence for BS law in any high-Tc SC (nor in any unconventional superconductor)
- No theory takes into account all the essential ingredients

This experiment

BS law

Pinning force uncertainty in the total force F uncertainty in velocity – force relation

Solution

Model pinning

(e.g., to interpret

surface impedance)

Create conditions

where pinning is

irrelevant

(our approach)

Unpinned

vortex liquid

state near Tc

Apply high current

so that the pinning

force is negligible

in front of the

Lorentz force

c

B ab

BSCCO single crystal:

b

a

Current excitation:

Voltage – current

(V – I)

characteristics

Voltage

response

V/I varies with I

up to the highest current

pinning is not negligible

Rab= dV/dI saturates (becomes current independent)

at the high current.

If Rab = dV/dI = const, then

for I → , V/I→ Rab

The differential resistance Rab measures the high-current limit of the resistance V/I

We assume that Rab reflects the free flux flow limit

High temperature:

sublinear B-depend-

dence

Low temperature:

T and B independent

resistance

Interpolating function:

Bc2(T) = Bc2(0)[1– (T/Tc)2]

with Bc2(0) = 120 tesla to give

as in Qiang Li et al.,

Phys. Rev. B 48, 9877 (1993).

Empirical form for the B and T dependence of the resistance:

Dependence of the resistance Rab on the local resistivities c and ab

Anisotropic quasi-2d sample:

I

V

- Strong anisotropy c >> ab
- shallow current penetration
- influence on the current density
- Rab depends on both c and ab

ab

t

c

l

Valid for linear response and for asymptotically

linear resistivities in the high-current limit

geometrical factor

Our samples are well in the thick sample limit

How to disentangle c and ab from Rab?

Multicontact method:

Vtop

I

Vtop ab

Vbottom c

ab

c

Vbottom

This experiment was done by

R. Busch, G. Ries, H. Werthner, G. Kreiselmeyer, and G. Saemann-Ischenko, Phys. Rev. Lett. 69, 522 (1992)

Problem: Busch et al. measured in the I→ 0 limit whereas we measured in the high-current limit

How to compare high-field and low-field resistances?

Go to the unpinned liquid phase!

With increasing current, the V-I curves are less and less nonlinear

For T > Tlin linear response "unpinned liquid phase”

(smooth crossover, no sharp change)

Magnetic field–temperature phase diagram

Bc2 upper critical field

TFOT first order transition line

Tirr magnetic irreversibility line

T2nd second magnetization peak

Vortex liquid

Magnetic field–temperature phase diagram

Bc2 upper critical field

TFOT first order transition line

Tirr magnetic irreversibility line

T2nd second magnetization peak

Glass?

Magnetic field–temperature phase diagram

Bc2 upper critical field

TFOT first order transition line

Tirr magnetic irreversibility line

T2nd second magnetization peak

Glass?

Unp. L.

Pinned liquid

Unpinned liquid phase

For T > Tlin the V-I curves

are linear

Analysis of the multicontact data of Busch et al.

Phys. Rev. Lett. 69, 522 (1992)

FIG. 3

- Digitize isothermal sections
- Sort out data for whichT > Tlin(B) (unpinned liquid)

Single crystal resistance

(same quantity as in our experiments)

Busch et al., Phys. Rev. Lett. 69, 522 (1992)

Unpinned

liquid

- Reproduces B/Bc2 scaling
- Reproduces logarithmic field dependence:
- The slope= 0.23 is in good agreement with our results

In-plane (ab-plane) resistivity

Busch et al., Phys. Rev. Lett. 69, 522 (1992)

Unpinned

liquid

- ab also exhibits B/Bc2 scaling
- Exponent of best power law fit: 0.75 0.01 (too good to be true?)

In-plane (ab-plane) resistivity

Busch et al., Phys. Rev. Lett. 69, 522 (1992)

Unpinned

liquid

- ab also exhibits B/Bc2 scaling
- Exponent of best power law fit: 0.75 0.01 (too good to be true?)

Out-of-plane (c-axis) resistivity

Busch et al., Phys. Rev. Lett. 69, 522 (1992)

Unpinned

liquid

- c also exhibits B/Bc2 scaling
- Given experimental forms for Rab and ab, we can write an experimental form for c using :

- Reproduces the maximum below Bc2 seen earlier:
- G. Briceño, M. F. Crommie, and A. Zettl, Phys. Rev. Lett.66, 2164 (1991); K. E.Gray and D. H. Kim, Phys. Rev.Lett. 70, 1693 (1993); N. Morozov et al., Phys. Rev. Lett. 84, 1784 (2000).

Comparison with thin film ab data

Z. L. Xiao, P. Voss-de Haan, G. Jakob, and H. Adrian, Phys. Rev. B 57, R736 (1998)

Reasonable agreement but systematic deviation from power law

(weaker than linear on log-log plot)

Comparison with thin film ab data

H. Raffy, S. Labdi, O. Laborde, and P. Monceau, Phys. Rev. Lett. 66, 2515 (1991)

P. Wagner, F. Hillmer, U. Frey, and H. Adrian, Phys. Rev. B 49, 13184 (1994)

M. Giura, S. Sarti, E. Silva,R. Fastampa, F. Murtas, R. Marcon, H. Adrian, and P. Wagner,Phys. Rev. B 50, 12920 (1994)

Z. L. Xiao, P. Voss-de Haan, G. Jakob, and H. Adrian, Phys. Rev. B 57, R736 (1998)

- Different thin film results do not agree with each other
- Common feature: weaker than power law, stronger than logarithmic B-dependence
- Thin film resistance is in-between single crystal Rab and ab
Macroscopic defects may force c-acis currents

- Thin film resistance may be a sample-dependent mixture of ab and c
(2d topology amplifies the effect of macroscopic defects)

Comparison with c-axis-configuration single crystal c data

N. Morozov, L. Krusin-Elbaum, T. Shibauchi, L. N. Bulaevskii, M. P. Maley, Yu. I. Latyshev,

and T. Yamashita, Phys. Rev. Lett. 84, 1784 (2000)

Empirical

form

- Excellent agreement with our empirical form (blue line):
- = 0.20 from the fit is in excellent agreement with our result
- Discrepancy: 0 = 3.6 (kcm)−1 from fit is different from 0≈ 8 (kcm)−1 inferred by Morozov et al. (Resistance decreases more slowly above the maximum than the fitting function.)

Quick summary of empirical forms

Unp. L.

Pinned

liquid

Sharp crossover at Tco from Rab = const (low T) to Rab log B (high T)

- For T < Tco: Rab = const
- For T > Tco: Rablog B
- Probable difference:
- intervortex correlations (interlayer?)
- Mismatch with thermodynamic
- vortex phases:
- No change in Rab when Tirr and Tlincrossed
- No anomaly in the low-current resistance at Tco

Rab = const

Rab = log B

Tco reflects transition in the dynamic vortex system?

Unpinned liquid dynamically restored for Tco < T <Tlin?

Dynamic ordering of vortices below Tco?

Other high-Tc materials: YBCO

Y. Tsuchiya et al., PRB 63, 184517 (2001): Microwave surface impedance in YBCO

ab-plane resistivity

from microwave surface impedance (arb. units)

Power law exponent agrees well with 3/4

in the high temperature limit.

No agreement at low temperature, but

this is not dynamic vortex system!

abc = const

Cancellation of power law exponents in ab and c

- cancellation of power law exponents
In conventional superconductors: ab DOS(B)

c DOS(B)

In a superconductor with line nodes DOS(B) B1/2

- sublinear B-dependence is not surprising,
but the origin of exponent 3/4 is not clear.

The response of the extended line nodes is not taken into account

in existing theories.

The cancellation of power law exponents may indicate a common origin of

ab plane and c axis dissipation.

Simultaneous in-plane and interplane phase slips?

Theoretical calculations of this mechanism are in disagreement with our results.

Conclusion

- Empirical forms for the magnetic field dependence of resistivities of BSCCO in the high-current limit:

- Some evidence that: FFF B3/4 holds in YBCO as well
- We speculated about a dynamic transition in the vortex system
- See also: Á. Pallinger, B. Sas, I. Pethes, K. Vad, F. I. B.Williams, and G. Kriza,
- Phys. Rev. B (in press).
- Validity in other high-Tc?
- Theoretical underpinnings?