Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8
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Bardeen-Stephen flux flow law disobeyed in Bi 2 Sr 2 CaCu 2 O 8+δ. G. Kriza, 1,2 A. Pallinger 1 , B. Sas 1 , I. Pethes 1 , K. Vad 3 , F. I. B.Williams 1,4 1 Research Institute for Solid State Physics and Optics, Budapest, Hungary

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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 bi 2 sr 2 cacu 2 o 8

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


Aim measure free flux flow fff resitivity in the high t c superconductor bi 2 sr 2 cacu 2 o 8 bscco

Aim: Measure Free Flux Flow (FFF) resitivity inthe high-Tc superconductor Bi2Sr2CaCu2O8+δ(BSCCO)

B  ab

Transport current JT

Abrikosov vortex

Bardeen–Stephen law (BS)


What is known of fff in high t c superconductors

What is known of ρFFFin high-Tc superconductors?

  • 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


Complication how to account for the pinning force

Complication: How to account for the pinning force?

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


Experiment

Experiment

c

B  ab

BSCCO single crystal:

b

a

Current excitation:

Voltage – current

(V – I)

characteristics

Voltage

response


Typical voltage current characteristics

Typical voltage – current characteristics

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


Temperature and field dependence of the high current differential resistance r ab

Temperature and field dependence of the high-current differential resistance Rab

High temperature:

sublinear B-depend-

dence

Low temperature:

T and B independent

resistance


Empirical form for the high current differential resistance r ab

Empirical form for the high-current differential resistance Rab

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:


Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8

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


Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8

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


Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8

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)


Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8

Magnetic field–temperature phase diagram

Bc2 upper critical field

TFOT first order transition line

Tirr magnetic irreversibility line

T2nd second magnetization peak


Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8

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?


Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8

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


Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8

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)


Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8

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


Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8

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?)


Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8

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?)


Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8

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).


Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8

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)


Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8

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)


Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8

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 (kcm)−1 from fit is different from 0≈ 8 (kcm)−1 inferred by Morozov et al. (Resistance decreases more slowly above the maximum than the fitting function.)


Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8

Quick summary of empirical forms


Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8

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: Rablog 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?


Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8

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!


Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8

abc = 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.


Bardeen stephen flux flow law disobeyed in bi 2 sr 2 cacu 2 o 8

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?


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