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

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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  1. 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

  2. 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)

  3. 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

  4. 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

  5. Experiment c B  ab BSCCO single crystal: b a Current excitation: Voltage – current (V – I) characteristics Voltage response

  6. 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

  7. Temperature and field dependence of the high-current differential resistance Rab High temperature: sublinear B-depend- dence Low temperature: T and B independent resistance

  8. 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:

  9. 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

  10. 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

  11. 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)

  12. Magnetic field–temperature phase diagram Bc2 upper critical field TFOT first order transition line Tirr magnetic irreversibility line T2nd second magnetization peak

  13. 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?

  14. 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

  15. 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)

  16. 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

  17. 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?)

  18. 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?)

  19. 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).

  20. 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)

  21. 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)

  22. 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.)

  23. Quick summary of empirical forms

  24. 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?

  25. 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!

  26. 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.

  27. 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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