High Frequency Electrodynamics of Superconductors

Proximity Electrodynamics
Analytical Models of Proximity Electrodynamics
Fundamental Electrodynamics of Superconductors
BCS d-wave Electrodynamics of Pr-Ce-Cu-O

Microwave Applications of Superconductors

Electric Field Effect on the Surface Impedance of Cuprate Superconductors
Consequences of d-wave Electrodynamics for Microwave Applications of the Cuprates

References

The proximity effect is a fascinating phenomenon. Consider a bone fide superconductor in contact with a non-superconducting metal. By virtue of the electrical contact between the two metals, some of the Cooper pairing correlations from the superconductor will "leak" into the normal metal, making it superconducting to some extent. These correlations are very short-ranged and spatially inhomogeneous. Our research concerns a new way to probe these correlations by means of their electrodynamic properties, such as magnetic screening and microwave losses.

Proximity Electrodynamics

  • We developed a simple analytical model for magnetic screening in proximity coupled bilayers. One consequence of the model is a prediction that rather generically Δ λ(T)~T at low temperatures in S/N bilayers.
  • We proved the above model to be useful by successfully fitting it to surface impedance data obtained at 11 GHz on Nb/Al, Nb/Cu and Nb/Ag proximity-coupled bilayers.
  • Another interesting question is whether a superconducting and ferromagnetic material can show a proximity effect. Ordinarily, uniform superconductivity and ferromagnetism are incompatible phenomena. We examined bilayer films made of a superconductor (Nb) and a spin-glass (Cu:Mn). The spin-glass is basically a dilute, low magnetic moment ferromagnet. We found clear evidence of proximity coupling between the two materials in our surface impedance experiments.5

Analytical Models of Proximity Electrodynamics

We developed a simple analytical model based on proximity effect physics for magnetic screening1 and finite frequency losses2,3 in proximity-coupled S/N bilayers. This model was applied to measurements of Rs,eff(T) and Xs,eff(T) of low-Tc S/N bilayers (Nb/Al, Nb/Cu, and Nb/Ag) made with the parallel plate resonator technique.4 The fits are remarkably good (see Fig. 1), and the parameter values for the S and N layers are quite reasonable.2 We take this to mean that the model captures the essential physics of proximity screening in the low-Tc systems.

Fig.1 Change in penetration depth and absolute surface resistance of Nb/Al proximity coupled bilayers. Both samples have a Nb base layer 3000Å thick and an Al layer bilayer of either 100Å or 600Å on top. Solid lines represent theoretical fits to the data. See references 1,2.

A by-product of this research was the discovery that S/N bilayers show an increase in penetration depth with temperature which is generically linear, rather than activated at low temperatures, i.e. Δλ(T)~T (for T << Tc).1 This is illustrated in Fig. 2, which shows Δλ(T)data for a YBCO single crystal and a Nb/Cu proximity coupled bilayer, as well as the analytical screening model for a proximity coupled S/N bilayer. We also demonstrated that the linear-in-T increase in penetration depth for the YBCO crystal is not likely due to proximity coupling to a normal metal `dead layer' on the surface of the crystal.1

Fig.2 Change in penetration depth of a high quality YBCO crystal, a Nb:3000Å/Cu:390Å proximity coupled bilayer, and the proximity screening theory low-temperature fit to the YBCO data. From Refs. 2, 3 and unpublished data.

1. Michael S. Pambianchi, Jian Mao, and Steven M. Anlage, "Magnetic Screening in Proximity-Coupled Superconductor / Normal-Metal Bilayers," Phys. Rev. B 50, 13659-13663 (1994).

2. Michael S. Pambianchi, S. N. Mao, and Steven M. Anlage, "Microwave Surface Impedance of Proximity-Coupled Nb/Al Bilayer Films," Phys. Rev. B 52, 4477-4480 (1995).

3. Michael S. Pambianchi, L. Chen, and Steven M. Anlage, "Complex Conductivity of Proximity-Superconducting Nb/Cu Bilayers," Phys. Rev. B 54, 3508-3513 (1996).

4.. M. Pambianchi, S. M. Anlage, E. S. Hellman, E. H. Hartford, M. Bruns, and S. Y. Lee, "Penetration Depth, Microwave Surface Resistance, and Gap Ratio in NbN and Ba1-xKxBiO3 Thin Films," Appl. Phys. Lett., 64, 244-246 (1994)

5. L. V. Mercaldo, Steven M. Anlage, and L. Maritato, "Microwave Surface Impedance of Superconducting (Nb) / Spin-Glass (CuMn) Bilayers," Phys. Rev. B 59, 4455-4462 (1999). cond-mat/9811347.

Fundamental Electrodynamics of Superconductors

Traditional (low transition temperature) superconductors have properties which are largely isotropic - meaning that electrons are bound into identical Cooper pairs in all directions inside the material. In contrast, the high transition temperature cuprate superconductors have highly anisotropic superconducting pairing; there are sheets of highly conducing material separated by poorly conducting material, and there is strong anisotropy within the planes themselves. This latter anisotropy comes from the complicated "d-wave" dance which the electrons execute when they pair up in the high transition temperature materials.


Until recently, it was thought that only one special class of cuprate superconductors did NOT perform this new kind of dance, but instead had isotropic pairing properties like the traditional superconductors. However, three recent papers in Physical Review Letters conclusively show that ALL classes of cuprate superconductors have the more complicated anisotropic pairing- considerably simplifying the task of understanding the fundamental interactions responsible for high transition temperature superconductivity. See the papers of:


C. C. Tsuei and J. R. Kirtley, Phys. Rev. Lett. 85, 182 (2000);
R. Prozorov, et al. Phys. Rev. Lett. 85, 3700 (2000);
J. D. Kokales, et al. Phys. Rev. Lett. 85, 3696 (2000).

  • We have discovered that the electrodynamics of Pr-Ce-Cu-O films and crystals are consistent with d-wave BCS superconductivity.
  • Vortex dynamics in superconductors at microwave frequencies. A graduate student, J. C. Booth, has developed a novel broadband (DC - 50 GHz) measurement of surface impedance in thin films.1 The method has been used to clearly identify a crossover from collective vortex behavior (vortex glass/liquid) to single-particle-like (mean field) dynamics as a function of frequency at fixed field and temperature.2

1. J. C. Booth, D. H. Wu, S. M. Anlage, "A Broadband Method for the Measurement of the Surface Impedance of Thin Films at Microwave Frequencies," Rev. Sci. Instrum., 65, 2082-2090 (1994).

2. Dong-Ho Wu, J. C. Booth, and Steven M. Anlage, "Frequency and Field Variation of Vortex Dynamics in YBa2Cu3O7-δ" Phys. Rev. Lett. 75, 525 (1995).

Microwave Applications of Superconductors

  • We have demonstrated that the electric field effect can modulate the surface impedance of superconductors through a modification of a thin surface layer by means of surface charge.
  • We have investigated the important consequences that d-wave superconductivity will have on microwave applications of the hole-doped cuprates.

Electric Field Effect on the Surface Impedance of Cuprate Superconductors

A strong electric field applied perpendicular to the surface of a superconductor will induce excess charge within a Thomas-Fermi screening length of the surface. This excess charge will change the local carrier concentration and hence change the normal and superconducting properties of the superconductor. These effects are especially noticeable when the superconducting film has a thickness approaching the charge screening length. In effect, this is a short range proximity effect in which superconductivity can be either enhanced or suppressed.

We were the first to demonstrate that these excess charges can be used to modulate the microwave conductivity and surface impedance of a superconducting film in a controllable manner.24,25 By adding holes (with an electric field) to the surface of under-doped YBCO, we decreased the magnetic penetration depth and the microwave surface impedance. The converse effect was also demonstrated. The model we developed to quantitatively explain these results was also quite successful.24,25 This result opens the possibility for future applications of this effect to electronically tunable microwave switches and delay lines.

Consequences of d-wave Electrodynamics for Microwave Applications of the Cuprates

Hole-doped cuprates have a strong d-wave component to the superconducting order parameter. We considered several important consequences this will have for high frequency applications of the cuprates, including: i) a finite intrinsic residual loss for YBCO, Rs,min ~ 1 μΩ at 10 GHz, ii) an intrinsic non-linear Meissner effect, limiting the ultimate linearity of devices like filters, transmission lines, delay lines, antennas, etc., and iii) an unusual sensitivity of the microwave losses to disorder, suggesting that more disordered cuprate materials may give lower losses than all but the most pure single crystals.9,26

REFERENCES CITED

1. Michael S. Pambianchi, Jian Mao, and Steven M. Anlage, "Magnetic Screening in Proximity-Coupled Superconductor / Normal-Metal Bilayers," Phys. Rev. B 50, 13659 (1994).

2. Michael S. Pambianchi, S. N. Mao, and Steven M. Anlage, "Microwave Surface Impedance of Proximity-Coupled Nb/Al Bilayer Films," Phys. Rev. B 52, 4477 (1995).

3. Michael S. Pambianchi, L. Chen, and Steven M. Anlage, "Complex Conductivity of Proximity-Superconducting Nb/Cu Bilayers," Submitted to Phys. Rev. B October, 1995).

4. M. Pambianchi, S. M. Anlage, E. S. Hellman, E. H. Hartford, M. Bruns, and S. Y. Lee, "Penetration Depth, Microwave Surface Resistance, and Gap Ratio in NbN and Ba1-xKxBiO3 Thin Films," Appl. Phys. Lett., 64, 244 (1994).

5. D. H. Wu , J. Mao, S. N. Mao, J. L. Peng, X. X. Xi, T. Venkatesan, R. L. Greene, and Steven M. Anlage, "Temperature Dependence of the Magnetic Penetration Depth and Surface Resistance of Nd1.85Ce0.15CuO4-y Superconducting Thin Films and Single Crystals," Phys. Rev. Lett. 70, 85 (1993).

6. S. N. Mao, X. X. Xi, S. Bhattacharya, Q. Li, J. L. Peng, J. Mao, D. H. Wu, S. M. Anlage, R. L. Greene and T. Venkatesan, "Oxidation and Reduction During Fabrication of Nd1.85Ce0.15CuO4-y Superconducting Thin Films," IEEE Trans. Appl. Supercond. 3, 1552 (1993).

7. S. N. Mao, X. X. Xi, Jian Mao, D. H. Wu, Q. Li, S. M. Anlage, T. Venkatesan, D. Prasad Beesabathina, L. Salamanca-Riba, and X. D. Wu, "Structural Characterization and Microwave Loss of Nd1.85Ce0.15CuO4-y Superconducting Thin Films on YSZ Buffered Sapphire," Appl. Phys. Lett., 64, 375 (1994).

8. Steven. M. Anlage, Dong-Ho Wu, Jian Mao, Sining Mao, X. X. Xi, T. Venkatesan, J. L. Peng, and R. L. Greene, "Surface Impedance Measurements of Cuprate Superconductors: Nd1.85Ce0.15CuO4-y - A Case Study," J. Supercond. 7, 453 (1994).

9. Steven. M. Anlage, Michael Pambianchi, Alp T. Findikoglu, C. Doughty, Dong-Ho Wu, Jian Mao, Si-ning Mao, X. X. Xi, T. Venkatesan, J. L. Peng and R. L. Greene, "The Electrodynamics of Oxide Superconductors," published in "Oxide Superconductor Physics and Nano-Engineering," edited by D. Pavuna and I. Bozovic, (SPIE Proceedings, Volume 2158, 1994), p. 39.

10. Steven. M. Anlage, Dong-Ho Wu, Jian Mao, Sining Mao, X. X. Xi, T. Venkatesan, J. L. Peng, and R. L. Greene, "The Electrodynamics of Nd1.85Ce0.15CuO4-y : Comparison with Nb and YBa2Cu3O7," Phys. Rev. B 50, 523 (1994).

11. Jian Mao, D. H. Wu, Steven M. Anlage, S. N. Mao, X. X. Xi, T. Venkatesan, J. L. Peng, R. L. Greene, "Temperature Dependence of the Surface Impedance of Nd1.85Ce0.15CuO4-y and YBa2Cu3O7," Physica C 235-240, 2013 (1994).

12. S. N. Mao, Jian Mao, X. X. Xi, D. H. Wu, Q. Li, S. M. Anlage, and T. Venkatesan, "Superconducting Nd2-xCexCuO4 Thin Films and Heterostructures on Sapphire," IEEE Trans. Appl. Supercond. 5, 1347 (1995).

13. Dong-Ho Wu, Jian Mao, and Steven M. Anlage, "Pairing Symmetry and Electrodynamics of Superconducting YBa2Cu3O7, Nd1.85Ce0.15CuO4-y, and Nb," J. Supercond. 8, in press (1995).

14. J. Chen, J. F. Zasadzinski, K. E. Gray, J. L. Wagner, and D. G. Hinks, "Point- Contact Tunneling Study of HgBa2CuO4+d: BCS-like Gap Structure," preprint, 1994.

15. A. Andreone, A. Cassinese, A. Di Chiara, R. Vaglio, A. Gupta, and E. Sarnelli, Phys. Rev. B 49, 6392 (1994).

16. C. W. Schneider, Z. H. Barber, J. E. Evetts, S. N. Mao, X. X. Xi, and T. Venkatesan Physica C 233, 77 (1994).

17. B. Stadlober, G. Krug, R. Nemetschek, R. Hackl, J. L. Cobb, and J. T. Markert, Phys. Rev. Lett. 74, 4911 (1995).

18. See the review by B. Levi in Physics Today 46, No. 5, 17 (1993).

19. V. Z. Kresin and S. A. Wolf, Phys. Rev. B 46, 6458 (1992).

20. R. A. Klemm and S. H. Liu, Phys. Rev. Lett. 74, 2343 (1995).

21. Jian Mao, Dong-Ho Wu, J. L. Peng, R. L. Greene, and Steven M. Anlage, "Anisotropic Surface Impedance of YBa2Cu3O7 Single Crystals," Phys. Rev. B (Rapid Communications), 51, 3316 (1995).

22. D. A. Bonn, et al., Phys. Rev. B. 47, 11314 (1993).

23. W. N. Hardy, et al., Phys. Rev. Lett. 70, 3999 (1993).

24. A. T. Findikoglu, C. Doughty, S. M. Anlage, Qi Li, X. X. Xi, and T. Venkatesan, "Effect of DC Electric Field on the Effective Microwave Surface Impedance of YBa2Cu3O7 /SrTiO3/YBa2Cu3O7 Trilayers," Appl. Phys. Lett., 63, 3215 (1993).

25. A. T. Findikoglu, C. Doughty, S. M. Anlage, Qi Li, X. X. Xi, and T. Venkatesan, "DC Electric Field Effect on the Microwave Properties of YBa2Cu3O7 /SrTiO3 Heterostructures," J. Appl. Phys. 76, 2937 (1994).

26. Jian Mao, Steven M. Anlage, J. L. Peng, and R. L. Greene, "Consequences of d-Wave Superconductivity for High Frequency Applications of Cuprate Superconductors," IEEE Trans. Appl. Supercond. 5, 1997 (1995).

27. J. C. Booth, D. H. Wu, and S. M. Anlage, "A Broadband Method for the Measurement of the Surface Impedance of Thin Films at Microwave Frequencies," Rev. Sci. Instrum. 65, 2082 (1994).

28. D.H. Wu, J.C. Booth, and S.M. Anlage, "Frequency and Field Variation of Vortex Dynamics in YBa2Cu3O7," Phys. Rev. Lett. 75, 2662 (1995).

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