How grain boundaries limit supercurrents in high-temperature superconductors


The interface properties of high-temperature (high-Tc) copper oxide superconductors have been of interest for many years, and play an essential role in Josephson junctions, superconducting cables and microwave electronics. In particular, the maximum critical current achievable in high-Tc wires and tapes is well known to be limited by the presence of grain boundaries, regions of mismatch between crystallites with misoriented crystalline axes. Studies of single artificially fabricated grain boundaries have revealed that the critical current Jc of a grain boundary junction depends exponentially on the misorientation angle. Until now microscopic understanding of this apparently universal behaviour has been lacking. We present here the results of a microscopic evaluation based on a construction of fully three-dimensional YBa2Cu3O7−δ grain boundaries using molecular dynamics. With these structures, we calculate an effective tight-binding Hamiltonian for the d-wave superconductor with a grain boundary. The critical current is then shown to follow an exponential suppression with grain boundary angle α. We identify the build-up of charge inhomogeneities as the dominant mechanism for the suppression of the supercurrent.

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Figure 1: Schematic diagram of an HTS symmetric grain boundary.
Figure 2: Top view of a calculated (410) grain boundary.
Figure 3: Tight-binding model for the CuO2 plane.
Figure 4: Charging of the CuO4 squares.
Figure 5: Supercurrent distribution.
Figure 6: Angle dependence of the critical current.


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This work was supported by DOE grant DE-FG02-05ER46236 (P.J.H.), and by the DFG through SFB 484 and TRR 80 (S.G., T.K., R.G. and J.M.) and a research scholarship (S.G.). We are grateful to Yu. S. Barash for important early contributions to the project and we acknowledge fruitful discussions with A. Gurevich and F. Loder. P.J.H. would also like to thank the Kavli Institute for Theoretical Physics for support under NSF-PHY05-51164 during the writing of this manuscript. The authors acknowledge the University of Florida High-Performance Computing Center for providing computational resources and support that have contributed to the research results reported in this article.

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R.G. applied the Slater–Koster technique to derive an effective tight-binding model Hamiltonian at the grain boundary and B.M.A. contributed in setting up the Bogoliubov–de Gennes equations for the calculation of the critical current. S.G. carried out the numerical calculations under the supervision of P.J.H. and T.K. J.M. contributed with his experience and knowledge about grain boundaries and the physical length scales involved. All authors contributed to the analysis of the results. P.J.H., T.K., J.M. and S.G. wrote the manuscript.

Correspondence to S. Graser.

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Graser, S., Hirschfeld, P., Kopp, T. et al. How grain boundaries limit supercurrents in high-temperature superconductors. Nature Phys 6, 609–614 (2010).

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