Electrodynamics of Abrikosov vortices: the field theoretical formulation

Abstract

Electrodynamic phenomena related to vortices in superconductors have been studied since their prediction by Abrikosov, and seem to hold no fundamental mysteries. However, most of the effects are treated separately, with no guiding principles.We demonstrate that the relativistic vortex worldsheet in spacetime is the object that naturally conveys all electric and magnetic information, for which we obtain simple and concise equations. Breaking Lorentz invariance leads to down-to-earth Abrikosov vortices, and special limits of these equations include for instance dynamic Meissner screening and the AC Josephson relation. On a deeper level, we explore the electrodynamics of two-form sources in the absence of electric monopoles, in which the electromagnetic field strength itself acquires the characteristics of a gauge field. This novel framework leaves room for unexpected surprises.

Keywords

Abrikosov vortex / electromagnetism / Maxwell equations / differential geometry / multivalued fields

References

[1] A. A. Abrikosov, Soviet J. Exp. & Theor. Phys., 1957, 5: 1174

[2] H. Rogalla and P. H. Kes (Eds.), 100 Years of Superconductivity, New York: CRC Press, 2011

[3] D. R. Nelson, Phys. Rev. Lett., 1988, 60(19): 1973

[4] B. Rosenstein and D. P. Li, Rev. Mod. Phys., 2010, 82(1): 109

[5] G. Blatter, M. V. Feigel’man, V. B. Geshkenbein, A. I. Larkin, and V. M. Vinokur, Rev. Mod. Phys., 1994, 66(4): 1125

[6] L. N. Bulaevskii and E. M. Chudnovsky, Phys. Rev. Lett., 2006, 97(19): 197002

[7] L. N. Bulaevskii and A. E. Koshelev, Phys. Rev. Lett., 2006, 97(26): 267001

[8] L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, No. 8 in Course of Theoretical Physics, Oxford: Pergamon, 1960

[9] A. J. Beekman and J. Zaanen, Type-II Bose–Mott insulators (in preparation).

[10] M. Henneaux and C. Teitelboim, Quantization of Gauge Systems, Princeton, NJ: Princeton University Press, 1992

[11] J. Polchinski, String Theory, Vol. I+II, Cambridge: Cambridge University Press, 1998

[12] H. B. Nielsen and P. Olesen, Nucl. Phys. B, 1973, 61: 45

[13] J. Schwinger, Particles, Sources and Fields, Reading, MA: Addison-Wesley, 1970

[14] H. Kleinert, Gauge Fields in Condensed Matter, Vol. I, Superflow and Vortex Lines, Singapore: World Scientific, 1989

[15] M. Tinkham, Introduction to Superconductivity, 2nd Ed., New York: McGraw-Hill, 1996

[16] A. J. Beekman, D. Sadri, and J. Zaanen, New J. Phys., 2011, 13: 033004

[17] B. D. Josephson, Phys. Lett., 4965, 16(3): 242

[18] S. Savel’ev, V. A. Yampol’skii, A. L. Rakhmanov, and F. Nori, Rep. Prog. Phys., 2010, 73(2): 026501

[19] R. G. Mints and I. B. Snapiro, Phys. Rev. B, 1995, 51(5): 3054

[20] K. F. Warnick and P. Russer, Turkish J. Electr. Eng. & Comp. Sci., 2006, 14(1): 153

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