Symmetric vortex solutions in the $$\text{U}(1)$$ and $$\text{SO}(5)$$ Ginzburg-Landau models of superconductivity.(English)Zbl 1271.35066

Berestycki, Henri (ed.) et al., Nonlinear PDEs in condensed matter and reactive flows. Proceedings of the NATO Advanced Study Institute on PDE’s in models of superfluidity, superconductivity and reactive flows, Cargèse, France, 21 June – 3 July 1999. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-0972-0/hbk). NATO ASI Ser., Ser. C, Math. Phys. Sci. 569, 323-337 (2002).
Summary: We present a summary of analytical and numerical results obtained with A. J. Berlinsky and T. Giorgi [Phys. Rev. B 60, No. 9, 6901–6906 (1999), http://arxiv.org/abs/cond-mat/9812283] on the core structure of symmetric vortices in a Ginzburg-Landau model based on S. C. Zhang’s $$\text{SO}(5)$$ theory of high temperature superconductivity and antiferromagnetism. We find that the usual superconducting vortices (with normal phase in the central core region) become unstable at a critical value of the chemical potential, giving rise to a new type of vortex profile with antiferromagnetic ordering in the core region. In the process we revisit the traditional $$\text{U}(1)$$-Ginzburg-Landau vortices and prove the uniqueness of symmetric solutions of degree $$d$$ for $$\kappa\geq | d|\sqrt 2$$.
For the entire collection see [Zbl 1028.00035].

MSC:

 35Q56 Ginzburg-Landau equations 76A25 Superfluids (classical aspects) 82D55 Statistical mechanics of superconductors
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