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Fourfold Symmetric Solutions to the Ginzburg Landau Equation for d-Wave Superconductors

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Abstract

We find and investigate the structure of solutions to the Ginzburg Landau equation for a high temperature superconductor with tetragonal symmetry. This is done near an isolated, rotationally symmetric d-wave vortex state with its core at the origin defined on all of \({\mathbb{R}^2}\). We prove that the solution’s s-wave component nucleates near the vortex core for temperatures just below the d-wave critical temperature. We further show that this causes the rotational symmetry to break and that the solution develops a fourfold symmetry with respect to a rotation by an angle of \({\frac{\pi}{2}}\).

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Authors and Affiliations

  1. CGGVeritas, 10300 Town Park Drive, Houston, Texas, 77072, USA

    Minkyun Kim

  2. Department of Mathematics, Purdue University, West Lafayette, IN, 47907-2067, USA

    Daniel Phillips

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  1. Minkyun Kim
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  2. Daniel Phillips
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Correspondence to Daniel Phillips.

Additional information

Communicated by I. M. Sigal

Research supported by NSF grant DMS-1109459.

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Kim, M., Phillips, D. Fourfold Symmetric Solutions to the Ginzburg Landau Equation for d-Wave Superconductors. Commun. Math. Phys. 310, 299–328 (2012). https://doi.org/10.1007/s00220-012-1430-2

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  • DOI: https://doi.org/10.1007/s00220-012-1430-2

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