高温超导反铁磁SO（5）模型的涡旋结构
Vortex Structures for an SO(5) Model of High-T_C Superconductivity and Antiferromagnetism
摘要：
本文研究了基于S。C.高温超导和反铁磁性的SO（5）理论。我们考虑一个完整的Ginzburg-Landau理论（Ginzburg-Landau标度参数Kappa）和一个高Kappa极限模型。在所有的情况下，我们发现，通常的超导涡旋（与正常阶段在中央核心区域）变得不稳定（而不是能量最小化）时，化学势跨越阈值水平，从而产生一个新的涡旋轮廓与反铁磁有序的核心区域。我们表明，这种相变的核心是由于从一个简单的本征值的线性化方程的分支。在极限大kappa模型中，我们证明了反铁磁核解总是非退化的局部能量极小解，并证明了物理相关解的精确多重性结果。
英文摘要：
We study the structure of symmetric vortices in a Ginzburg-Landau model based on S. C. Zhang's SO(5) theory of high temperature superconductivity and antiferromagnetism. We consider both a full Ginzburg-Landau theory (with Ginzburg-Landau scaling parameter kappa) and a high-kappa limiting model. In all cases we find that the usual superconducting vortices (with normal phase in the central core region) become unstable (not energy minimizing) when the chemical potential crosses a threshold level, giving rise to a new vortex profile with antiferromagnetic ordering in the core region. We show that this phase transition in the cores is due to a bifurcation from a simple eigenvalue of the linearized equations. In the limiting large kappa model we prove that the antiferromagnetic core solutions are always nondegenerate local energy minimizers and prove an exact multiplicity result for physically relevent solutions.
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