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arXiv 1102.4484cond-mat.supr-concond-mat.mes-hall
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介观双带超导圆柱中的孤子态

Soliton states in mesoscopic two-band-superconducting cylinders

S. V. Kuplevakhsky, A. N. Omelyanchouk, Y. S. Yerin

备注：
15 pages, 3 figures
发表信息：
Low Temp. Phys. 37, 667 (2011)
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摘要：

在Ginzburg-Landau方法的框架下，我们提出了一个在外部平行磁场中介观（薄壁）双带超导柱中特定孤子态的自洽理论。当超导序参量的每个分量的相绕组数不同时，这种状态出现在“约瑟夫森型”带间耦合的存在下。我们在一定的无量纲参数$ε\approx\frac{\mathcal{L}_{m}}{\mathcal{L}_{k}}\ll1$中计算了系统的吉布斯自由能，直到二阶项，其中$\mathcal{L}_{m}$和$\mathcal{L}_{k} $分别是磁感应系数和动力学感应系数。我们得到了完整的精确孤子解。从局部和全局（热力学）稳定性的角度对这些解进行了深入的分析。特别是，我们表明，旋转对称性破缺所造成的孤子的形成引起的零频率旋转模式。虽然孤子态被证明是介稳态的，但最低单孤子态和介稳态零孤子态之间的最小能隙可以远小于后者的磁吉布斯自由能，只要带内“穿透深度”有很大不同，带间耦合很弱。我们的研究结果可能适用于一个广泛的类介观双连接结构呈现双带超导。

英文摘要：

In the framework of the Ginzburg-Landau approach, we present a self-consistent theory of specific soliton states in mesoscopic (thin-walled) two-band-superconducting cylinders in external parallel magnetic fields. Such states arise in the presence of "Josephson-type" interband coupling, when phase winding numbers are different for each component of the superconducting order parameter. We evaluate the Gibbs free energy of the sysyem up to second-order terms in a certain dimensionless parameter $ε\approx\frac{\mathcal{L}_{m}}{\mathcal{L}_{k}}\ll1$, where $\mathcal{L}_{m}$ and $\mathcal{L}_{k} $ are the magnetic and kinetic inductance, respectively. We derive the complete set of exact soliton solutions. These solutions are thoroughly analyzed from the viewpoint of both local and global (thermodynamic) stability. In particular, we show that rotational-symmetry-breaking caused by the formation of solitons gives rise to a zero-frequency rotational mode. Although soliton states prove to be thermodynamically metastable, the minimal energy gap between the lowest-lying single-soliton states and thermodynamically stable zero-soliton states can be much smaller than the magnetic Gibbs free energy of the latter states, provided that intraband "penetration depths" differ substantially and interband coupling is weak. The results of our investigation may apply to a wide class of mesoscopic doubly-connected structures exhibiting two-band superconductivity.

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