de Gennes边界条件与Ginzburg-Landau方程立方度的相互作用对超导薄膜性质的影响
Influence of the interplay between de Gennes boundary conditions and cubicity of Ginzburg-Landau equation on the properties of superconducting films
摘要：
本文分析了直膜边缘受外推长度为$Λ$的Robin型边界条件作用的Ginzburg-Landau（GL）方程的精确解，着重讨论了三次GL项系数$β$与de Gennes距离$Λ$之间的相互作用及其对带材温度$T$的影响。载流子密度$n_s$也起着非常重要的作用，它自然地作为GL方程的积分常数出现。所获得的结果的物理解释是基于$n_s$依赖的有效势$V_{eff}({\bf r})$所创建的非线性项及其对相应的薛定谔方程的最低本征值的影响。特别地，对于大的立方度，温度$T$成为$Λ$独立的增长$β$的线性递减函数，因为在这个极限中，边界条件不能改变非常强的$V_{eff}$。结果表明，温度的增加，这是在线性GL制度的负de Gennes距离，被消灭的增长立方。在这种情况下，减小的$T$仅以唯一密度$n_s^{(0)}$通过其体积值$T_c$，并且相应的外推长度$Λ_{T=T_c}$是$β$的解析函数，其性质被详细讨论。对于小于$n_s^{(0)}$的密度，温度保持在$T_c$以上，对于大体积饱和到由$n_s$和负$Λ$确定的值，而对于$n_s>n_s^{(0)}$，超导性被在某个温度$T>T_c$下增长的GL非线性破坏，这取决于$Λ$，$n_s$和$β$。证明了对于大体积样品，浓度$n_s^{(0)}$转化为本体样品的密度。
英文摘要：
Exact solutions of the Ginzburg-Landau (GL) equation for the straight film subjected at its edges to the Robin-type boundary conditions characterized by the extrapolation length $Λ$ are analyzed with the primary emphasis on the interaction between the coefficient $β$ of the cubic GL term and the de Gennes distance $Λ$ and its influence on the temperature $T$ of the strip. Very substantial role is played also by the carrier density $n_s$ that naturally emerges as an integration constant of the GL equation. Physical interpretation of the obtained results is based on the $n_s$-dependent effective potential $V_{eff}({\bf r})$ created by the nonlinear term and its influence on the lowest eigenvalue of the corresponding Schrödinger equation. In particular, for the large cubicities, the temperature $T$ becomes $Λ$ independent linearly decreasing function of the growing $β$ since in this limit the boundary conditions can not alter very strong $V_{eff}$. It is shown that the temperature increase, which is produced in the linear GL regime by the negative de Gennes distance, is wiped out by the growing cubicity. In this case, the decreasing $T$ passes through its bulk value $T_c$ at the unique density $n_s^{(0)}$ only, and the corresponding extrapolation length $Λ_{T=T_c}$ is an analytical function of $β$ whose properties are discussed in detail. For the densities smaller than $n_s^{(0)}$, the temperature stays above $T_c$ saturating for the large cubicities to the value determined by $n_s$ and negative $Λ$ while for $n_s>n_s^{(0)}$ the superconductivity is destroyed by the growing GL nonlinearity at some temperature $T>T_c$, which depends on $Λ$, $n_s$ and $β$. It is proved that the concentration $n_s^{(0)}$ transforms for the large cubicities into the density of the bulk sample.
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