1202.2322 (O. Olendski)
O. Olendski
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 $\Lambda$ are analyzed with the primary emphasis on
the interaction between the coefficient $\beta$ of the cubic GL term and the de
Gennes distance $\Lambda$ 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 Schr\"{o}dinger
equation. In particular, for the large cubicities, the temperature $T$ becomes
$\Lambda$ independent linearly decreasing function of the growing $\beta$ 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 $\Lambda_{T=T_c}$ is an analytical function of $\beta$ 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 $\Lambda$ 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 $\Lambda$, $n_s$ and $\beta$. It is
proved that the concentration $n_s^{(0)}$ transforms for the large cubicities
into the density of the bulk sample.
View original:
http://arxiv.org/abs/1202.2322
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