The temperature dependence features of the order parameter in unconventional superconductors with spin-singlet pairing interaction

We calculate the temperature dependence of the superconducting order parameter in unconventional superconductors within the framework of the one loop variational perturbation theory. For simplicity, we assumed cylindrical Fermi surface and tried the order parameter in the form of series

$$
\Delta(\varphi) = \Delta_s + \sum_{n=1}\Delta_n\cos(2n\varphi)
$$,

where $\varphi$ is the polar angle measured from the $k_x$ axis. The components $\Delta_s$, $\Delta_n$ are found by minimizing the free energy functional of the system.

We used the model potential discussed in work [1]

$$
V(\varphi_1 - \varphi_2) = a_0 + \sum_{n=1} a_n\cos(n(\varphi_1 - \varphi_2)),
$$

$$
a_0 = V_{max} + \frac{\delta}{\pi}(V_{min} - V_{max}),\quad a_n = \frac{2}{\pi n}\sin\left(\frac{n\delta}{2}\right)\,(1+(-1)^n)(V_{min} - V_{max}).
$$.

Here $V_{min}, V_{max}, \delta$ are model parameters. It was shown that higher harmonics of the order parameter appear for certain parameters of the pairing potential.

On the basis of numerical simulation, it was also shown that the higher harmonics of the order parameter depend on temperature in a significantly different way than BCS one.

The results are discussed in the context of experiments on the temperature dependence of the superconducting condensate density in thin-film cuprates [2].

[1] D. J. Scalapino, E. Loh, J. E. Hirsch, Physical Review B, 34, 8190 (1986).
[2] I. Hetel, T.R. Lemberger, M. Randeria, Nature, 3, 700 (2007).