Nonmonotonic d-wave gap effects on critical parameters in cuprate superconductors

Abstract

We study the impact of nonmonotonic d-wave superconducting gap symmetry, incorporating higher-order harmonics beyond the typical d-wave form, on the properties of cuprate superconductors. Key superconducting parameters (superfluid density, ${\rho }_s$, critical current density, $J_c$, London penetration depth, ${\lambda }_L$, and upper critical field, $H_{c2}$) were calculated using the Chandrasekhar-Einzel approach, incorporating the temperature and angular dependence of the superconducting gap. Results reveal a non-monotonic $J_c$ dependence on the $\cos \left(6\theta \right)$ term contribution, suggesting an optimal balance between $\cos \left(2\theta \right)$ and $\cos \left(6\theta \right)$ for maximizing $J_c$. The temperature dependence of the London penetration depth is significantly influenced by the nonmonotonic d-wave gap. While the pure d-wave model accurately describes superfluid density of pure Bi-2212, deviations emerge in optimally doped Tl-2201 and are pronounced in electron-doped Sr_0.9La_0.1CuO₂. Calculated $H_{c2}\left(T\right)$ values agree well with experimental data from Bi2201 and Tl-2201, particularly at low temperatures where the pure d-wave model deviates, emphasizing the importance of higher-order harmonics.