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In this work we study the role of the heat diffusion equation in simulating the resistive state of superconducting films. By analyzing the current-voltage and current-resistance characteristic curves for temperatures close to $T_c$ and various heat removal scenarios, we demonstrate that heat diffusion notably influences the behavior of the resistive state, specially near the transition to the normal state, where heat significantly changes the critical current and the calculated resistance. Furthermore, we show how the efficiency of the substrate has important effects in the dynamics of the system, particularly for lower temperatures. Finally, we investigate the hysteresis loops, the role of the film thickness and of the Ginzburg-Landau parameter, the findings accounting for heat diffusion in accurately modeling the resistive state of superconducting films and provide valuable insights into its complex dynamics. To accomplish these findings, we have used the $3D$ generalized Ginzburg-Landau equation coupled with the heat diffusion equation., Comment: Published in Physica C: Superconductivity and its applications

We propose a superconducting diode device comprising a central superconducting film flanked by two wires carrying an applied DC bias, suitably chosen so as to generate different asymmetric field profiles. Through numerical simulations of the coupled Ginzburg-Landau and heat-diffusion equations, we show that this design is capable of efficiently breaking the reciprocity of the critical current in the central superconductor, thus promoting the diode effect in response to an applied AC current. By adjusting the DC bias in the wires, we find the optimum inhomogeneous field profile that facilitates the entrance of vortices and antivortices in a given polarity of the applied AC current and impede their entrance in the other polarity. This way, the system behaves as an ideal superconducting half-wave rectifier, with diode efficiencies surpassing 70%. Furthermore, we detail the behavior and diode efficiency of the system under different experimental conditions, such as the substrate heat transfer coefficient and the sweep rate of the external current., Comment: 13 pages, 14 figures

By using the full 3D generalized time dependent Ginzbug-Landau equation we study a long superconducting film of finite width and thickness under an applied transport current. We show that, for sufficiently large thickness, the vortices and the antivortices become curved before they annihilate each other. As they approach the center of the sample, their ends combine, producing a single closed vortex. We also determine the critical values of the thickness for which the closed vortex sets in for different values of the Ginzburg-Ladau parameter. Finally, we propose a model of how to detect a closed vortex experimentally., Comment: 9 pages, 10 figures, accepted for publication in Phys. Rev. B

Within the framework of the generalized time-dependent Ginzburg-Landau equations, we studied the influence of the magnetic self-field induced by the currents inside a superconducting sample driven by an applied transport current. The numerical simulations of the resistive state of the system show that neither material inhomogeneity nor a normal contact smaller than the sample width are required to produce an inhomogeneous current distribution inside the sample, which leads to the emergence of a kinematic vortex-antivortex pair (vortex street) solution. Further, we discuss the behaviors of the kinematic vortex velocity, the annihilation rates of the supercurrent, and the superconducting order parameters alongside the vortex street solution. We prove that these two latter points explain the characteristics of the resistive state of the system. They are the fundamental basis to describe the peak of the current-resistance characteristic curve and the location where the vortex-antivortex pair is formed., Comment: 9 pages, 6 figures. Accepted for publication in Scientific Reports