Figure 1

(Color online) Magnetization as a function of the external magnetic field for different current densities $\gamma =0$, 0.2, 0.4, and 0.8, respectively. The arabic numerals indicate the total vorticities of the system.Reuse & Permissions

Figure 2

(Color online) Contour plots of $\left|\psi \right|$ at $\gamma =0.4$ for different fields $H/H_{c2}=0$, 0.38, 0.44, 0.45, 0.54, 0.65, 0.7, 0.76, and 0.85, respectively. The dots represent the vortex core positions in the system with low $\left|\psi \right|$ value. The index numbers (0)–(8) in each plot also present the total vorticity $L$ in the system.Reuse & Permissions

Figure 3

(Color online) (a1)–(e1) and (a2)–(e2) are contour plots of the distribution of the magnitude of the order parameter $\left|\psi \right|$ and their corresponding phase $\phi$ at $H/H_{c2}=0.5$ with the applied current density $\gamma =0.8$ along $x$ direction at different time: (a1) and (a2): 77.76; (b1) and (b2): 86.04; (c1) and (c2): 95.688; (d1) and (d2): 98.28; and (e1) and (e2): 104.4. The arrows illustrate the direction and the speed of the vortex motion.Reuse & Permissions

Figure 4

(Color online) (a) Time evolution of free-energy (blue curve), magnetization (red curve), and vorticity (magenta segment lines) of the square superconducting system with $\gamma =0.8$ and $H/H_{c2}=0.5$. The dashed vertical lines a–e guide the eyes for the evolution corresponding to the snapshots shown in Fig. 3. (b) Time evolution of free energy in the designated patches with the same size for the process of the giant vortex formation. The insets show the snapshots at point b, c, and d, which have been framed in Figs. 3b, 1, 2, 3, 1.Reuse & Permissions

Figure 5

(Color online) Contour plots of (a) $\left|\psi \right|$ and (b) $\phi$ of the order parameter with $H/H_{c2}=0.9$ and $\gamma =0.8$ at certain time in the simulation.Reuse & Permissions