Figure 1

Plots of the vector potential with the superconducting gauge fixed by the method described in the text.Reuse & Permissions

Figure 2

Plots of the curvilinear coordinates lines of the Schwartz-Christoffel mapping. The deformed circular lines are the result of the mapping of equally space circular lines defined in a circle geometry onto to polygons. The radial lines are the result of the mapping of equally spaced radial lines, defined in the circle, onto the polygons.Reuse & Permissions

Figure 3

Plot of the nucleation curve in the $T$-$H$ space for different geometries: triangle, square, pentagon, hexagon, and circle. $A$, $\xi \left(T\right)$, $\Phi$, and ${\Phi }_0$ denote the area of the sample, the coherence length of the superconducting condensate, the magnetic flux passing thought the sample, and the magnetic flux quantum, respectively.Reuse & Permissions

Figure 4

Plots of the distribution of the superconducting order parameter$\left|\Psi \right|$, in the natural logarithmic scale, for the triangle, square, pentagon, hexagon, and circle geometries for different vorticities $L=$ 0, 1, 2, 3, 4, 5, and 6 (counting from left to right), where the magnetic field in magnetic flux quanta is $\Phi /{\Phi }_0$ $=$ 1, 3, 4, 5.5, 7, 8, 9, respectively. The color scale goes from red (dark gray) where superconductivity is strong, through yellow (light gray) to blue (dark gray). This color scheme is present in all figures that show the density of the superconducting condensate. The vortices appear as blue (dark gray) spots in the middle of the sample. Figure 5 shows the zooms from the areas of the present figure enclosed by white dashed boxes.Reuse & Permissions

Figure 5

Zoom of the superconductor order parameter patterns with antivortices shown in Fig. 4 by dashed boxes. The color scale differs from the one in the respective panels of the Fig. 4. The patterns correspond, from left to right, to the pairs  (geometry,  number of vortices,  vorticity number): (triangle, 3, 2); (triangle, 6, 5); (square, 4, 3); (pentagon, 5, 4); (hexagon, 6, 5).Reuse & Permissions

Figure 6

Vector potential with the superconducting gauge fixed so the vector potential lines become parallel to the boundary, as described in the text.Reuse & Permissions

Figure 7

Distribution of the superconducting order parameter, in the natural logarithmic scale, in the deformed hexagon for vorticities $L=$ 0, 1, 2, 3, 4, 5, and 6 (counting from left to right, from top to bottom), where the magnetic field in magnetic flux quanta is $\Phi /{\Phi }_0$ $=$ 1, 3, 4, 5.5, 7, 8, 9, respectively. The vortices appear as blue (dark gray) spots in the middle of the sample.Reuse & Permissions

Figure 8

Plots of the experimental sample border defined as N1 in Fig. 1 of Ref. [33], the adjusted curve (created by the method described in the text for the value of $R_s=0.95$) and the associated polygon, displayed by a thick light green (light gray) line, a full black line (on top of the thick line) and a dotted line (with squares on the corners), respectively.Reuse & Permissions

Figure 9

Plot of the vector potential of corresponding to a homogeneous perpendicular magnetic field in the superconducting gauge for the shape defined in Fig. 8.Reuse & Permissions

Figure 10

Experimental distributions and simulations to the experimental sample referred in the text, and also an indicative $H$-$T$ diagram showing the points of the experimental measurements and simulations. (Bottom left) The experimental data from the left panel of Fig. 4 in Ref. [33]. these experimental data are composed of four scanning tunneling microscopy measurements at zero-bias conductance for the magnetic fields indicated inside these measurements. The vortices cores appear as small bright spots. (Bottom right) The simulation patterns with the respective vorticity next to each. The simulated patterns that can be compared with the experimental patterns are to the near right of the corresponding patterns. The simulation patterns are in the natural logarithmic scale that goes from red (dark gray) to yellow (light gray) to blue (dark gray). In the patterns is possible to see the center of the vortices as small blue (dark gray) spots in the center of the samples. (Top right) The $T$-$H$ diagram showing the superconductivity nucleation curve (in black), the experimental line (red), and the adjusted experimental line (see main text, dashed blue line). On top of these lines, small squares and open circles, with the same colors of the respective lines, indicate the points corresponding to the simulations and the experimental distributions. Dashed vertical lines indicate the magnetic flux of the simulated patterns. The vorticity and magnetic flux values of the simulated patterns were added on the top of the dashed lines.Reuse & Permissions