Multiquanta Vortex Entry and Vortex-Antivortex Pattern Expansion in a Superconducting Microsquare with a Magnetic Dot

We investigate the nucleation of superconductivity in a microsquare with a magnetic dot on top. The cusplike behavior of the calculated normal-superconducting phase boundaries, $T_c(H)$, shows a transition between short-period to long-period oscillations when going from positive to negative applied fields, $H$. Vorticity changes by more than $1$, indicating multiquanta vortex entries, have been detected along this asymmetric $T_c(H)$ boundary. The dot also expands dramatically the symmetry-consistent vortex-antivortex patterns, thus facilitating their experimental observation.

Figure 1

Calculated field profile of a magnetic dot with $M_{\mathrm{dot}}=18{\varphi }_0$, $R=0.4a$, $l=0.033a$, and $z=-0.0025a$ (here $a$ is the sample’s length), together with a schematic drawing of the superconducting square with the magnetic dot on top.

Figure 2

(a) Magnetic field dependence of the energy of the lowest Landau level corresponding to each irrep in presence of the magnetic dot presented in Fig. 1, together with (b) the results with no dot. The intersections between these Landau levels determine the phase boundaries shown in the insets. Note the dramatic change in the cusplike behavior of these $S/{\xi }^2(T)$ curves, from long-period oscillations between $-38.7\lesssim \varphi /{\varphi }_0\lesssim -7.8$ to short-period oscillations for positive fields. The zoom in (a) illustrates the presence in the phase boundary of transitions between vortex patterns where the vorticity changes by more than $1$. $X$- and $Y$-axis labels in the insets are the same as in the main figures.

Figure 3

Magnetic field dependence of the total vorticity of the sample at the normal-superconducting phase boundary for four different magnetizations of the dot. When $M_{\mathrm{dot}}$ increases, $|L|$ shows an oscillating behavior for negative $\varphi$ values with vorticity changes by more than $1$.

Figure 4

Change in the $|\psi {|}^2$ distribution at the vorticity transitions observed for $\varphi =-38.7{\varphi }_0$ [(a) and (b)] and $\varphi =-7.8{\varphi }_0$ [(c) and (d)], the magnetic fields that limit the long-period oscillations regime in Fig. 2a. These transitions coincide with a change in the topology of the vortex patterns that may favor the simultaneous nucleation of one or more antivortices in each one of the corners of the sample.

Figure 5

A comparison between the vortex-antivortex patterns that can be observed for $L=3$ (a) with and (b) without the magnetic dot. As can be seen, the vortex pattern rotates $45°$ and expands dramatically in the presence of the magnetic dot.