Formation of Multiple-Flux-Quantum Vortices in Mesoscopic Superconductors from Simulations of Calorimetric, Magnetic, and Transport Properties

Because of strong flux confinement in mesoscopic superconductors, a “giant” vortex may appear in the ground state of the system in an applied magnetic field. This multiquanta vortex can then split into individual vortices (and vice versa) as a function of, e.g., applied current, magnetic field, or temperature. Here we show that such transitions can be identified by calorimetry, as the formation or splitting of a giant vortex results in a clear jump in measured heat capacity versus external drive. We attribute this phenomenon to an abrupt change in the density of states of the quasiparticle excitations in the vortex core(s), and further link it to a sharp change of the magnetic susceptibility at the transition—proving that the formation of a giant vortex can also be detected by magnetometry.

Figure 1

The energy of different vortex states for an $\mathrm{Al}$ superconducting disk of radius $R=850\mathrm{nm}$ and thickness $d=100\mathrm{nm}$, at $T=0.8T_c$, for taken $\xi (0)=100\mathrm{nm}$ and $\kappa =1.2$. Solid lines indicate giant-vortex states and dashed lines represent multivortex states. Insets show the density of the superconducting condensate for a $L=2$ vortex state in multi and giant form.

Figure 2

The heat capacity as a function of magnetic field, for states with vorticity 2 and 3 of the sample considered in Fig. 1. The insets depict the vortex configuration before and after the multi-to-giant vortex transition.

Figure 3

The integrated zero-energy density of states (LDOS) as a function of the magnetic field for $L=3$, for a superconducting disk with the same parameters as in Fig. 1. (a)–(c) are the representative contour plots of LDOS in the disk, at indicated magnetic fields. Interestingly, $N(0)[a]\approx N(0)[b]\approx N(0)[c]$.

Figure 4

The multi-to-giant vortex transition revealed through the sharp change in magnetic susceptibility as a function of applied magnetic field, showing direct correlations with the heat capacity, for states with vorticity 2 and 3. Shaded areas indicate the observed regions of giant-vortex formation in both quantities.

Figure 5

The absolute and relative size of the jump at the multi-to-giant vortex transition, in (a) $\chi (H)$ curves, and (b) $C(H)$ curves, for vorticity $L=2$, 3, and 4.