Description
of
the simulations : Bound state configurations of vortices found in highprecision largescale numerical minimzation of the twocomponent GinzburgLandau free energy in the type1.5 regime. The variational problem is defined using a finite element formulation provided by Freefem++ framework. A nonlinear conjugate gradient algorithm is used to find the minima of the energy. More details about the numerical methods employed to study can be found in a Supplementary Material Letter. In the following, we present evolution from initial configurations being either a giant vortex, or a diluted collection of vortices. The displayed quantities: From left to right, on the first line are plotted the magnetic field, and condensate densities and . On the second line, the supercurrents moduli and and which is nonzero when there appears the phase difference between both components. 
1.
Superconductors with two active bands:
we first consider the case where both components are below their
critical temperature (i.e. they are both active). The first band
is the stronger while the second one is weaker. Movie 1 : corresponds to Figure 2 of the paper. If the embedded video does not start, play the .avi movie. Movie
1
: The ground state of a flux quanta configuration in
type1.5 superconductor (i.e. ). The
parameters of the potential are and , while the electric charge is
Movie 2 : corresponds to Figure 3 of the paper. If the embedded video does not start, play the .avi movie. Movie
2
: The ground state of a flux quanta configuration
using the same parameter set as in Movie
1. Here the global 8folded discrete symmetry of the cluster has
been broken toward a less symmetric configuration (a 3folded discrete
symmetry) in favor of a regular vortex lattice in the cluster. There is
again a competition between typeIlike (normal circular cluster with a
boundary current) and typeIIlike tendencies (vortex lattice).
Movie 3 : corresponds to Figure 4 of the paper. If the embedded video does not start, play the .avi movie. Movie
3
: Magnetic ground state of an vortex configuration
with a stronger electric charge coupling (parameters of the
potential are the same as in Movie 1).
This
shows the behavior of the system with respect to a charge
increase. Increasing the electric charge decreases penetration length
and thus pushes the system towards typeI regime i.e. with more
circular boundary.
Movie 4 : corresponds to Figure 3 of the paper. If the embedded video does not start, play the .avi movie. Movie
4
: Magnetic ground state of an vortex configuration
with the parameter set given by Movie
1, but with and added Josephson coupling . Although the Josephson term introduced an energy penalty
for phase difference, it has little effect on the vortex cluster
boundary where the high magnetic pressure still generates strong phase
difference gradients.
Movie 5 : If the embedded video does not start, play the .avi movie. Movie
5
: Magnetic ground state of an vortex configuration. parameters of the potential
are and , while the electric charge is and added Josephson coupling . Although the Josephson term introduced an energy penalty
for phase difference, it has little effect on the vortex cluster
boundary where the high magnetic pressure still generates strong phase
difference gradients.
Movie 6 : If the embedded video does not start, play the .avi movie. Movie
6
: Magnetic ground state of an vortex configuration. parameters of the potential
are and , while the electric charge is and added Josephson coupling . Although the Josephson term introduced an energy penalty
for phase difference, it has little effect on the vortex cluster
boundary where the high magnetic pressure still generates strong phase
difference gradients.

2.
Superconductor
with one active and one passive bands and strong interband Josephson
coupling: here we consider the case where one band is below
its
critical temperature (i.e. active) while the second band has superfluid
density only because interband proximity effect (i.e. passive). Movie 7 : corresponds to Figure 6 of the paper. If the embedded video does not start, play the .avi movie. Movie
7 : A bound state of an vortex configuration in
case when superconductivity in the second band is due to
interband proximity effect and the Josephson coupling is
strong . Other parameters are , , .
Simulations show the increased importance of nonpairwise interactions which lead to formation of vortex chains rather than a compact cluster. Movie 8 : corresponds to Figure 7 of the paper. If the embedded video does not start, play the .avi movie. Movie
5
: A bound state of an vortex configuration in
case when superconductivity in the second band is due to
interband proximity effect and the Josephson coupling is
strong . Other parameters are , , .
We start with a diluted initial configuration where vortices are located with the attractive range of their twobody potential. However instead of contracting, initially the vortex cluster expands, thus showing that the evolution is dominated by nonpairwise inyteraction. Once the group breaks into several subgroups of vortices and thus gets rid of some of the multibody forces, the subclusters start to shrink. The intervortex distance within each subcluster in the final configuration is smaller than that in the initial configuration despite the expansion in the initial stage of the evolution. 