Evidence of controlling vortex matter via a superconducting Nanobridge

We theoretically investigate the magnetic response on a three-dimensional superconducting nanobridge system, which is compound of two parallel parallelepiped (samples) connected through a nanobridge of size $\mathbf{L}$ and thickness $\mathbf{x}$, which mediates interactions between them. This study is conducted in the presence of a magnetic field $\mathbf{H}$ and the transport of a direct current $\mathbf{J}$. We use the well-know time dependent Ginzburg-Landau theory ($\mathbf{TDGL}$) for analyzed the possible effects on the density Gibbs free energy $\mathbf{F}$, magnetization $\mathbf{M}$, and superconducting electronic Cooper pair density $|\psi|^{2}$. We are interested in studying two cases: varying the $\mathbf{L}$ and $\mathbf{x}$ of the nanobridge in the absence of induced $\mathbf{J}$, and including the induction of external $\mathbf{J}$ for fixed $\mathbf{L}$ and $\mathbf{x}$. We find that $\mathbf{L}$ and $\mathbf{x}$ play an essential role in stabilizing (controlling) vortex states in the nanobridge, and the presence of induced $\mathbf{J}$ ($\mathbf{J}>0$ and $\mathbf{J}<0$), with a fixed $\mathbf{L}$ and $\mathbf{x}$, causes the movement of vortex states in the nanobridge just when $\mathbf{J}$ is induced at both faces of superconducting nanobridge system.