First, we need to figure what is the minimum amount of superconductor that we'll lose when making the cut. Optimally, we can cut the large cube net into two smaller cube nets without any waste at all. Let's start by trying to find such a cube net:
The blue and yellow parts are pretty simple cube wraps, so after the cut, we can easily make the required two ...
Since I cannot post pictures in a comment, here's my question in clearer terms:
Did I form a square by drawing lines between dots? (I know I did. Does it count, though?)
(For better visibility, I deviated from the apparent standard of using near-imperceptible shade changes, and marked the relevant dots with bell peppers instead.)