Magnetism and superconductivity in nanoarchitectures

We examine states of electrons confined to the conduction band of an intrinsic semiconductor that is cut up into various geometric shapes. In the case of a repetitive pattern such as an antidot lattice, mini-Bloch sub-bands condense out of the conduction band. We find a fit of the lowest mini-band to a tight-binding approximation; this enables comparison with Hubbard and Hubbard-like models. With the Coulomb interaction being taken into account, it is easily seen that the ground state favors an antiferromagnetic phase, a ferromagnetic phase and ultimately, a superconductive phase, depending on electron concentrations. The critical temperatures increase with inverse effective mass, 1/m*.