Topological Frustration Can Lead to Superconductivity

We analyse charge motion in geometries composed solely of interconnecting 'diamonds'. Since a diamond is composed of two edge-sharing triangles, these geometries are topologically frustrated. The motion of a single particle across atoms which have restricted valence leads to a type of paramagnetism with only short range correlations in these geometries. When two particles meet in a diamond their behaviour is more bosonic than fermionic, which leads to a form of BCS pairing theory. The attraction can be interpreted as the pair locally unfrustrating the geometrys and a resulting local regaining of lost kinetic energy leads to the attraction.