Superconducting three-dimensional networks in a magnetic field: Frustrated systems

Making use of the de Gennes–Alexander network equation, we have investigated the transition temperature of three-dimensional superconducting networks in a magnetic field. For the magnetic field $H(0.75<{\mathrm{Ha}}^2/{\Phi }_0<2.25),$ a superconducting tetrahedron has a nonsuperconducting vertex because of the frustration. In contrast to this, the C60 fullerene network shows antifluxons when the magnetic field is normal to one of the pentagons and hexagons, because of the frustration that comes from the rotational symmetry around these polygons.