Parity effects in stacked nanoscopic quantum rings

The ground state and the dielectric response of stacked quantum rings are i nvestigated in the presence of an applied magnetic field along the ring axi s. For odd number of N of rings and an electric field perpendicular to the axis, a linear Stark effect occurs at distinct values of the magnetic field . At those fields energy levels cross in the absence of electric field. For even values of N a quadratic Stark effect is expected in all cases, but th e induced electric polarization is discontinuous at those special magnetic fields. Experimental consequences for related nanostructures are discussed.