Parity Effects in Stacked Nanoscopic Quantum Rings

The ground state and the dielectric response of stacked quantum rings are investigated in the presence of an applied magnetic field along the ring axis. For odd number $N$ 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 the induced electric polarization is discontinuous at those special magnetic fields. Experimental consequences for related nanostructures are discussed.