Dynamic and static dipole polarizability of an Aharonov–Bohm ring

The properties of nanoscale rings are sensitive to Aharonov–Bohm fluxes threading the ring. In particular, neighboring angular momentum eigenstates become degenerate in cases of half-integer flux. Such degeneracies have a profound effect on the dipole polarizability leading to a divergent response. We analyze circular finite-width nanorings and derive a simple and compact expression for the polarizability valid for arbitrary ring geometry, frequency and magnetic flux. The dipole response is significantly reduced by finite-width effects, yet divergencies at half-integer flux are predicted irrespective of width. Finally, a non-divergent (but large) response is restored through a non-perturbative treatment of both magnetic and electric fields.