Discontinuity of capacitance at the onset of surface superconductivity

The effect of the magnetic field on a capacitor with a superconducting electrode is studied within the Ginzburg-Landau approach. It is shown that the capacitance has a discontinuity at the onset of the surface superconductivity $B_{\mathrm{c}3}$ which is expressed as a discontinuity in the penetration depth of the electric field into metals. Estimates show that this discontinuity is observable with recent bridges for both conventional and high-$T_{\mathrm{c}}$ superconductors of the type-II.