The magnetoelectric effect due to a semispherical capacitor surrounded by a spherical topologically insulating shell

Abstract

We calculate the magnetic field produced by a capacitor formed by two semispherical perfectly conducting plates of radius a, subjected to a potential difference and surrounded by a spherical shell of a topologically insulating material having internal radius r1 and external radius r2. Fixing r2 = 1 μm and considering the case where the shell touches the metallic plates, i. e. when r1 = a, we find that the maximum magnetic field occurs at the external surface of the shell when r1≲ 0.75 μm. For these cases we examine the effect in the two remaining variables: the thickness of the shell and axial angular dependence of the magnetic field. For r1 = 0.5 μm we find a highly isotropic angular distribution with an average field of magnitude G. The angular anisotropy increases with r1, yielding for r1 = 0.62 μm and for r1 = 0.75 μm. These magnitudes fall within the sensitivities of magnetometers based upon nitrogen-vacancy centers in diamond, as well as of devices using scanning SQUID magnetometry. In the latter case we obtain fluxes in the range of (6 − 10) × 10−10 G cm2 for a pickup loop of radius 10 μm centered at the axial symmetry axis and located parallel to the equatorial plane at distances ranging from 2 to 6 μm from the center of the capacitor.