A short note on the eigenvalues of regular Hall-plates

Abstract

This note is about uniform, plane, singly connected, regular Hall-plates with an arbitrary number of contacts exposed to a uniform magnetic field of arbitrary strength. In practice, the regular symmetry is the most common one. If the Hall-plates are mapped conformally to the unit disk, regular symmetry means that all contacts are equally large and all contact spacings are equally large, yet the contact spacing may be different from the size of the contacts. The indefinite conductance matrices of such Hall-plates are circulant matrices, whose complex eigenvalues are computed in closed form.