The local magnetic field of spin-momentum locked states and fractional effects

Abstract

We claim that fractionally charged quasi-particles arise in a conducting layer in presence of an external magnetic field perpendicular to it, as a consequence of spin-momentum locking. The presence of fractionary quasi-particles is checked by two independent methods, both based on the residual local magnetic field that determines the topological properties of the layer. The methods correspond to the Chern-Simons index and the direct visualization of the local field component perpendicular and very close to the layer. We assume doubly periodic states in the layer, described in terms of orthonormal functions, which were recently developed in Ref. [1]. Our results stem from the three-term decomposition of the kinetic energy [2,3], which shows that the Rashba term is already contained in the Schrödinger kinetic energy.