Anyons with anomalous gyromagnetic ratio & the Hall effect

TL;DR

This paper introduces a new relativistic model for spinning anyons with arbitrary gyromagnetic ratio, revealing novel Hall effects and extending previous non-relativistic models related to planar Galilei group extensions.

Contribution

It proposes a new set of equations for spinning anyons that incorporate any gyromagnetic ratio and generalize existing models, including a novel version of the Bargmann-Michel-Telegdi equations in 2+1 dimensions.

Findings

System becomes singular at critical field values.

For g ≠ 2, only Hall law motions are allowed.

Secondary Hall effect appears at another critical field value.

Abstract

Letting the mass depend on the spin-field coupling as $M^2=m^2-(eg/2c^2)F_{\alpha\beta}S^{\alpha\beta}$, we propose a new set of relativistic planar equations of motion for spinning anyons. Our model can accommodate any gyromagnetic ratio $g$ and provides us with a novel version of the Bargmann-Michel-Telegdi equations in 2+1 dimensions. The system becomes singular when the field takes a critical value, and, for $g\neq2$, the only allowed motions are those which satisfy the Hall law. For each $g\neq2,0$ a secondary Hall effect arises also for another critical value of the field. The non-relativistic limit of our equations yields new models which generalize our previous ``exotic'' model, associated with the two-fold central extension of the planar Galilei group.