Anomalous Hall Effect for semiclassical chiral fermions

TL;DR

This paper explores the behavior of semiclassical chiral fermions under electric and magnetic fields, revealing phenomena like side jumps and spiraling motion, and analyzing their angular momentum conservation.

Contribution

It introduces a detailed analysis of semiclassical chiral fermions' dynamics in electromagnetic fields, highlighting effects analogous to non-commutative mechanics.

Findings

Chiral fermions exhibit side jumps in electric fields.

Spiraling motion occurs in magnetic fields.

Angular momentum conservation explains the transverse shift.

Abstract

Semiclassical chiral fermions manifest the anomalous spin-Hall effect: when put into a pure electric field they suffer a side jump, analogous to what happens to their massive counterparts in non-commutative mechanics. The transverse shift is consistent with the conservation of the angular momentum. In a pure magnetic field instead, spiraling motion is found. Motion in Hall-type perpendicular electric and magnetic fields is also studied.