Induced quantum numbers in the (2+1)-dimensional electron gas

TL;DR

This paper investigates the properties of an electron gas confined to two dimensions, proposing a simple method to calculate induced spin density and analyzing fluxon excitations in both relativistic and nonrelativistic regimes.

Contribution

It introduces a straightforward approach using a (0+1)-dimensional effective theory to compute induced spin density in a 2D electron gas under magnetic fields.

Findings

Fluxon excitations act as half-fermions in the relativistic case.

Fluxon excitations behave as fermions in the nonrelativistic case.

The method simplifies calculations of induced quantum numbers in 2D electron systems.

Abstract

A gas of electrons confined to a plane is examined in both the relativistic and nonrelativistic case. Using a (0+1)-dimensional effective theory, a remarkably simple method is proposed to calculate the spin density induced by an uniform magnetic background field. The physical properties of possible fluxon excitations are determined. It is found that while in the relativistic case they can be considered as half-fermions (semions) in that they carry half a fermion charge and half the spin of a fermion, in the nonrelativistic case they should be thought of as fermions, having the charge and spin of a fermion.