The guide to the guiding center aka pseudo-momentum operator construction

TL;DR

This paper develops a gauge-invariant method for constructing guiding center operators in magnetic fields, enabling accurate descriptions of Landau levels and carrier behavior in graphene.

Contribution

It introduces a strictly gauge-invariant approach to guiding center operators, applicable to both classical Landau levels and quasi-relativistic carriers in graphene.

Findings

Gauge-invariant equations for Landau levels formulated

Application to quasi-relativistic carriers in graphene demonstrated

Enhanced understanding of magnetic field effects on quantum states

Abstract

The strictly gauge invariant approach to the construction of the analog of guiding center integrals of motion in spatially homogeneous/inhomogeneous constant magnetic fields is considered. With their help the gauge invariant equations, describing the wave functions of highly degenerate Landau levels in the classical non-relativistic case, are formulated. The proposed gauge-invariant approach was used also for the construction of the equations describing the quasi-relativistic carriers behavior in the homogeneous/inhomogeneous magnetic field in the single layer graphene.