# Long-wavelength gauge symmetry and translations in a magnetic field for Dirac electrons in graphene

## TL;DR

This paper explores a long-wavelength gauge symmetry in 2D electron systems under magnetic fields, explaining the insensitivity of certain phenomena like cyclotron resonance and quantum Hall effect to Coulomb interactions, with a focus on graphene.

## Contribution

It introduces a new gauge symmetry concept that clarifies why some quantum phenomena in 2D electron systems are unaffected by interactions, especially in graphene.

## Key findings

- Long-wavelength gauge symmetry explains insensitivity of cyclotron resonance and Hall conductance to Coulomb interactions.
- Differences in cyclotron-resonance and quantum Hall effect between graphene and conventional 2D electrons are analyzed.
- The symmetry provides a unified framework for understanding many-body phenomena in 2D electron systems.

## Abstract

In two-dimensional (2D) electron systems in a magnetic field, the Coulomb interaction among charge carriers, under Landau quantization, essentially governs a variety of many-body phenomena while there are also phenomena, such as the (integer) quantum Hall effect, that appear unaffected by the interaction. It is pointed out that the response of 2D electrons to spatially-uniform potentials and fields enjoys a long-wavelength gauge symmetry, associated with cyclotron motion of electrons, that leaves the Coulomb interaction invariant and that thus naturally explains why cyclotron resonance (as implied by Kohn's theorem) and the quantized Hall conductance appear insensitive to the interaction. It is discussed, in the light of this new long-wavelength gauge symmetry, how Dirac electrons in graphene and conventional 2D electrons differ in cyclotron-resonance characteristics and the quantum Hall effect.