Effective Interactions of Planar Fermions in a Strong Magnetic Field-the Effect of Landau Level Mixing

TL;DR

This paper develops a theoretical framework to analyze how Landau level mixing affects the current operators and edge currents in planar fermion systems under strong magnetic fields, considering various interactions.

Contribution

It introduces a systematic approach to incorporate Landau level mixing into the field theory of planar fermions, including electromagnetic and local interactions.

Findings

Landau level mixing significantly influences current operators.

Edge current calculations reveal effects of Landau level mixing.

The framework applies to systems with Coulomb and time-dependent interactions.

Abstract

We obtain expressions for the current operator in the lowest Landau level (L.L.L.) field theory, where higher Landau level mixing due to various external and interparticle interactions is sytematically taken into account. We consider the current operators in the presence of electromagnetic interactions, both Coulomb and time-dependent, as well as local four-fermi interactions. The importance of Landau level mixing for long-range interactions is especially emphasized. We also calculate the edge-current for a finite sample.