Euler - Heisenberg effective action and magnetoelectric effect in multilayer graphene

TL;DR

This paper analyzes the effective field theory of multilayer graphene under magnetic and electric fields, revealing magnetoelectric effects and corrections to the effective action relevant for understanding its quantum properties.

Contribution

It provides explicit calculations of the effective action and its corrections in multilayer graphene, highlighting magnetoelectric phenomena and imaginary parts related to electric fields.

Findings

Calculated the effective action in magnetic fields for multilayer graphene.

Derived first-order corrections due to in-plane electric fields.

Discussed the magnetoelectric effect and imaginary part of the effective action.

Abstract

The low energy effective field model for the multilayer graphene (at ABC stacking) is considered. We calculate the effective action in the presence of constant external magnetic field $B$ (normal to the graphene sheet). We also calculate the first two corrections to this effective action caused by the in-plane electric field $E$ at $E/B \ll 1$ and discuss the magnetoelectric effect. In addition, we calculate the imaginary part of the effective action in the presence of constant electric field $E$ and the lowest order correction to it due to the magnetic field ($B/E \ll 1$).