# Dynamical symmetry breaking, magnetization and induced charge in graphene: Interplay between magnetic and pseudomagnetic fields

## TL;DR

This paper explores how strains and magnetic fields in graphene influence quantum phenomena like symmetry breaking, mass generation, and valley polarization, revealing new ways to control electronic properties for valleytronic applications.

## Contribution

It demonstrates the independent control of magnetization and dynamical mass in graphene valleys through strain and magnetic fields, and uncovers the effects of pseudomagnetic fields on induced charge and symmetry breaking.

## Key findings

- Strain and magnetic fields break chiral, parity, and time-reversal symmetries in graphene.
- Pseudomagnetic fields induce vacuum charge and parity anomaly.
- Combined real and pseudomagnetic fields enable valley polarization control.

## Abstract

In this paper, we investigate the two competing effects of strains and magnetic fields in single-layer graphene to explore its impact on various phenomena of quantum field theory, such as induced charge density, magnetic catalysis, symmetry breaking, dynamical mass generation and magnetization. We show that the interplay between strains and magnetic fields produces not only a breaking of chiral symmetry, as it happens in QED$_{2+1}$, but also parity and time-reversal symmetry breaking. The last two symmetry breakings are related to the dynamical generation of a Haldane mass term. We find that it is possible to modify the magnetization and the dynamical mass independently for each valley, by strain and varying the external magnetic field. Furthermore, we discover that the presence of a non-zero pseudomagnetic field, unlike the magnetic one, allows us to observe an induced "vacuum" charge and a parity anomaly in strained graphene. Finally, because the combined effect of real and pseudomagnetic fields produces an induced valley polarization, the results presented here may provide new tools to design valleytronic devices.