# Spin-valley skyrmions in graphene at filling factor $\nu=-1$

## TL;DR

This paper models and classifies various quantum Hall skyrmions in graphene at filling factor =-1, exploring their textures, energies, and potential experimental imaging methods under different anisotropy conditions.

## Contribution

It introduces a CP3 field theory for skyrmions in graphene, visualizes their textures, and discusses novel entanglement and deflated pseudospin skyrmions with energy dependence analysis.

## Key findings

- Classified all skyrmion types across anisotropy parameters
- Visualized skyrmion textures on Bloch spheres and honeycomb lattice
- Analyzed energy and size dependence on anisotropy and magnetic field

## Abstract

We model quantum Hall skyrmions in graphene monolayer at quarter filling by a theory of CP3 fields and study the energy minimizing skyrmions in presence of valley pseudospin anisotropy and Zeeman coupling. We present a diagram of all types of skyrmions in a wide range of the anisotropy parameters. For each type of skyrmion, we visualize it on three Bloch spheres, and present the profiles of its texture on the graphene honeycomb lattice, thus providing references for the STM/STS imaging of spin-pseudospin textures in graphene monolayer in quantum Hall regime. Besides the spin and pseudospin skyrmions for the corresponding degrees of freedom of an electron in the N=0 Landau level, we discuss two unusual types -- the "entanglement skyrmion" whose texture lies in the space of the entanglement of spin and pseudospin, as well as the "deflated pseudospin skyrmion" with partial entanglement. For all skyrmion types, we study the dependence of the energy and the size of a skyrmion on the anisotropy parameters and perpendicular magnetic field. We also propose three ways to modify the anisotropy energy, namely the sample tilting, the substrate anisotropy and the valley pseudospin analogue of Zeeman coupling.