# Symmetry breaking and skyrmionic transport in twisted bilayer graphene

## TL;DR

This paper investigates the role of skyrmion textures in explaining the non-monotonic magnetoresistance observed in twisted bilayer graphene, proposing a novel mechanism involving topological charge carriers influenced by magnetic fields.

## Contribution

It introduces the idea that skyrmion textures, linked to the non-zero Chern numbers of flat bands, can account for transport phenomena in twisted bilayer graphene, offering new insights into correlated insulating states.

## Key findings

- Skyrmion textures can explain non-monotonic magnetoresistance.
- Spin Zeeman splitting affects skyrmion excitations.
- Proposed experimental tests for the skyrmion-based model.

## Abstract

Motivated by recent low-temperature magnetoresistance measurements in twisted bilayer graphene aligned with hexagonal Boron Nitride substrate, we perform a systematic study of possible symmetry breaking orders in this device at a filling of two electrons per Moir\'e unit cell. We find that the surprising non-monotonic dependence of the resistance on an out-of-plane magnetic field is difficult to reconcile with particle-hole charge carriers from the low-energy bands in symmetry broken phases. We invoke the non-zero Chern numbers of the twisted bilayer graphene flat bands to argue that skyrmion textures provide an alternative for the dominant charge carriers. Via an effective field-theory for the spin degrees of freedom, we show that the effect of spin Zeeman splitting on the skyrmion excitations provides a possible explanation for the non-monotonic magnetoresistance. We suggest several experimental tests, including the functional dependence of the activation gap on the magnetic field, for our proposed correlated insulating states at different integer fillings. We also discuss possible exotic phases and quantum phase transitions that can arise via skyrmion-pairing on doping such an insulator.