Skyrmion and Tetarton Lattices in Twisted Bilayer Graphene

Abstract

Recent experiments on twisted bilayer graphene show an anomalous quantum Hall (AQH) effect at filling of $3$ electrons per moirè unit cell. The AQH effect arises in an insulating state with both valley- and ferromagnetic order. We argue, that weak doping of such a system leads to the formation of a novel topological spin texture, a `double-tetarton lattice'. The building block of this lattice, the `double-tetarton', is a spin configuration which covers $1/4$ of the unit-sphere twice. In contrast to skyrmion lattices, the net magnetization of this magnetic texture vanishes. Only at large magnetic fields more conventional skyrmion lattices are recovered. But even for large fields the addition of a single charge to the ferromagnetic AQH state flips hundreds of spins. Our analysis is based on the investigation of an effective non-linear sigma model which includes the effects of long-ranged Coulomb interactions.

New name for the topological texture at zero field; details on implementation of Coulomb interactions

References in corpus (4)

• Flat Bands in Slightly Twisted Bilayer Graphene
• Continuum Model of the Twisted Bilayer
• Origin of band gaps in graphene on hexagonal boron nitride
• Skyrmion fractionalization and merons in chiral magnets with easy-plane anisotropy

Cited by in corpus (14)

• Statics and Dynamics of Skyrmions Interacting with Pinning: A Review
• Topological spin crystals by itinerant frustration
• Phase Shift in Skyrmion Crystals
• Quantum Geometry and Stability of Moiré Flatband Ferromagnetism
• Skyrmions in twisted bilayer graphene: stability, pairing, and crystallization
• Stabilization mechanisms of magnetic skyrmion crystal and multiple-$Q$ states based on momentum-resolved spin interactions
• A hierarchy of multi-moment skyrmion phases in twisted magnetic bilayers
• Short-range Crystalline Order-Tuned Conductivity in Cr${}_2$Si${}_2$Te${}_6$ van der Waals Magnetic Crystals
• Prediction of polarization vortices, charge modulation, flat bands, and moiré magnetism in twisted oxide bilayers
• Mechanisms for Magnetic Skyrmion Catalysis and Topological Superconductivity
• Spintwistronics: Photonic bilayer topological lattices tuning extreme spin-orbit interactions
• Chiral Stoner magnetism in Dirac bands
• Four-Spin Interactions as a Route to Multiple-Q Topological Magnetic Order
• Mean-field Modelling of Moiré Materials: A User's Guide with Selected Applications to Twisted Bilayer Graphene