Charge distribution and spin textures in magic-angle twisted bilayer graphene

TL;DR

This paper investigates the coexistence of spin and charge density waves in magic-angle twisted bilayer graphene, revealing doping-dependent spin textures and nematic distortions, with implications for understanding its ground state properties.

Contribution

It introduces a self-consistent calculation of charge and spin density waves, including charge inhomogeneity, in twisted bilayer graphene, which was not thoroughly explored before.

Findings

Density wave order is stable across doping levels from -4 to +4 electrons.

Spin texture transitions from collinear to coplanar with doping.

Local spin magnetization exceeds charge density variation unless doping is high.

Abstract

We examine the coexisting spin and charge density waves as a possible ground state of the magic-angle twisted bilayer graphene. When interactions are not included, the spectrum of the material has 4 (8 if spin is taken into account) almost flat almost degenerate bands. Interactions break down the degeneracy forming an order parameter which is usually assumed to be a spin density wave with a preset spin structure. Here we take into account a possible charge density wave contribution to the order parameter, that is, inhomogeneous distribution of the charge density within a twisted graphene supercell. We also calculate self-consistently the spin structure of the order parameter. We find that the density wave order is stable in the whole doping range from $-4$ to $+4$ extra electrons per supercell. The spin texture changes from collinear at zero doping to almost coplanar at finite doping. The density wave order shows nematic distortion when we dope the system. We demonstrate that the local spin magnetization is much stronger than the charge density variation, unless the doping exceeds $3$ extra electrons or holes per supercell.