# Charge Smoothening and Band Flattening due to Hartree corrections in Twisted Bilayer Graphene

## TL;DR

This paper demonstrates that Coulomb interactions in doped twisted bilayer graphene smooth out charge inhomogeneities, flatten the electronic bands, and influence the material's correlated phases, using real-space Hartree calculations.

## Contribution

It introduces a self-consistent Hartree approach on a relaxed lattice to show how Coulomb interactions modify charge distribution and band structure in doped twisted bilayer graphene.

## Key findings

- Charge inhomogeneities are smoothed by Coulomb interactions.
- Flat bands become further flattened with doping.
- Van Hove singularity remains pinned at the Fermi level.

## Abstract

Doping twisted bilayer graphene away from charge neutrality leads to an enormous buildup of charge inhomogeneities within each Moir\'{e} unit cell. Here we show, using unbiased real-space self-consistent Hartree calculations on a relaxed lattice, that Coulomb interactions smoothen this charge imbalance by changing the occupation of earlier identified `ring' orbitals in the AB/BA region and `center' orbitals at the AA region. For hole doping, this implies an increase of the energy of the states at the ${\bf \Gamma}$ point, leading to a further flattening of the flat bands and a pinning of the Van Hove singularity at the Fermi level. The charge smoothening will affect the subtle competition between different possible correlated phases.