# Electrically Tunable Flat Bands and Magnetism in Twisted Bilayer Graphene

## TL;DR

This paper demonstrates that by tuning the twist angle in bilayer graphene, one can create flat bands and induce ferromagnetism, which can be controlled electrically, offering a platform for strong correlation effects.

## Contribution

It introduces a method to generate flat bands and magnetic states in twisted bilayer graphene at a specific twist angle, tunable by electric fields, expanding the potential for electronic applications.

## Key findings

- Flat bands occur at a twist angle of approximately 0.8°
- Doping half-fills these flat bands leading to ferromagnetic order
- Electric fields can quench magnetic order by breaking inversion symmetry

## Abstract

Twisted graphene bilayers provide a versatile platform to engineer metamaterials with novel emergent properties by exploiting the resulting geometric moir\'{e} superlattice. Such superlattices are known to host bulk valley currents at tiny angles ($\alpha\approx 0.3 ^\circ$) and flat bands at magic angles ($\alpha \approx 1^\circ$). We show that tuning the twist angle to $\alpha^*\approx 0.8^\circ$ generates flat bands away from charge neutrality with a triangular superlattice periodicity. When doped with $\pm 6$ electrons per moir\'e cell, these bands are half-filled and electronic interactions produce a symmetry-broken ground state (Stoner instability) with spin-polarized regions that order ferromagnetically. Application of an interlayer electric field breaks inversion symmetry and introduces valley-dependent dispersion that quenches the magnetic order. With these results, we propose a solid-state platform that realizes electrically tunable strong correlations.