Electrically-tunable flat bands and magnetism in twisted bilayer graphene

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 with 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.