Correlations in moiré heterostructures from atomistic modeling*

Van-der-Waals moiré heterostructures have proven to be highly tunable materials that display a wide variety of anomalous and correlated states of matter (correlated insulators, superconductivity, nematicity). We present how several of these phenomenæ found in different graphene-based multilayer structures can be explained from tight-binding models on the Ångström scale using realistic interactions. We employ the random phase approximation in twisted bilayer graphene with and without Hartree interactions to describe correlated insulating states at integer fillings [1] and further use this method to propose ABC graphene twisted relative to another sheet of graphene as a highly tunable platform for correlated insulating and superconducting states. Functional renormalization group methods are used to characterize the magnetic phases in twisted bilayer graphene for realistic interaction profiles [2] and nematic orderings in twisted double bilayer graphene [3].

[1] Phys. Rev. B 100, 155145 (2019)
[2] Phys. Rev. B 102, 085109 (2020)
[3] arXiv:2009.11645 [cond-mat.str-el]