Analytical renormalization group approach to competing orders at charge neutrality in twisted bilayer graphene

We investigate twisted bilayer graphene near charge neutrality using a generalized Bistritzer-MacDonald continuum model, accounting for corrugation effects. The Fermi velocity vanishes particular twist angles properly reproducing the physics of celebrated magic angles. Using group representation theory, we identify all contact interaction potentials compatible with symmetries model. This enables us to two classes quartic interactions leading either opening gap or nematic ordering. then implement renormalization analysis study competition between these angle approaching first value. combined theory-renormalization reveals that proximity favors occurrence layer-polarized, gapped state spatial modulation interlayer correlations, which call insulator.