Quantum phase transitions in 2D moiré Dirac materials

Moire materials provide a new opportunity for the investigation of quantum phase transitions in two-dimensional Dirac systems due to unprecedented experimental control. In particular, the relative interaction can be tuned via a twist angle so that it is possible to overcome the critical interaction strength needed to induce a quantum phase transition for Dirac fermions. We study possible patterns for spontaneous symmetry breaking in a Dirac fermion model motivated by twisted bilayer graphene at charge neutrality. These include the spontaneous generation of a gap, but also of a splitting in energy or wave vector of the Dirac points. We employ a renormalisation group treatment and discuss quantum critical behavior for different numbers of fermion flavours such as spin or valley.