Competing interactions at charge neutrality in twisted bilayer graphene

In the unusual event the velocity of electrons in a material vanishes, interactions between them take the lead. This leads to states of matter with properties at odds with those of standard materials. The last two years have witnessed a major revival in this physics following the experimental discovery that two twisted sheets of graphene provided the appropriate conditions for the emergence of a plethora of interaction-induced states. Exotic states were identified in this twisted bilayer, such as superconductivity and more recently a state, analogous to the nematic phase of liquid crystals, which spontaneously displays electronic inhomogeneities. Theoretically, the study of such problems is notoriously challenging, as many phenomena compete. In our manuscript, we provide new methodology to understand the physics of "twisted bilayer graphene" analytically, and find that the system chooses to settle in a phase we call a "nematic insulator," in accord with experimental findings.

Facts and FAQs

• analytical approach to interlayer coupling which captures magic angle
• group theory classification and RG treatment of all allowed contact interactions
• handle correlated phases in materials with a vanishing kinetic energy scale, in a fully analytic and unbiased fashion
• dominant new instability at magic angle is C₃-symmetry-breaking
• first RG paper on TBG