Wigner Crystallization in Twisted Bi-layer Graphene

Study of strongly correlated phases took an interesting turn recently by the surprising discovery of high-Tc superconductivity in twisted sheets of graphene. The electronic properties of each graphene-layer can be described by non-interacting electrons. However, in a twisted bi-layer graphene (TBLG), close to the `magic angles', the kinetic energy of the electrons is heavily quenched. This causes interactions to dominate, paving way for strong correlation. In this talk, I disucss arXiv: 1804.01101 and 1810.00884. We first compute quasiparticle interaction energy and kinetic energy to obtain their ratio, $r_s$, which quantifies the extent of strong correlation. This ratio crossing unity already signals departure from a perturbative regime (or Fermi liquid behavior). For $r_s$ larger than 37, the system minimizes the strong Coulomb repulsion by forming electronic crystals, called Wigner crystals. We show that TBLG near magic angles exhibits $r_s$ much larger than this critical value, facilitating a hierarchy of metal-insulator transitions. Pressure enhances such crustallization. In light of Wigner crystallization we discuss various aspects of the recent experiments and show remarkable agreement with this scenario.