Cascade of transitions in twisted bilayer graphene -- the Van Hove scenario

Abstract

Measurements of compressibility in twisted bilayer graphene showed a cascade of phase transitions with increasing electron or hole filling n, and STM measurements showed that in a wide range of n one of the Van Hove peaks in the density of states remains close to the chemical potential. Motivated by these experiments, we analyze the pattern of spontaneous symmetry breakings for itinerant fermions near a Van Hove singularity. We make use of an approximate SU(4) symmetry of the manifold of spin/isospin (valley) orders, analyze the Landau free energy, and show that the structure of the spin/isospin order parameter changes with increasing |n| via a cascade of phase transitions. We compute the feedback from different spin/isospin orders on fermions and argue that each order splits the initially 4-fold degenerate Van Hove peak in a particular fashion, consistent with the STM data, and gives rise to a sharp change of compressibility, thus providing a unified interpretation of STM and compressibility data for twisted bilayer graphene. Our results follow from a generic analysis of an SU(4)-symmetric Landau functional and are valid beyond a specific fermionic model used to derive the functional.

Superconductivity induced by the inter-valley Coulomb scattering in a few layers of graphene

“…On the theoretical side, it is universally accepted that the band flattening and the vicinity of the van Hove singularities to the Fermi level enhance the role of the electronic interactions in TBG, TTG, RTG and BBG, favoring the formation of symmetry broken phases (see eg the Refs. [8][9][10][11][12][13]). However, the debate on the mechanism at the origin of the superconductivity in these systems is still open.…”