Symmetries as the guiding principle for flattening bands of Dirac fermions

Since the discovery of magic-angle twisted bilayer graphene (TBG), flat bands in Dirac materials have become a prominent platform for realizing strong correlation effects in electronic systems. Here we show that the symmetry group protecting the Dirac cone in such materials determines whether a Dirac band may be flattened by the tuning of a small number of parameters. We devise a criterion that, given a symmetry group, allows for the calculation of the number of parameters required to make the Dirac velocity vanish. This criterion is employed to study band flattening in twisted bilayer graphene and in surface states of 3D topological insulators. Following this discussion, we identify the symmetries under which the vanishing of the Dirac velocity implies the emergence of perfectly-flat bands. Our analysis allows us to construct additional model Hamiltonians that display perfectly-flat bands at certain points in the space of parameters: the first is a toy model of two coupled 3D TI surfaces, and the second is a quasi-crystalline generalization of the chiral model of TBG.Comment: 21 pages, 12 figures, Accepted to Physical Review

Geometric Stiffness in Interlayer Exciton Condensates

Recent experiments have confirmed the presence of interlayer excitons in the ground state of transition metal dichalcogenide (TMD) bilayers. The interlayer excitons are expected to show remarkable transport properties when they undergo Bose condensation. In this work, we demonstrate that quantum geometry of Bloch wavefunctions plays an important role in the phase stiffness of the Interlayer Exciton Condensate (IEC). Notably, we identify a geometric contribution that amplifies the stiffness, leading to the formation of a robust condensate with an increased BKT temperature. Our results have direct implications for the ongoing experimental efforts on interlayer excitons in materials that have non-trivial geometry. We provide quantitative estimates for the geometric contribution in TMD bilayers through a realistic continuum model with gated Coulomb interaction, and find that the substantially increased stiffness allows for an IEC to be realized at amenable experimental conditions