In this talk, I will present a theory of interaction-induced band-flattening in strongly correlated electron systems. I will begin by illustrating an inherent connection between flat bands and index theorems and presenting a generic prescription for constructing flat bands by periodically repeating local Hamiltonians with topological zero modes. Specifically, a Dirac particle in an external, spatially periodic magnetic field can be cast in this form. We (arxiv.org/pdf/2308.16440.pdf) have shown a condition on the field to produce perfectly flat bands and provided an exact analytical solution for the flat band wave functions. I will then explore an interacting model of Dirac fermions in a spatially inhomogeneous field. We will see that certain Hubbard-Stratonovich configurations exist that ``rectify'' the field configuration, inducing band flattening. We will briefly see an explicit model where this localization scenario is energetically favorable -- specifically in Dirac systems with nearly flat bands, where the energy cost of rectifying textures is quadratic in the order parameter, whereas the energy gain from flattening is linear. We will then talk about the same mechanism in twisted bilayer graphene. At last, we will discuss alternative symmetry-breaking channels, especially superconductivity, and propose that these interaction-induced band-flattening scenarios represent a generic non-perturbative mechanism for spontaneous symmetry breaking, pertinent to many strongly-correlated electron systems.

Pizza and drinks will be served after the seminar in ATL 2117.