Abstract

We propose a general principle for the low-energy theory of narrow bands with concentrated Berry curvature and Fubini-Study metric in the form of a map to Anderson-plus models composed of heavy fermions hybridizing and interacting with semi-metallic modes. The construction resolves the obstruction preventing topological bands from being realized in a local Hamiltonian acting on the low-energy degrees of freedom. The concentrated quantum geometry is reproduced through band inversion with a dispersive semi-metal, leaving a nearly flat, trivial band that becomes the heavy fermion. The approach is illustrated for twisted bilayer graphene, the twisted checkerboard model, and the Lieb lattice, and is argued to apply broadly to narrow/flat-band systems with concentrated quantum geometry.

Abstract

We propose a general principle for the low-energy theory of narrow bands with concentrated Berry curvature and Fubini-Study metric in the form of a map to Anderson-plus models composed of heavy fermions hybridizing and interacting with semi-metallic modes. The construction resolves the obstruction preventing topological bands from being realized in a local Hamiltonian acting on the low-energy degrees of freedom. The concentrated quantum geometry is reproduced through band inversion with a dispersive semi-metal, leaving a nearly flat, trivial band that becomes the heavy fermion. The approach is illustrated for twisted bilayer graphene, the twisted checkerboard model, and the Lieb lattice, and is argued to apply broadly to narrow/flat-band systems with concentrated quantum geometry.

Abstract

We propose a general principle for the low-energy theory of narrow bands with concentrated Berry curvature and Fubini-Study metric in the form of a map to Anderson-plus models composed of heavy fermions hybridizing and interacting with semi-metallic modes. The construction resolves the obstruction preventing topological bands from being realized in a local Hamiltonian acting on the low-energy degrees of freedom. The concentrated quantum geometry is reproduced through band inversion with a dispersive semi-metal, leaving a nearly flat, trivial band that becomes the heavy fermion. The approach is illustrated for twisted bilayer graphene, the twisted checkerboard model, and the Lieb lattice, and is argued to apply broadly to narrow/flat-band systems with concentrated quantum geometry.

Abstract

We propose a general principle for the low-energy theory of narrow bands with concentrated Berry curvature and Fubini-Study metric in the form of a map to Anderson-plus models composed of heavy fermions hybridizing and interacting with semi-metallic modes. The construction resolves the obstruction preventing topological bands from being realized in a local Hamiltonian acting on the low-energy degrees of freedom. The concentrated quantum geometry is reproduced through band inversion with a dispersive semi-metal, leaving a nearly flat, trivial band that becomes the heavy fermion. The approach is illustrated for twisted bilayer graphene, the twisted checkerboard model, and the Lieb lattice, and is argued to apply broadly to narrow/flat-band systems with concentrated quantum geometry.