Lifetime and spectral function of topological heavy fermions

TL;DR

This paper develops an analytic theory for quasiparticle dispersion and lifetime in the topological heavy fermion Mott semimetal, revealing well-defined low-energy quasiparticles influenced by strong correlations and quantum geometry.

Contribution

It introduces a controlled approximation method to analyze quasiparticle properties in a topological heavy fermion model with flat bands and hybridization.

Findings

Emergence of well-defined low-energy quasiparticles with dispersion proportional to interaction strength.

Spectral properties are resolved near the Fermi level, indicating strong correlation effects.

Results are relevant for spectroscopic experiments like quantum twisting microscopy.

Abstract

Twisted bilayer graphene provides a paradigmatic platform for exploring the interplay between electronic topology and strong correlations. Within the topological heavy fermion model [Song and Bernevig, Phys. Rev. Lett. 129, 047601 (2022)], topology and electron interactions are brought together by including a weak hybridization between the bands of itinerant $c$- and localized $f$-electrons. Hybridization infuses concentrated Berry curvature into the $f$-band, while leaving it flat. These band features have motivated recent proposals of a Mott semimetal phase above the flavor-ordering temperature at charge neutrality. In this work, we develop an analytic theory of the quasiparticle dispersion and lifetime in the Mott semimetal. We reformulate the interacting flat-band Hamiltonian as an on-site Hubbard interaction defined on a set of non-orthogonal orbitals, and compute the electron Green's function using the equation-of-motion method, in close analogy with the Hubbard-III approximation. Unlike the conventional Hubbard model, in our case this approximation is controlled by a well-defined small parameter in the theory. We evaluate the electron self-energy and demonstrate the emergence of well-defined low-energy quasiparticles with the dispersion and relaxation rate proportional to the interaction strength. The quasiparticle spectrum is well-resolved in energy and in momentum down to the very vicinity of the Fermi level. Our results illustrate unconventional spectral properties arising from strong correlations and nontrivial quantum geometry, and have direct relevance for spectroscopic probes such as quantum twisting microscope experiments.