The low energy excitation spectrum of magic-angle semimetals

TL;DR

This paper investigates the excitation spectrum of a 2D Dirac semimetal with incommensurate potential, revealing how quasiperiodicity induces minibands, flat bands, and critical points characterized by vanishing quasiparticle residue and emergent superlattices.

Contribution

It provides a detailed analysis of the spectral properties at the magic-angle transition using the kernel polynomial method, highlighting the effects of quasiperiodicity on quasiparticle behavior.

Findings

Spectral weight redistribution due to miniband formation.

Vanishing quasiparticle residue at the transition.

Power-law suppression of quasiparticle residue.

Abstract

We theoretically study the excitation spectrum of a two-dimensional Dirac semimetal in the presence of an incommensurate potential. Such models have been shown to possess magic-angle critical points in the single particle wavefunctions, signalled by a momentum space delocalization of plane wave eigenstates and flat bands due to a vanishing Dirac cone velocity. Using the kernel polynomial method, we compute the single particle Green's function to extract the nature of the single particle excitation energy, damping rate, and quasiparticle residue. As a result, we are able to clearly demonstrate the redistribution of spectral weight due to quasiperiodicity-induced downfolding of the Brillouin zone creating minibands with effective mini Brillouin zones that correspond to emergent superlattices. By computing the damping rate we show that the vanishing of the velocity and generation of finite density of states at the magic-angle transition coincides with the development of an imaginary part in the self energy and a suppression of the quasiparticle residue that vanishes in a power law like fashion. Observing these effects with ultracold atoms using momentum resolved radiofrequency spectroscopy is discussed.