Low energy excitation spectrum of magic-angle semimetals

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 wave functions, signaled 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 a finite density of states at the magic-angle transition coincide 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.