Low energy excitation spectrum of magic-angle semimetals

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