The low energy excitation spectrum of magic-angle semimetals

The low energy excitation spectrum of a Dirac semimetal in an incommensurate potential is studied theoretically. This system possesses a magic-angle phase transition with a vanishing velocity and delocalization of plane wave eigenstates. By computing the single particle Green’s function using the kernel polynomial method we clearly demonstrate the successive formation of minibands that live on larger and larger moire’ lattices. Across the magic-angle transition we demonstrate that the imaginary part of the single particle self energy becomes non-zero comcomitant with the breakdown of the semimetallic quasiparticle excitations.