Title: Randomness, Quasiperiodicity, and Dirac Points
We will discuss the effects of short-range disorder and quasiperiodicity on semimetals with Dirac points in two and three dimensions. Semimetals have garnered a significant amount of attention in recent years following the discovery of graphene and topological Dirac and Weyl materials. Disorder is a marginally relevant perturbation in two-dimensions, and as a result a finite density of states is generated destabilizing the semimetal. Interestingly, randomness is too strong even for three-dimensional Weyl and Dirac semimetals to survive, rare regions of the random potential induce resonances that endow the system with a finite density of states, as we have established in lattice models for Dirac and Weyl semimetals . To remove rare regions, we replace randomness with a quasiperiodic potential, and as a result stabilize the three-dimensional Weyl semimetal phase. We discover a sharp quantum phase transition into a diffusive metal phase, with a clear non-analyticity in the density of states . We demonstrate that this transition can be described by a delocalization transition in momentum space: the quasiperiodic potential destabilizes the ballistic plane wave eigenstates. Due to the weakness of quasiperiodicity, we are able to generalize this transition to two-dimensions. We track the velocity of the Dirac cone and will show the nature of excitations at the semimetal to metal phase transition. Lastly, we will discuss our preliminary results on the effects of interactions and constructing effective models at this novel semimetal-to-metal phase transition.