Effect of Coulomb screening on the discrete scale invariance of quasibound states in three-dimensional topological semimetals

Abstract

We study the energy spectrum of Weyl fermions in a topological semimetal in the presence of a central charged impurity. When the strength of the charge exceeds a critical value, an infinite family of quasibound states appear that show characteristic signatures of discrete scale invariance. The invariance is broken by the presence of screening or a finite mass. If these terms are small enough the quasibound states still exist, but there can be perturbations of the shallowest quasibound states. These special quasibound states manifest themselves in the local density of states as well as the relative phase, which can be observed by scanning tunneling microscopy. Such effects that are usually associated with the relativistic quantum electrodynamics of strong fields become observable in topological materials.