Impurities in Dirac and Weyl semimetals.

Abstract

In this thesis impurities in a variety of lattices are studied. When there is an impurity in a lattice, electrons will bind to them. They will form bound states with a certain energy ω, and this energy is dependent on the impurity potential U. We have studied the relation between the energy of an impurity induced state and the impurity potential ω(U) in a 1D lattice, 2D square lattice, a Dirac semimetal like graphene and a Weyl semimetal like TaAs. To do this we used the Green’s function and T-matrix formalism and applied it to these cases. We found that the 1D lattice obeys ω(U) ∼ U^2, the 2D lattice obeys ω(U) ∼ exp(1/U) , the Dirac semimetal obeys ω(U) ∼ U and finally the Weyl semimetal follows ω(U) ∼ 1/U . These results can be experimentally tested using a scanning tunneling microscope by measuring the linear density of states (LDOS) for certain values of the impurity potential.