Relativistic free fermions in an elastic medium with screw dislocations

Abstract

We study the Dirac equation for free fermions in an elastic medium with a linear topological defect or distortion analogous to a screw dislocation. We obtain its wave functions for free particle and the corresponding energy spectrum, as well as the fermionic current density. Furthermore, we provide the energy–momentum density for four well-known forms: Einstein, Landau–Lifshitz, Papapetrou and Bergmann–Thomson.