Efeitos da violação de simetria de Lorentz sobre o modelo de Kronig-Penney

Abstract

The breaking of Lorentz symmetry and its possible eects on physical systems has been a topical issue in actual investigations, belonging to a precision program for establishing the limits of this symmetry in nature. These studies are not constrained to the eld theory or high energy systems, since they also involve other areas, like condensed matter physics. In this work we revisit the Kronig-Penney model, rst addressed by means the Schrodinger equation, and second by means of the Dirac equation in its quantum-relativistic version. We revise the nonrelativistic and relativistic Kronig-Penney model, achieving the energy bands relations to both cases. We verify that in the case of relativistic KP model the eects entail in an energy band reduction, if compared to the non-relativistic case. The same happens to gaps but in a less signicant way. In the sequel, we investigate the eects of the Lorentz-violating term, ψb ̄ μγ5γ

μψ, belonging to the fermionic

sector of the SME of Colladay & Kostelecky, on the Kronig-Penney model. Here, b μ represents the Lorentz-violating backgroud. As an initial step, we obtain the associated free particle spinor solutions of the modied Dirac equation. We use such spinors to develop the KP model with Lorentz violation and achieve the modied band relations. We verify that the procedure become specially simplied for the unidimensional case, p = (0, 0, 0, pz), for the spacelike conguration of the background, b = (0, 0, 0, bz). The energy band relation has the same general structure from that obtained without LV, with the dierence that dimensionless quantity Γ, dened in that work, carries now the dependence on the Lorentz-violating term. It still misses to analyse how the LV terms aects the band energy structure.