Efeitos da torção em matéria condensada

Abstract

In this work, we study the e ects of torsion due a topological defect distribution (screw dislocations) in the dynamics of a free particle with spin in an elastic solid. When a particle moves in this medium, the e ect of the torsion associated with the distribution of defects is analogous to that of an applied magnetic eld, but with some subtle di erences. In order to understand the quantum behavior of the particle in this system, we rst turn to the classical part, calculating its equations of motion and tracing its trajectory through the geodesics, proving the behavior analogous to that of an applied magnetic eld generating the elastic Landau levels, nevertheless such particle can not be con ned to two dimensions. Spinning particles are subjected to the spin-torsion coupling similar to the Zeeman e ect, with the characteristic of being insensitive to the charge signal. A possible application, treated in this study, for this defect density, is in the Hall conductivity of the Integer Quantum Hall E ect, which we call elastic Hall-like conductivity. In order to have a better physical intuition of this problem, we plot some graphs of the elastic Hall-like conductivity as a function of temperature and chemical potential.