On the Role of a Torsion-like Field in a Scenario for the Spin Hall Effect

Starting from an action that describes a Dirac fermion, we propose and analyze a model based on a low-relativistic Pauli equation coupled to a torsion-like term to study Spin Hall Effect (SHE). We point out a very particular connection between the modified Pauli equation and the (SHE), where what we refer to torsion as field playing an important r\^ole in the spin-orbit coupling process. In this scenario, we present a proposal of a spin-type current, considering the tiny contributions of torsion in connection with geometrical properties of the material.