An anisotropic rotating cosmic string with Lorentz violation: thermodynamics and Landau levels

In this work, we generalize the spacetime induced by a rotating cosmic string, taking into account anisotropic effects due the breaking of the Lorentz violation. In particular, we explore the energy levels of a massive spinless particle that is covariantly coupled to a uniform magnetic field aligned with the string. Subsequently, we introduce a scalar potential featuring both a Coulomb-type and a linear confining term and comprehensively solve the Klein-Gordon equations for each configuration. Finally, by imposing rigid-wall boundary conditions, we determine the Landau levels when the linear defect itself possesses magnetization. Notably, our analysis reveals the occurrence of Landau quantization even in the absence of gauge fields, provided the string possesses spin. Finally, the thermodynamic properties are computed as well in these scenarios.