Fermions in G\"odel-type background space-times with torsion and the   Landau quantization
  In this paper, we analyze Dirac fermions in G\"odel-type background space-times with torsion. We also consider the G\"odel-type spacetimes embedded in a topological defect background. We show that relativistic bound states solutions to the Dirac equation can be obtained by dealing with three cases of the G\"odel-type solutions with torsion, where a cosmic string passes through these three cases of the space-time. We obtain the relativistic energy levels for all cases of the G\"odel-type solutions with torsion with a cosmic string, where we show that there exists an analogy with the Landau levels for Dirac particles. We also show that the presence of torsion in the space-time yields new contributions to the relativistic spectrum of energies and that the presence of the topological defect modifies the degeneracy of the relativistic energy levels. 
G. Q. Garcia, J. R. de S. Oliveira, K. Bakke and C. Furtado
hep-th gr-qc quant-ph