Massless Dirac-like fermions under external fields: a nonminimal   coupling approach
  We investigate the unusual properties of quasirelativistic massless fermions under a magnetic or electric field by means of nonminimal couplings. Within this approach, the spin-orbit coupling (SOC) effects are properly generated in the energy spectrum of the quasiparticles. By including a magnetic field, $B$, we show that the spin splitting of Landau Levels (LL) obeys a $\sqrt{B}$ linear dependence with SOC, typical of relativistic particles. Moreover, our calculated spectrum of LLs resembles the behavior of the three-dimensional (3D) massless Kane fermions. Using a nonminimal coupling with an external electric field, we demonstrate that a Rashba-like SOC naturally appears into the relativistic equations and apply to the case of two-dimensional (2D) massless Dirac fermions. Still considering our proposed approach, the Hall conductivity is also computed for the 2D case under transverse electric field both at zero and finite temperatures for a general chemical potential. The results feature a typical quantization of the Hall conductivity at low temperatures, when the absolute value of the gap opened by the electric field is larger than the considered chemical potential. 
E. Marcelino, E. S. Santos and R. Rivelino
cond-mat.mes-hall