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We investigate the unusual properties of quasirelativistic massless fermionsunder a magnetic or electric field by means of nonminimal couplings. Withinthis approach, the spin-orbit coupling (SOC) effects are properly generated inthe energy spectrum of the quasiparticles. By including a magnetic field, $B$,we show that the spin splitting of Landau Levels (LL) obeys a $\sqrt{B}$ lineardependence with SOC, typical of relativistic particles. Moreover, ourcalculated spectrum of LLs resembles the behavior of the three-dimensional (3D)massless Kane fermions. Using a nonminimal coupling with an external electricfield, we demonstrate that a Rashba-like SOC naturally appears into therelativistic equations and apply to the case of two-dimensional (2D) masslessDirac fermions. Still considering our proposed approach, the Hall conductivityis also computed for the 2D case under transverse electric field both at zeroand finite temperatures for a general chemical potential. The results feature atypical quantization of the Hall conductivity at low temperatures, when theabsolute value of the gap opened by the electric field is larger than theconsidered chemical potential.

Massless Dirac-like fermions under external fields: a nonminimal coupling approach