Here, ω ω c is the cyclotron frequency which is linearly dependent of the applied magnetic field and the charge of the particle. There are two distinct features between the Landau level quantization for 2D Schrödinger fermions (ordinary matter) and 2D Dirac fermions. First, the energy for Schrödinger fermions is linearly dependent with respect to the integer quantum number n , whereas it exhibits a square-root dependence for the Dirac fermions. This key difference plays an important role in the experimental verification of Dirac matter. Furthermore, for n = 0 there exists a 0 energy level for Dirac fermions which is independent of the cyclotron frequency ω ω c and with that of the applied magnetic field. For example, the existence of the zeroth Landau level gives rise to a quantum Hall effect where the Hall conductance in quantized at half-integer values.