Conductivity of the graphene in the transversal magnetic field: Relaxation time approximation with Monte-Carlo method

• We calculate the graphene magnetoconductivity within τ-approximation.
• We calculate the graphene magnetoconductivity with the Monte-Carlo method.
• We investigate the conductivity dependence on the magnetic field intensity.
• We calculate the relaxation time in graphene with the Monte-Carlo method.
• The analytical results are shown to be confirmed by the numerical calculation.

The components of the conductivity tensor of graphene placed in a constant magnetic field that oriented transversely the graphene layer are calculated. The calculation is performed on the basis of the Boltzmann equation, written in the relaxation time approximation. The method for the numerical determination of the relaxation time taking into account the electron–phonon interaction explicitly is offered. The dependences of the relaxation time on the magnetic field intensity and on the temperature are found with this method.