3D massive Dirac fermions with chemical potential in external magnetic field: Current-current correlation function

The response of fermionic system to external gauge fields in presence of non-quantized magnetic field is determined by current-current correlation function ${\mathrm{\Pi }}_{\mu \nu }(\mathbf{B})$. We study $2D$ dimensional Dirac electron system and calculate current-current correlation function in a presence of magnetic field $B$, chemical potential $\eta$ and gap $m$.