  In two - loop effective Lagrangian, the low - temperature expansion of the
$QED_{3+1}$ with a constant magnetic field and a finite chemical potential is
performed. We then calculate the total fermion density, some components of
polarization operator and de Hass -van Alphen oscillations. We find that there
is a significant contribution from two-loop expansion to magnetization and
fermion density for higher values of chemical potentials.
