Study of a two-dimensional electron gas in a magnetic field. I. Weak field

A many-body theory of a two-dimensional electron gas in a magnetic field is presented. The field dependence of the Fermi momentum shows a two-dimensional peculiarity. It consists of the spin-dependent paramagnetic part and the orbital diamagnetic part. The former increases more strongly with rₛ than the latter. The paramagnetic and diamagnetic susceptibilities are found as functions of rₛ. The field-dependent ground-state energy is evaluated. Its paramagnetic part decreases steadily with rₛ, while the diamagnetic part shows a maximum. No such maximum has been found for the three-dimensional case in the same approximation which is valid for high density and low magnetic fields. From the susceptibilities, an effective g factor and an effective mass are derived. They are given approximately by g*g=1+0.87×10⁶n^-1/2 or more accurately by g*2g²=1+1.74×10⁶n^-1/2-0.708×10¹²n^-1 and by m*m=1+3.21×10⁴n^-1/2, where n is the number density.