Study of two-dimensional electrons in a magnetic field. II. Intermediate field

Abstract

Taking into consideration the first-order-exchange and ring diagrams, we present a theory of two-dimensional (2-D) electrons in a magnetic field under the de Haas-van Alphen condition. The Fermi momentum or the chemical potential of the system oscillates with the magnetic field, its interaction term being characterized by a factor ${\left(\frac{e^2}{p_0}\right)}^{\frac{3}{4}}={\left(2^{\frac{1}{2}}{r}_s\right)}^{\frac{3}{4}}$. Due to a 2-D peculiarity, the susceptibility oscillates as in the ideal case without a constant phase $-\frac{\pi }{4}$ characteristic of the three-dimensional case. A relation between the amplitude of the oscillating susceptibility and the field and temperature is derived. The energy variation is like $a^{4}cos\left(\frac{\pi {\epsilon }_0}{a^2}\right)$, where $a^2$ represents the field energy and ${\epsilon }_0$ is the Fermi energy for the ideal case, i.e., $2\pi \hslash$, in the units $\hslash =1\mathrm{}$ and $2m=1$, where $n$ is the number density. The amplitude of the energy oscillation increases with the field strength squared. A new specific-heat formula is also presented.