STUDY OF 2-DIMENSIONAL ELECTRONS IN A MAGNETIC-FIELD .2. INTERMEDIATE FIELD

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 (e2p0)34=(212rs)34. Due to a 2-D peculiarity, the susceptibility oscillates as in the ideal case without a constant phase -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 a4cos(0a2), where a2 represents the field energy and 0 is the Fermi energy for the ideal case, i.e., 2, in the units =1 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. © 1979 The American Physical Society.