Monotonic Behaviors in Semimetals in Strong Magnetic Fields

In sufficiently strong magnetic fields, all except the lowest of the Landau levels of electrons or holes in a semimetal may have crossed over the Fermi level. At sufficiently low temperatures, the probability of an electron or a hole being in the levels other than the lowest one then becomes negligibly small. Under these conditions, the motion of the charge carriers is essentially of one degree of freedom. Associated with such motion, the density of the charge carriers, the chemical potential, the total energy, the magnetic moment, and the specific heat exhibit monotonic variations in an increasing magnetic field. A theoretical analysis is presented to show these monotonic behaviors. Both zero temperature and low temperature are considered. The condition and the behavior of a magnetic-field-induced semimetal-semiconductor transition are discussed and compared with experimental work. A possible specific-heat anomaly is indicated.