Hole Landau Levels Research Articles

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.

Shubnikov-de Haas Effect in Bismuth

The oscillatory component of the transverse magnetoresistance of single crystals of bismuth has been measured at 1.15\ifmmode^\circ\else\textdegree\fi{}K. The magnetic field range was 700 to 23 000 G. Measurements were taken in the three principal planes. The experimental results may be explained on the basis of two sets of carriers. No evidence was found for the third and fourth carriers reported recently. For holes we find ${{\ensuremath{\beta}}_{11}}^{2}=75.4\ifmmode\times\else\texttimes\fi{}{10}^{+28}{({{E}_{F}}^{h})}^{2}$ ${\mathrm{erg}}^{\ensuremath{-}2}$, ${\ensuremath{\beta}}_{11}{\ensuremath{\beta}}_{33}=7.25\ifmmode\times\else\texttimes\fi{}{10}^{+28}{({{E}_{F}}^{h})}^{2}$ ${\mathrm{erg}}^{\ensuremath{-}2}$; for electrons, ${\ensuremath{\alpha}}_{11}{\ensuremath{\alpha}}_{33}=23.3\ifmmode\times\else\texttimes\fi{}{10}^{30}{({{E}_{F}}^{e})}^{2}$ ${\mathrm{erg}}^{\ensuremath{-}2}$, and the tilt angle is 4\ifmmode^\circ\else\textdegree\fi{}. Here ${E}_{F}$ is the Fermi energy measured in ergs. The effects of spin splitting of hole Landau levels is observed at 70\ifmmode^\circ\else\textdegree\fi{} from the $z$ axis, from which we find ${g}_{3}\ensuremath{\cong}62$ (assuming ${g}_{1}\ensuremath{\ll}{g}_{3}$).

EffectivegFactor of Electrons and Holes in Bismuth

Shubnikov-de Haas type oscillations have been studied in bismuth in magnetic fields up to 88 kG. Oscillations are observed which have been attributed to the hole band in bismuth. A machine calculation of the density of states and of the Fermi level as a function of magnetic field is used to fit the data. The calculation is based on the nonparabolic (two-band) model of the electron band, and includes the possibility of spin splitting for both electrons and holes. It correctly predicts the observed change in Fermi energy with magnetic field. We find that the hole Landau levels are indeed split by spin. The spin splitting is almost twice the Landau level spacing along the trigonal axis and is extremely small perpendicular to the trigonal axis. Spin splitting is also observed for electrons. We find that the spin splitting is about one-third the orbital splitting in the heaviest mass direction and about 10% larger than the orbital splitting in the light mass direction. Our observations imply that there are important states both above and below the hole band. This is in direct contradiction to the Abrikosov and Falkovskii model which considers only one set of states (either above the hole band or below) with which the hole band interacts.

Landau Levels and Cyclotron Resonance of Holes in Germanium

Landau levels of holes in germanium are calculated in the case of the static magnetic field parallel to the [111] axis to determine cyclotron resonance spectrum theoretically. The calculations are not confined to the special point, k H =0, i.e. to the levels for the vanishing value of the wave vector component along the field. The shapes of the magnetic sub-bands are thus obtained with the same values of the effective mass parameters as those of Goodman. The calculations also include the warping effect of the valence band with a reasonable approximation. The positions of peaks of cyclotron resonance absorption and their relative intensities are determined numerically from the calculated Landau levels. The theoretical absorption spectrum is shown to be modified significantly from the one in which the assumption, k H =0, is made. The results are compared with the recent experimental data of Hensel. It is found that most of the experimental peaks can be assigned by the calculated spectrum. Some of them which...