Ultrasonic Quantum Oscillations Research Articles

Quantum oscillations and Fermi surfaces of Sn- and Pb-doped Bi

The Fermi surfaces of bismuth single-crystal samples doped with tin and lead have been investigated by means of the techniques of ultrasonic quantum oscillations (UQO) and Shubnikov-de Haas (SdH) oscillations. Experiments were carried out in the temperature range 1.2-4.2 K using longitudinal ultrasonic waves of frequencies up to 70 MHz and in magnetic fields up to 2.3 T. The excess hole densities of single-crystal samples obtained from the analysis of UQO and SdH oscillations data, residual resistivity ratio (RRR) and Hall-effect measurements are in the range of 3*1023 to 1.4*1025 m-3. The Fermi-surface geometry of carriers was determined from the angular dependence of the periods of UQO and SdH oscillations. The major effect of doping of bismuth with Sn (or Pb) is to decrease the Fermi energy. On increasing the amount of doping, the pockets in the L-point conduction band became progressively smaller. Further increase of the dopant concentration leads to the disappearance of the L-electron pockets and the appearance of L holes. The experimental results have shown that the Fermi surfaces of acceptor-doped bismuth crystals are similar to those of pure bismuth and that the Lv valence band is the mirror image of the Lc conduction band.

Ultrasonic quantum oscillations and the magnetic field dependence of the Fermi energy in semimetallic Bi1-xSbxalloys

Ultrasonic quantum oscillations in pure Bi and semimetallic Bi1-xSbx alloys (x=0.012, 0.019, 0.033) have been investigated. Experiments were carried out in the temperature range 1.2-4.2K using longitudinal ultrasonic waves of frequencies up to 90 MHz propagated along the trigonal axis. Magnetic fields between 0.05 and 2.3 T were applied in the yz and xz planes. The angular dependence of the peak positions was studied. The Landau and spin quantum numbers of the oscillation peaks were obtained from the experimentally measured periods and peak positions of the oscillations. The experimental data indicate that, for most orientations of the magnetic field in the yz plane, the magnetic energy levels of electrons in the alloys studied can be described successfully by the ellipsoidal non-parabolic (ENP) model. The magnetic field dependence of the Fermi energy and the carrier density were calculated in the framework of the ENP model for electrons and the parabolic band for holes, using the previously determined band parameters. The magnetic field values at which the electrons in each pocket enter the quantum limit were deduced from the magnetic field dependence of the carrier density. The quantum limit fields obtained from calculations agree with the experimentally predicted values. It is concluded that within the magnetic field range studied the variation of the Fermi energy with magnetic field has a negligible effect on the period of ultrasonic quantum oscillations from light electrons.

Ultrasonic quantum oscillations in semimetallic Bi1-xSbxalloys

The electronic properties of pure Bi and semimetallic Bi1-xSbx alloys (x=0.012, 0.019, 0.033) have been investigated by means of magnetoacoustic attenuation in the DHVA region. Experiments were carried out in the temperature range 1.2-4.2K using longitudinal ultrasonic waves of frequencies up to 100 MHz propagated along the trigonal axis. Magnetic fields between 0.05 and 2.3 T were applied in the yz and xz planes. The Fermi-surface sections and effective masses of electrons were obtained from the angular dependence of the measured periods of ultrasonic quantum oscillations. With increasing antimony concentration the cyclotron masses and the densities of electrons in the alloys decrease, but the shape and the tilt angle of the electron ellipsoids do not change. The electron Fermi surface in the alloys contracts toward its centre, preserving its shape. The temperature and magnetic field dependence of the amplitudes of DHVA-type oscillations were studied and electron cyclotron masses at the Fermi level and the Dingle temperature were obtained. The effects of impurities and dislocations on the lineshape and the Dingle temperature were considered.

An investigation of the third-zone Fermi surface of aluminium using ultrasonic quantum oscillations

The ultrasonic quantum oscillation technique has been used to study the third-zone Fermi surface of aluminium. 90 MHz longitudinal ultrasonic waves were used at a temperature of 1.4K in fields up to 8.7 T. The results are compared to the de Haas-van Alphen effect results of Larson and Gordon (1967) and to the theoretical model of Ashcroft (1963). The observations are consistent, several branches being extended by this work and two new branches discovered. A further new branch is probably ascribable to magnetic breakdown. Giant quantum oscillations were also observed.

Ultrasonic quantum oscillations in white tin at 0.1K

An investigation of ultrasonic quantum oscillations in white tin has been carried out with the sample cooled to 0.1K in a helium dilution refrigerator. 90 MHz longitudinal ultrasonic waves were used and an electromagnet provided fields up to 2.0 T. The frequency from an orbit attributable to the neck on the fourth-zone electron surface was seen for the first time. Despite the low magnetic field, several orbits attributable to magnetic breakdown were also observed, two of these for the first time.

Ultrasonic study of spin-splitting of landau levels in bismuth

A study has been made, using ultrasonic quantum oscillations, of the spin-splitting factor of electrons and of holes in bismuth with the magnetic field direction varied in the XZ plane. The results are consistent with the general picture of spin-splitting in bismuth.

Butterflies and cigars

In his interesting article on ultrasonic quantum oscillations in the May 1976 issue of Physics Bulletin (page 213), Dr L Mackinnon ventures to speculate that the pieces of Fermi surface called the butterflies might actually exist in zinc and cadmium. However, it should be pointed out that consideration of electron–hole compensation effectively rules out this possibility.

Ultrasonic quantum oscillations and the Fermi surface of lead

Ultrasonic quantum oscillations have been studied in lead single crystals using 70-110 MHz longitudinal waves at about 1.3K in magnetic fields up to over 7 T. The results are interpreted in terms of the Fermi surface; they confirm the presently accepted third-zone surface and they show the presence of electron pockets in the fourth zone, previously believed to be empty. The fourth-zone occupancy is shown to be about 4*10-3 electrons per atom.

Quantum oscillations in ultrasonic absorption and the Fermi surface of indium

Ultrasonic quantum oscillations have been studied in indium single crystals, using 10-310 MHz longitudinal waves at 1.2 to 1.3K in magnetic fields up to 6T. The observed frequencies arise from the Fermi surface in the third zone, and are in good agreement with de Haas-van Alphen effect data. Observations of crystal twinning in the samples support the view that periods attributable to alpha arms come from beta arms in the twin and that therefore the alpha arms do not exist. It is possible though that the displaced beta arms may be distorted. Effective cyclotron masses have been deduced from the temperature variation of oscillation amplitude.

Ultrasonic Quantum Oscillations in Chromium

Measurements of quantum oscillations in the ultrasonic attenuation have been made to investigate the Fermi surface of chromium in the "single-$\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}$" state. Several frequency branches were followed over the entire Fermi surface and many of these data agree with earlier de Haas-van Alphen and ultrasonic results. Three branches display harmonic behavior which is exact when the measuring field is in the basal plane, but which deviates smoothly from exactness as the field is rotated toward $\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}$. The most likely explanation of this feature is that of magnetic breakdown among nonextremal orbits on the Fermi surface. The lack of degeneracy of the branches at certain symmetry axes prevented identifying the data with the location of sections of the Fermi surface. The data in one family of branches agree point by point with the de Haas-van Alphen results when the measuring field is near the basal plane, but differ as the field approaches $\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}$. For the remaining data, symmetry arguments may not be applicable because of changes in the topology caused by magnetic breakdown.

Ultrasonic quantum oscillations and the Fermi surface of zinc

Abstract The Fermi surface of zinc has been studied by means of quantum oscillations in the acoustic attenuation. Three long periods have been detected which correspond to the needle and monster regions and these have been interpreted on the nearly free electron surface as modified by Stark (1964) and Cohen and Falicov (1960). In addition, magnetic breakdown effects have been investigated and previous work on the effective g-values associated with the needles extended.