Fermi Surface Of Zinc Research Articles

Stress-induced changes in the Fermi surface of zinc

The effects of uniaxial stress ( sigma 33) and pressure on the principal sections of the Fermi surface of zinc are calculated. Agreement with experimental work is good. The results are expressed as the sum of a kinetic energy contribution and a potential energy contribution. It is shown that the kinetic contribution is generally rather similar to the free-electron prediction, and that where results differ from free-electron theory this is due mainly to the influence of the potential contribution. Both the kinetic and potential contributions are expressed as the product of an intrinsic factor, which depends on the bandstructure, and an extrinsic factor which depends primarily on the stress. This separation makes it possible to see how different stresses differ in their effects on a given section, and how sections differ between themselves for a given stress. The changes of shape produced by stress are illustrated.

Effect of changes in the lattice parameters on the Fermi surface of zinc

The effect of changes in the lattice parameters on the Fermi surface of zinc is calculated. The results of the calculations are in reasonably good agreement with experimental data.

Oscillatory magnetostriction and the stress dependence of the Fermi surface of aluminum, indium, zinc, and magnesium

Oscillatory magnetostriction and de Haas-van Alphen measurements have been made in aluminum, indium, zinc, and magnesium between 1.3 and 4.2K and in magnetic fields up to 22 kOe. From these results we determined the stress dependence of several orbits on the third band Fermi surfaces of aluminum and indium and some orbits on the Fermi surfaces of zinc and magnesium. The experimental values are in agreement with the results of simple OPW (orthogonalized plane wave) calculations in which the stress dependence of the pseudopotential is obtained from the Heine-Abarenkov-Animalu form factor in a local screening approximation. We observed angular constancy in the stress dependence of the orbits, and a model is presented to account for this. We also discuss the possibility of stress-induced Lifshitz transitions, and show how the free-electron model should be used to predict changes in the Fermi surface under hydrostatic pressure and uniaxial stress.

Ultrasonic studies of the electronic structure of hexagonal metal crystals II. Superconducting state in zinc and cadmium

Measurements have been made of the temperature dependence of the attenuation of longitudinal ultrasound in the superconducting states of pure zinc and cadmium for propagation along the and <0001>, <101 ¯ 0> and <112 ¯ 0> directions, at frequencies from 40 to 160 MHz. This temperature dependence has been interpreted in terms of an energy gap parameter A = 2∆(0)/ kT c . In zinc, for T < ½ T c , A was found to be 3.41 ± 0.1, 3.79 ± 0.1 and 3.64 ± 0.1 for the <0001>, <101 ¯ 0> and <122 ¯ 0> directions respectively. The corresponding values for cadmium were 3.29 ± 0.1, 2.80 ± 0.1 and 3.87 ± 0.1. A simple model proposed by Hays for the distribution of the energy gaps on the Fermi surface of zinc does not explain these results, and a more realistic model has been proposed. The main features of the proposed energy-gap distributions in zinc and cadmium are that the electrons on the third band lens have larger energy gaps than those on the second band monster, over which there is a large and complicated variation.

Correlation between anisotropy in the normal-state mass renormalization and anisotropy in the superconducting energy gap for zinc

A nonlocal pseudopotential model for the Fermi surface and band structure of zinc together with the cyclotron resonance data is used to calculate the orbital average of the normal-state mass renormalization λCRi for numerous cyclotron orbits on the Fermi surface of zinc. We find that the mass renormalization λk is constant for each sheet of the Fermi surface but that it varies from sheet to sheet. Using the Eliashberg equation, this anisotropy in λk is correlated to anisotropy in the superconducting energy gap Δk. For zinc we predict three distinct energy gaps, in the ratio of 2.30:1.76:1.00, corresponding respectively to the lens, the monster, and the cap sheets of the Fermi surface. Experimental evidence for this anisotropy in Δk is provided by various measurements of the electronic properties in the superconducting state such as the low-temperature specific heat, microwave absorption, ultrasonic attenuation, effect of alloying on the critical temperature, and the temperature dependence of the critical field. We show that the results of these experiments are consistent with our predictions.

Fermi Surface of Zinc: Radio-Frequency Size Effect

The Fermi surface of zinc is determined from calipers obtained through rf size-effect measurements. The 6- to 8-MHz rf measurements were performed at 1.2\ifmmode^\circ\else\textdegree\fi{}K on high-purity monocrystals of zinc approximately 0.5 mm in thickness. The Fermi surface was calipered using samples whose normals to the surfaces were parallel to one of the three principal symmetry directions, [0001], [$10\overline{1}0$], and [$11\overline{2}0$], with magnetic field rotations in the plane of the sample. Calipers are assigned to definite orbits on the first- and second-band hole surfaces and the third-band electron surface. The third-band electron "lens" is found to be smooth and round with a major diameter of 1.737 ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ and varying less than 0.5% in the basal plane. The minor diameter has a caliper of 0.556 ${\mathrm{\AA{}}}^{\ensuremath{-}1}$. Calipers are given for the first-band hole surface and the spin-orbit-induced gaps between the first and second bands are discussed. The second-band hole surface is discussed in detail with the assignment of 30 series of calipers to definite orbits on this sheet of the Fermi surface. Both the first and second bands of holes are found to have considerably smaller cross sections than predicted by the single-orthogonalized-plane-wave construction. Detailed comparisons to a recent pseudopotential calculation of the energy bands and the Fermi surface are made. No calipers were observed that could be assigned to the third-band "stars" or the fourth-band electron "cigars."

Band Structure and Fermi Surface of Zinc and Cadmium

Band Structure and Fermi Surface of Zinc and Cadmium

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.

Effect of Pressure and Magnetic Field on the Connectivity of the Fermi Surface of Zinc

Effect of Pressure and Magnetic Field on the Connectivity of the Fermi Surface of Zinc

Magnetic Breakdown Effects in the Galvanomagnetic Properties of Zinc

The galvanomagnetic properties of several single-crystal specimens of high-purity zinc have been investigated. The results of this investigation are presented and a Fermi-surface topology consistent with the data is discussed. Many of the detailed features of the galvanomagnetic properties are found to result from the effects of magnetic breakdown. The open orbit parallel to the hexagonal axis is modified but not eliminated by magnetic breakdown at fields of about 17.5 kG. A "giant orbit" of the type previously observed in magnesium is found in zinc. This orbit results from magnetic breakdown across the energy gap near $K$ which separates the second-band hole sheet from portions of the third-band electron sheets. Magnetic breakdown across this same energy gap gives rise to discrete bands of open trajectories in the basal plane when the direction of the magnetic field is tilted away from the hexagonal axis in the ($10\overline{1}0$) and ($11\overline{2}0$) crystallographic planes. The transition region of the magnetic breakdown which gives rise to the giant orbit is investigated in detail, and the large quantum oscillations which have been previously observed in the transport properties of zinc are shown to be a transition-region phenomenon. The oscillations appear to result from an oscillatory breakdown probability which, in turn, arises from oscillations in the density of states associated with the Landau levels of the needle-shaped portion of the Fermi surface of zinc. An analysis of the detailed shape of the oscillations indicates that the Landau levels of the needle are split into discrete spin levels with a very large effective $g$ factor. The three values of the effective $g$ factor which are compatible with the present data are ${g}^{*}=90$, ${g}^{*}=180$, and ${g}^{*}=360$, but an investigation with higher magnetic-field strengths will allow a unique choice to be made. No evidence has yet been obtained that yields a direct confirmation of the quasi-particle states predicted by Pippard.

Band Structure and Fermi Surface of Zinc

The band structure of zinc is calculated using a modified orthogonalized-plane-wave method and the Hartree-Fock calculations of neutral zinc by Piper. The band structure is obtained in a form which allows it to be extended readily to slight distortions of the lattice. The calculated structure is compared to an experimental band structure obtained by adjusting the matrix elements to fit de Haas-van Alphen observations of the zinc Fermi surface. The band energies do not differ by more than 0.04 ry for the two treatments. The Fermi surface from the experimental band structure is drawn in some detail. One matrix element is found to be only 0.004 ry, requiring an analysis of magnetic breakdown in the interpretation of experiments. The probability of band-to-band transitions, calculated explicitly in the high-field limit, is continued into the low-field range with a result equivalent to Blount's low-field result. The formulas for the intermediate range are applied to zinc.