: Transport effects were studied in a bismuth single crystal at liquid helium temperatures in a magnetic field. The thermal conductivity was found to be almost entirely due to lattice con ductivity; therefore, the experimental coefficients determined were limited to the following: the isothermal transverse magnetoresistivity, the isothermal Hall resistivity, the (adiabatic) thermoelectric coefficient, the (adiabatic) Nernst-Ettinghausen coefficient, and the trans verse magnetothermal resistivity. The Peltier tensor coefficients were expected (from the Onsager relations) to be too small to be measure able and thus, were not studied here. All these effects, except the thermal resistivity coefficient, exhibit Schubnikov-de Haas type oscillations. The kinetic coefficients of certain transport effects were computed from the experimental coefficients and compared with available theories. A rough analysis of the gross effects was made by a decomposition of each coefficient into a sum of different band contributions, each band being approximated by a Lorentz term. General but not complete agreement between experiment and theory is achieved for both two-band and multi-band models.

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=AD0403642&Location=U2&doc=GetTRDoc.pdf

Electron transport phenomena in bismuth at liquid helium temperatures, part 1

Shubnikov-de Haas effect was observed in Bi and Bi 100- x Sb x alloys ( x is the atomic percentage of Sb) with x =0.1, 0.5 and 1.4 in pulsed high magnetic fields up to 45 T. It was found that the relative amplitude of quantum oscillation was greatly enhanced, by doping a small amount of Sb into pure Bi. An explanation is made for the enhancement of Shubnikov-de Haas oscillation based upon the theory of the diffusion size effect, assuming that the bulk electron-hole recombination time is much smaller in Bi 100- x Sb x than in Bi.

Magnetoresistance Study of Bi and Bi–Sb Alloys in High Magnetic Fields. I. Enhancement of Shubnikov-de Haas Oscillation Amplitude in Bi–Sb Alloys

Recently linearized versions of the augmented plane wave (APW) method have been introduced. The quadratic-APW (QAPW) method is presented which is a more general formulation of the linear-APW (LAPW) methods. Here the exact radial solution inside the muffin-tin (MT) sphere is replaced by its Taylor expansion with respect to the energy, truncated after the quadratic term, i.e. with higher accuracy when compared with the standard LAPW method which uses only the linear term. The standard LAPW method is obtained as a special case from our formulation. Similarly to the standard LAPW method, the energy independent APW's are formed from approximate radial wave functions which lead to the secular equations linear in energy. The analysis of the solution inside the MT-sphere shows that the eigenvalue error is proportional to (E-E0)6 in the method suggested as compared with (E-E0)4 for the standard LAPW method. As an application both non-self-consistent and self-consistent calculations are presented for the band structure of FCC copper metal.

Quadratic augmented plane wave method for self-consistent band structure calculations

Quantum oscillations of magnetoresistance and thermomagnetic power of AsxSb1−x (0 ≦ x ≦ 1) alloys in stationary magnetic fields up to 15 T at low temperatures (1.9 ≦ T ≦ 17 K) are investigated. In the alloys, with x ≦ 0.3, the quantum oscillations of thermomagnetic power with a “giant” amplitude are observed. The peculiarities of the energy spectrum reconstruction are determined and the composition range in which a break of the hole necks occurs is defined. It is established that AsSb alloys are semimetals in which overlapping of the hole and electron terms in the first approximation increases linearly with increasing x.



[Russian Text Ignored]

Quantum Oscillations of Magnetoresistance and Thermomagnetic Power and the Fermi Surface of As-Sb Alloys

The two-band model described here, based on the parabolic dispersion law and elastic scattering approximation is capable to explain many aspects of the Shubnikovde Haas effect, although the elastic scattering approximation is not suitable for ail experiments mentioned. We have satisfactorily explained the phase shift between oscillations of different components of the resistivity tensor. The oscillation amplitude of the longitudinal magnetoresistance Bi can also be well fitted. These effects have been interpreted by authors of the experiments [2, 3] in another way, based on the assumption of dominant contribution of inter-level scattering. They obtain a worse fit and also their Dingle temperatureT
D=15 K is less realistic thanT
D=3 K suitable for the fitting presented in section 5b of this paper. It has also been shown that the oscillation amplitude of the transverse and nondiagonal (Hall) components of the resistivity is strongly affected by the difference between the numbers of electrons and holes. This effect might also be responsible for the large enhancement of the oscillation amplitude due to alloying in Bi, doped with Sb [1], as in available samples the precise compensation is usually not achieved.

Oscillation amplitudes of the Shubnikov-dehaas effect

The developed version of the augmented plane wave method yields eigenvalues and eigenfunctions with higher accuracy than the standard LAPW, preserving its computational efficiency.

Linearized augmented plane wave method utilizing the quadratic energy expansion of radial wave functions

Numerical solution of the radial schrödinger equation in the inverse cubic scale

The matrix elements of the coordinate, the momentum and the gradient of the potential give equivalent interband transition probabilities when the initial and the final states are exactly known In calculations based on the muffin-tin potential the approximate core state is assumed to be completely localized in one muffin-tin Then the different matrix elements are no longer equivalent They are related by expressions involving the amplitudes of the wave functions and their logarithmic derivatives at the muffin-tin radius The discussion and the numerical example show that the most appropriate form for the numerical calculation turns out to be the matrix element of the gradient of the potential

Soft x-ray transition probability: calculation based on the muffin-tin potential

The Kubo formula and the CPA averaging procedure are used to express the thermogalvanomagnetic coefficients for the electrons described by the parabolic dispersion law and scattered by the zero-range randomly distributed static impurities. Their dependence on the magnetic fields is calculated numerically, and the results are compared with the approximate treatment based on the Poisson summation formula.

Quantum oscillations of the thermogalvanomagnetic transport coefficients: CPA model calculation

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