Fermi Surface Model Research Articles

Open orbits in Hg3-δAsF6

Open orbits in the linear-chain mercury compound Hg3- delta AsF6 were investigated by the induced torque method at a temperature of 1.3K with magnetic fields up to 8.5 T. There is a primary open orbit in the (001) direction for all field directions in the (001) plane. It runs along electron and hole Fermi surface cylinders directed parallel to the direction kc. There are also open orbits in (01n) directions where n>or=2. They result from magnetic breakthrough with a breakdown field of approximately 6.6 T between electron and hole cylinders. The results confirm the Fermi surface model formed from one-dimensional bands and show that there is a variation in the separation of electron and hole cylinders along the direction kc.

Ultrasonic attenuation in copper at low temperatures

Ultrasonic attenuation in copper at low temperatures has been analysed in terms of electron-electron and electron-phonon interactions. The contribution due to electron-electron interactions has been evaluated using a simplified spherical Fermi-surface model with an isotropic Umklapp transition probability. We observe that the contribution to the attenuation constant (α) due to electron-electron scattering in copper at 3 K is about 10% of the electron-phonon contribution. We have also considered the viscous attenuation and the induction attenuation mechanisms simultaneously in copper as suggested by Orlov and find that our results improve the existing theoretical data considerably.

The Fermi surface of In 5Bi 3 from DHVA measurements

De Haas van Alphen data on In 5Bi 3 single crystals in magnetic fields up to 35 T are presented. A Fermi surface model is proposed based on symmetry considerations, on the angle dependency of the data and on the compensation of electron- and hole-pieces. The model is additionally based on the observation of high effective masses for the dominant pieces of the Fermi surface, indicating a flat character of the corresponding energy bands.

Field dependence of the galvanomagnetic coefficients in lead single crystals

The authors have measured the transverse magnetoresistance and the Hall coefficient of lead single crystals for the field along the (100) and the (110) axes. Emphasis has been placed on their field dependence and on their temperature dependence in the intermediate-field range. The field-dependent galvanomagnetic coefficients have also been computed by path integration based on the 4 OPW Fermi surface model. The agreement between experiment and the computation is very good, though some discrepancies remain for the field along the (110) axis in the high-field range. At lower temperatures, some deviation from Kohler's rule is found in the low-field Hall coefficient.

Transverse Magnetoresistance and Shubnikov-de Haas Effect in Intermetallic Compounds InBi and In2Bi

The transverse magnetoresistance of intermetallic compounds InBi and In 2 Bi have been studied at 4.2 K in magnetic fields up to 100 kOe. Shubnikov-de Haas oscillations of InBi were observed for the fields over 60 kOe. The results indicate that InBi is a compensated metal with all closed orbits. These are compared with a Fermi surface model proposed already by Schirber et al . In 2 Bi is an uncompensated metal with an open orbit along the direction. The present results are compared with the nearly free electron model which contains a multiply connected Fermi surface.

Magnetoacoustic oscillations and the Fermi surface of LaAg

Magnetoacoustic oscillations in LaAg at low temperatures and high magnetic fields are presented. The de Haas-Shubnikov frequencies are interpreted using a Fermi surface model deduced from a band structure calculation.

Fermi surface ofHg3−δAsF6andHg3−δSbF6

Measurements of the de Haas --- van Alphen frequencies in ${\mathrm{Hg}}_{3\ensuremath{-}\ensuremath{\delta}}\mathrm{As}{\mathrm{F}}_{6}$ and ${\mathrm{Hg}}_{3\ensuremath{-}\ensuremath{\delta}}\mathrm{Sb}{\mathrm{F}}_{6}$ show that the Fermi surface of these compounds consists of cylinders with axes parallel to the $c$ direction. A detailed model of the Fermi surface of these mercury linear-chain compounds is constructed for conduction electrons in the mercury chains. The cross-sectional areas of the Fermi-surface cylinders are accounted for by the Fermi-surface model. Cyclotron masses measured for some of the orbits are in satisfactory agreement with those predicted by the model. The excellent agreement between measured and predicted cross-sectional areas for both compounds shows that the model is valid for a range of values of the incommensurability parameter $\ensuremath{\delta}$.

Macroscopic description of the giant quadrupole resonance in rotating nuclei

The distorted Fermi-surface model is generalized to study the giant quadrupole resonance behaviour in rotating nuclei. The mathematical problems of the model are solved with the help of the tensor virial method of Chandrasekhar and Lebovitz.

Helicon Resonance on Thallium

The dimensional resonance of helicon waves in thallium has been studied at 1.3 K in the magnetic field H applied along [0001]. From data of the fundamental resonance the carrier concentration is determined as 2.0 ×10 22 cm -3 , which is in good agreement with the value obtained from a dc measurement of the Hall effect. Considering the Fermi surface (FS) model of Holtham and Priestley, it follows that the major carrier in thallium is hole for H //[0001], which fact is also confirmed by the dc measurement. The analysis of half-value widths of resonance peaks reveals that the magnetoresistivity saturates at the higher field region. This is consistent with the FS model demonstrating the absence of an open orbit just for H //[0001].

Electrical resistivity of alkali metals at low temperatures

Abstract The contribution of electron-electron Umklapp scattering processes in the electrical resistivity of sodium, potassium, rubidium, and cesium at low temperatures has been evaluated using a simplified spherical Fermi surface model with an isotropic transition probability. Our values of the electrical resistivity so obtained compare fairly well with the recent experimental results for sodium, potassium, and rubidium. Our results also compare fairly well with the other available data in the literature.

Electron interactions and the electrical resistivity of alkali metals at low temperatures

The contribution of the electron-electron umklapp scattering processes to the electrical resistivity of sodium, potassium, rubidium and cesium at low temperatures has been evaluated using a simplified spherical Fermi-surface model with an isotropic transition probability. Our values of the electrical resistivity so obtained compare fairly well with the recent experimental values for sodium, potassium and rubidium. Our theoretical results have also been compared with the other available data in the literature due to Lawrence and Wilkins and MacDonald and Geldart.

Transverse Magnetoresistance of LaB6

The transverse magnetoresistance of LaB 6 , single crystals has been studied at 1.5 K in magnetic fields up to 60 kOe. Open orbits along [110] and [001] are observed for H along θ=27° (from [001]) in the (1\bar10) plane and at most field directions (except near θ=0°) in the (010) plane, respectively. The [001] direction is a singular field direction. The low frequency oscillations with the order of 10 4 gauss are superimposed on the monotonic magnetoresistance. Present results are consistent with a multiply-connected Fermi surface model proposed already from de Haas-van Alphen experiments.

Ultrasonic attenuation in potassium at low temperatures

Abstract The contribution of the electron-electron interactions to the ultrasonic attenuation in potassium at low temperatures has been evaluated using a simplified spherical Fermi-surface model with an isotropic umklapp transition probability. Our results show that the e-e scattering processes contribute very little to the ultrasonic attenuation in K at low temperatures as compared to the electron-photon interactions.

Magnetoresistance of aluminium computed by the path-integral method

The field dependence of the magnetoresistance of aluminium is computed by the path-integral method on the basis of the 4-OPW Fermi surface (FS) model. The published data of electron-phonon relaxation time at 20 K and those of electron-Ag impurity scattering time are introduced. The computed magnetoresistance is highly enhanced by the anisotropy in the relaxation time. The results obtained explain the previously discovered anomalous dependence of the magnetoresistance on temperature and impurity concentration tolerably well.

Phonon-limited mean free path in the Sondheimer oscillation of aluminum

The phonon-limited part of the electron mean free path l Hp ,in aluminum has been investigated by the Sondheimer size effect for a magnetic field along the three principal crystallographic orientations in the temperature range 1.8–12 K. It is found that l Hp decreases with temperature approximately as T −3 and varies from 1.4 × 10−3 to 1.3 × 10−2 cm, with the orbits responsible for the oscillations at 20 K. The results are in agreement with a calculation based on the 4-OPW Fermi surface model and the anisotropic electron-phonon scattering time given by Leung et al.

Field-dependent tensor study of carrier transport in antimony and its alloys

Abstract Magnctoresistivity tensor components have been measured as a function of orientation and magnetic field in single crystals of antimony and its p-type alloys with tin (up to 1.0 at.%) and germanium (up to 2.2 at.%). The components of the electron and hole mobility tensors, the carrier densities and the tilt angles of the Fermi surface pockets have been computed from the experimental results by a Monte-Carlo minimization procedure on the basis of a multi-valley, ellipsoidal Fermi surface model. The validity of the field-dependent tensor method has first been checked on antimony itself by comparing the computed model parameters with those obtained previously by tlie low-field method: the good agreement obtained establishes that the field-dependent tensor technique applies to the gaivanomagnetic effects of antimony and should be capable of extension to its alloys. Details of the temperature and concentration dependences of the carrier transport properties have been obtained for the antimony alloys fo...

Quantum oscillations of thermopower of gallium single crystals

We present experimental results of the transverse thermopower of high- purity gallium single crystals in magnetic fields up to 41.8kG. Giant quantum oscillations in the magnetothermopower appear for a magnetic field parallel to the c-axis and a temperature gradient ▽ T along the b-axis. The results are compared with the existing data of the transverse magneto- resistivity, the de Haas-van Alphen effect as well as with the Fermi surface model of gallium due to Reed's calculation.

Phonons and superconductingp-state pairing in Pd

We present an analytical calculation of the electron-phonon parameters for $s$- and $p$-state pairing in Pd, ${\ensuremath{\lambda}}_{0}^{\mathrm{ph}}$ and ${\ensuremath{\lambda}}_{1}^{\mathrm{ph}}$. The calculation is based on Doniach's six half-sphere Fermi-surface model for the heavy $d$ electrons, a Debye and an Einstein model for intra- and intersphere phonon-scattering processes, respectively, and the LCMTO (linear combination of muffin-tin orbitals) representation to obtain the electron-phonon matrix elements. The group-theoretical method of Allen is employed in solving the anisotropic gap equation at the multiply sheeted Fermi surface for $s$- and $p$-state pairing interactions. The phonon-mediated interaction, ${I}^{\mathrm{ph}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}},{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}^{\ensuremath{'}})$ is attractive for all momentum transfers, $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ensuremath{-}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}^{\ensuremath{'}}$, and yields the BCS parameter, ${\ensuremath{\lambda}}_{0}^{\mathrm{ph}}=0.153$, in agreement with Papaconstantopoulos et al. Our results for $p$-state pairing is ${\ensuremath{\lambda}}_{1}^{\mathrm{ph}}=0$, when Einstein phonon model is used for both intra- and intersheet scattering processes and ${\ensuremath{\lambda}}_{1}^{\mathrm{ph}}=0.089{\ensuremath{\lambda}}_{0}^{\mathrm{ph}}$ when the Debye model is applied to the small-momentum intrasheet transitions of the Cooper pairs. The weakness of the $p$-state interaction is due to the cancellation between the contributions from intrasheet scattering and from large-momentum intersheet scattering processes. A detailed discussion of the results is presented in terms of the parameters of our electron-phonon model.

Square Fermi surface model for conduction in linear chain mercury compounds: Hg3−δAsF6

Abstract The unusual temperature dependence of the electrical resistivity of Hg 3− δ AsF 6 ( δ = 0.18−0.22) is discussed in the framework of a nearly square Fermi surface model. This model predicts a T 3 dependence of the resistivity, in close agreement with the recently observed T 2.8 dependence.

Hall coefficient of dilute Al-Ga and Al-Ag alloys

The Hall coefficients of dilute Al-Ga and Al-Ag alloys are calculated in the intermediate magnetic-field range by path integration. The 4-OPW (orthogonalized plane wave) Fermisurface model is used. The anisotropic electron-impurity relaxation time is included. The computational procedure of the path-integral calculation is described. The calculated Kohler plot agrees well with experiment. The effect of the anisotropy in the relaxation time on the feature of the Kohler plot of the alloys is discussed.