Crystal Momentum Space Research Articles

Fermi surfaces in Nb3Sn through positron annihilation

In order to understand superconductivity in A15 structure compounds, two-dimensional angular correlation of positron annihilation radiation (2D-ACPAR) has been measured in a single crystal of Nb3Sn for three orientations (100), (110) and (210). Also band-structure calculations using the self-consistent linear muffin-tin orbital (LMTO) method are performed for Nb3Sn. A comparison between experiment and theory at different stages of the analysis shows in general good agreement. The measured momentum distributions are folded to the crystal momentum space, followed by a three-dimensional reconstruction of the occupation density. The extracted Fermi surfaces (FS) reveal the presence of a cube-shaped hole pocket, responsible for the high superconducting transition temperature (Tc=18 K), which seems to be a feature of all FS of high-Tc A15 compounds.

Effects of Imperfect Fermi-Surface Nesting on Properties of Itinerant Electron Antiferromagnet

In the itinerant electron theory of antiferromagnetism one postulates that the Fermi surface of the metal has two sheets which can be brought into point-by-point fit by a translation in the crystal momentum space. The wave vector of the spin-density wave corresponds to the amount of translation. In real metals the pieces of Fermi surface do not nest exactly. We have explored some consequences of imperfect Fermi-surface nesting on the basis of a one-band model. We find that there exists a minimum value of the interaction strength below which antiferromagnetism does not occur; and when antiferromagnetism does occur the ratio 2Δ0/kTN is always greater than 3.5. These results were also obtained in more elaborate model of Kimball and Falicov. However, in contrast to Kimball and Falicov, we find a second-order phase transition at TN. This is perhaps due to the oversimplification of our model. If the exchange interaction is not strong enough to stabilize antiferromagnetism, the result is a nearly antiferromagnetic material in which a new type of paramagnon may be found. Some physical properties of these virtual modes are discussed.

Two-Stream Instability in Hot-Electron Systems of Many-Valley Semiconductors

Feasibility of observing growing two-stream instability arising from the interaction of hot electrons in many-valley semiconductors (germanium and silicon) has been investigated by the use of Boltzmann equation. The anisotropy of the band structure has been incorporated in the dispersion relation by successive coordinate transformations and by the Herring-Vogt transformation in crystal momentum space. Drift velocities, temperatures, and densities of individual valleys have been calculated by modifying the theory of Reik and Risken and using these values the dispersion relationships have been evaluated for the (1, 0, 0), (1, 1, 1), and (1, 1, 0) directions for germanium and for the (1, 1, 1) and (1, 0, 0) direction for silicon. The calculation based on the collisionless Boltzmann equation shows a positive growth rate for the (1, 1, 1) direction in germanium, but collision damping is so severe in the hot electron region that no net growth of instability may occur. In all other cases, both in germanium and silicon the waves are damped at all wavevectors even without collision damping because of Landau damping.

The Calculation of Metallic Hall Constants: Topological Aspects and Applications to Copper

The theoretical prediction of the Hall constant in metals appropriate to high magnetic fields depends, in part, on a repeated computation of a specific topological invariant: Each of several parallel two-dimensional planes in crystal-momentum space must be analyzed to find, on a single sheet of the Fermi surface, the number of nonintersecting closed contours that surround an arbitrary point. This number is related to the effective sign of the charge of the “relevant” electronic carriers in the plane — carriers whose contribution to the Hall constant is based on their orbital area. Applications of the technique discussed in this paper have been made to the Pippard model for copper, and various carrier contours are illustrated that were found in the course of three calculations of the Hall constant in cases where the magnetic field direction lay along a principal crystallographic axis.

Phonon-drag thermomagnetic effects in n-germanium

An investigation of the thermomagnetic properties of extrinsic germanium shows that the phonon-drag contribution far outweighs that due to electron diffusion at all temperatures except when near intrinsic. All the results are understandable theoretically in terms of a model which assigns to each ellipsoidal energy shell in crystal-momentum space an anisotropic phonon-drag Peltier tensor. The temperature and energy dependence of the two components of this tensor give valuable information on the law of phonon-phonon scattering. The transverse high-field magnetoresistance, and at high temperatures the thermomagnetic effects, are found to be sensitive to small amounts of surface conduction.

Phonon-Drag Thermomagnetic Effects inn-Type Germanium. I. General Survey

In a magnetic field H and a thermal gradient $\ensuremath{\nabla}T$, a conductor develops a Nernst field $\ensuremath{-}B\mathrm{H}\ifmmode\times\else\texttimes\fi{}\ensuremath{\nabla}T$ and its thermoelectric power $Q$ depends on H. These two effects have been measured for a number of single-crystal six-armed samples of high-purity $n$-type germanium, with various orientations, at fields up to 18 000 gauss and at a number of temperatures from the liquid-hydrogen range to the onset of intrinsic conduction; the most detailed measurements were made near liquid air temperature. Both the Nernst coefficient $B$ and the quantity $\ensuremath{\Delta}Q=Q(\mathrm{H})\ensuremath{-}Q(0)$ are compounded additively out of terms arising from diffusion of the electrons and terms arising from their anisotropic scattering by the phonons moving from hot to cold. The latter terms are strongly predominant at low temperatures. They give rise to a positive contribution ${B}_{p}$ to the low-field $B$ which outweighs the negative electron-diffusion contribution for $Tl175\ifmmode^\circ\else\textdegree\fi{}$K, and which can be expressed in terms of Hall mobility ${\ensuremath{\mu}}_{H}$ and phonon-drag thermoelectric power ${Q}_{p}$ by ${B}_{p}=\frac{{\ensuremath{\zeta}}_{p}|{Q}_{p}|{\ensuremath{\mu}}_{H}}{c}$ with ${\ensuremath{\zeta}}_{p}\ensuremath{\approx}0.25$ over most of the range. Theoretically and experimentally, $\mathrm{BH}\ensuremath{\rightarrow}0$ as $H\ensuremath{\rightarrow}\ensuremath{\infty}$. As expected, $\ensuremath{\Delta}Q(\mathrm{H})$ resembles the magnetoresistance both in its anisotropy and in its variation with H. All the results are understandable theoretically in terms of a model which assigns to each ellipsoidal energy shell in crystal-momentum space an anisotropic phonon-drag Peltier tensor with principal components ${\ensuremath{\Pi}}_{p\mathrm{II}}$ in the high-mass direction, ${\ensuremath{\Pi}}_{p\ensuremath{\perp}}$ in the low-mass direction. The data show that $\frac{{\ensuremath{\Pi}}_{p\mathrm{II}}}{{\ensuremath{\Pi}}_{p\ensuremath{\perp}}}\ensuremath{\gg}1$ but the mass-relaxation-time anisotropy $\frac{{{m}_{\mathrm{II}}}^{*}{\ensuremath{\tau}}_{\ensuremath{\perp}}}{{{m}_{\ensuremath{\perp}}}^{*}{\ensuremath{\tau}}_{\mathrm{II}}}\ensuremath{\approx}17$. The effective average of ${\ensuremath{\Pi}}_{p\mathrm{II}}$ and ${\ensuremath{\Pi}}_{p\ensuremath{\perp}}$ increases slightly with decreasing energy of the shell, as it should if the relaxation times of the phonons vary with wave number $q$ at a rate between ${q}^{\ensuremath{-}1}$ and ${q}^{\ensuremath{-}2}$. A more quantitative analysis is possible and will be given in a forthcoming paper.