Fermi Surface Average Research Articles

Electron-phonon interactions in transition metals

The tight-binding method is used to calculate 〈I2〉, the Fermi surface average of the squared electron-phonon coupling constant for 4d b.c.c.—transition metals and alloys. When nonorthogonality effects are properly included, our results for 〈I2〉 agree very well with empirical values. Moreover, the variation of 〈I2〉 can be understood in simple physical terms.

Electron-phonon coupling in the transition metals: Electronic aspects

The electron-phonon coupling parameter $\ensuremath{\lambda}$ may be written as the product of three factors: the Fermi-energy density of states, $N({E}_{F})$, the Fermi-surface average of the electron-phonon interaction, $〈{I}^{2}〉$, and an effective inverse lattice force constant $\ensuremath{\Phi}$. We have calculated $〈{I}^{2}〉$ and $N({E}_{F})$ for 11 $4d$ transition-metal systems using the rigid muffin-tin approximation. We find a large but understandable variation in $〈{I}^{2}〉$ which is in good agreement with the empirical variation in $〈{I}^{2}〉$. $〈{I}^{2}〉$ varies approximately as the inverse second power of the atomic volume and as the first power of the amount of $l=3$ Fermi-energy state density within the Wigner-Seitz cell. We discuss the implications of our findings in regard to the search for systems with higher superconducting transition temperatures.

Sum Rule for Crystalline Metal Surfaces

We have derived a sum rule for the electronic scattering phase shifts in a metal, produced by a planar boundary surface. The sum rule, which states that a weighted Fermi-surface average of the asymptotic phase of the electronic wave function in the presence of a metal surface is equal to $\frac{\ensuremath{-}\ensuremath{\pi}}{4}$, is derived for the case where explicit account is taken of the energy bands and crystalline structure of the solid. This extends the sum rule originally stated by Sugiyama for a jellium model of a metal. Modifications of the sum rule in the presence of an applied electric field and for complex band structure are also considered.

Optical and Thermal Effective Masses of Copper

The optical and thermal masses of copper have been calculated from a phase-shift model of the Fermi surface and Fermi velocity. The total area of the Fermi surface is also determined. The results yield a Fermi-surface average of the renormalization of the band velocity in copper by the electron-phonon interaction, and suggest that the quasiparticle current in copper is reduced by quasiparticle interactions.

Phase Rule for Wave Functions near Metallic Surfaces

It is shown that a weighted Fermi-surface average of the asymptotic phase of the electronic wave function in the presence of a metallic surface is equal to $\ensuremath{-}\frac{1}{4}\ensuremath{\pi}$. We thus give a rigorous proof of a theorem appearing in the work of Sugiyama. An asymptotic expression for the amplitude of the charge-density wave associated with a metallic surface is also derived.

Influence of Quasiparticle Interactions on the Optical Effective Mass of Metallic Copper

Experimental measurements of the optical mass of copper are interpreted to yield a Fermi-surface average of the Landau parameter which relates the current carried by a quasiparticle excitation to its velocity.