Frozen-phonon Approach Research Articles

Electron-phonon interactions in the copper oxides: Implications for the resistivity.

The effects of strong Coulomb correlations on the electron-phonon interaction are calculated using a frozen-phonon approach applied to the extended Hubbard, infinite-{ital U} Hamiltonian. As the insulator is approached the electron-phonon interaction becomes progressively weakened due to the inability to transfer charge. Both the magnitude and concentration {ital x} dependence of {ital m}{sup *}/n are consistent with experiment. While there are no clear experimental trends for variations of 1/{tau} with {ital x}, the magntiude is in agreement with the data. That the calculated electron-phonon contribution to {rho} is nearly linear and found to account for most of the observed magnitude must be recognized in estimating the importance of other electronic or magnetic scattering contributions to the linear resistivity.

Vibrational frequencies via total-energy calculations. Applications to transition metals

The important longitudinal ($\frac{2}{3},\frac{2}{3},\frac{2}{3}$) vibrational modes in Mo, Nb, and bcc Zr as well as the $H$- point modes in Mo and Nb have been studied using the frozen-phonon approach. These entirely first-principles calculations involve the precise evaluation of the total crystalline energy as a function of lattice displacement and yield calculated phonon frequencies to within a few percent of the experimental values. Anharmonic terms are readily obtained and are found to be very important for causing the tendency toward the $\ensuremath{\omega}$-phase instability in bcc Zr. The charge densities and single-particle energies obtained in the course of the calculations allow a detailed analysis of the electronic response to lattice distortions and the mechanisms causing phonon anomalies. The calculations also provide first-principles benchmarks at a few wave vectors where the validity of phenomenological models can be tested or their parameters determined.

Microscopic analysis of interatomic forces in transition metals with lattice distortions

It is now possible to calculate accurately vibrational frequencies for transition metals entirely from first principles using the frozen-phonon approach. In addition, the interatomic forces arising from the electronic response to a particular phonon distortion can be calculated by making use of the Hellmann-Feynman theorem. Analysis of these forces helps in visualizing the complicated microscopic interactions responsible for phonon anomalies. The techniques and analysis are demonstrated for the important longitudinal ($\frac{2}{3}$,$\frac{2}{3}$,$\frac{2}{3}$) phonon in Mo, Nb, and bcc Zr. The stiffening of this mode as the electron-per-atom ratio increases from Nb to Mo is shown to arise from a development of directional bonding. The precipitous dip in this mode for the high-temperature bcc phase of Zr and the instability of bcc Zr towards the formation of the $\ensuremath{\omega}$ phase are related to the $d$-electron screening and details of the electronic structure.

Calculation of the lattice dynamical properties of Ge

The lattice dynamical properties of Ge are studied employing a frozen phonon approach within an ab initio density-functional pseudopotential formalism. Using the atomic number, atomic mass, and crystal structure as the only input information, we calculate phonon frequencies and mode Grüneisen parameters at Γ and X and the third-order anharmonic parameter for the zone center optical mode. The results are in excellent agreement with available experimental data. An analysis of various energy contributions to the TA ( X) mode shows that the proper inclusion of the exchange-correlation energy is crucial for accurate microscopic studies of lattice dynamics.