Ab initio Lattice Dynamics and Infrared Dielectric Response

Abstract

Methods for theoretically evaluating lattice dynamics, anharmonic effects and related optical properties from first principles are designed and implemented. Applications of density-functional theory and the pseudopotential approximation are adapted, via the Born-Oppenheimer approximation, the Hellmann-Feynman force theorem, and wave-commensurate supercells, to a direct calculation of the Born-von Karman force constants. With a symmetry analysis and interpolation of Born-von Karman force constants, the complete phonon spectra are obtained for the cubic systems Ar, Si, Ge, and diamond, and for the stacked hexagonal system, graphite. The phonon spectra for the polar materials GaAs and GaP, in which the degeneracy between longitudinal and transverse optical modes is lifted, are also calculated. The splitting is a consequence of the macroscopic field associated with long-range Coulombic interactions and longitudinal displacements. Diagramatically-derived expressions for the finite lifetime of the Raman mode arising from phonon-phonon interactions are calculated for Si, Ge, and diamond from first principles, and agree with experiment to within uncertainty. The infrared absorption spectra of GaAs and GaP are calculated from first principles through the phonon anharmonic self-energy (phonon-phonon interaction) and the Born effective charges (photon-phonon interaction). Several aspects of the spectra are in detailed agreement with the experimental spectra, including the strong temperature dependence of the far-infrared absorption due to the onset of difference processes; the linewidth and asymmetric lineshape of the reststrahlen; the spectral structure of the absorption by two-phonon modes, and overall oscillator strengths. The theory allows for the identification of narrow spectral transmission bands with an ionic mass mismatch in the case of GaP. Analytic and complete calculations are performed for the ion-ion displacement correlation function in solid Ar, and agree well. The correlations are evaluated for arbitrary lattice vector and Cartesian displacement directions, and their pressure dependence leads to the conjecture that anharmonic effects are less prominent at higher pressures.