Phonons and related properties of extended systems from density-functional perturbation theory

TL;DR

The paper surveys density-functional perturbation theory (DFPT) as a robust, first-principles framework for lattice dynamics in crystals, connecting vibrational properties to electronic structure via the Born-Oppenheimer surface.It details theoretical foundations, linear and nonlinear response formalisms, and practical implementations (plane-wave pseudopotentials, ultrasoft potentials, and all-electron methods), as well as alternative approaches like dielectric matrices and frozen phonons.A wide range of applications is reviewed, including phonons in bulk crystals, alloys, surfaces, and high-pressure phases, with emphasis on agreement with experiment and insight into dielectric, piezoelectric, and anharmonic phenomena.The work highlights the 2n+1 theorem for efficiently computing higher-order responses and underscores DFPT’s growing role in predicting material properties and guiding experimental interpretation across condensed-matter systems.

Abstract

This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudo-potential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long wave-length vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.

Figures (14)

• Figure 1: Calculated phonon dispersions and densities of states for binary semiconductors GaAs, AlAs, GaSb, and AlSb. Experimental data are denoted by diamonds. (Reproduced from bulkoni.)
• Figure 2: Second-order Raman spectrum of AlSb in the $\Gamma_1$ representation at room temperature; the solid line represents the theoretical calculation, the dashed line is the experimental spectrum. (Reproduced from AlSbRaman.)
• Figure 3: Calculated phonon dispersions for fcc simple metal Al and Pb and for the bcc transition metal Nb. Solid and dashed lines refer to different smearing widths (0.3 and 0.7 eV, respectively). Experimental data are denoted by diamonds. (Reproduced from SdGmetalli.)
• Figure 4: Upper panel: calculated GGA phonon dispersions (solid lines) for magnetic bcc Fe compared to inelastic neutron scattering data (solid diamond) and to dispersions calculated within local spin density approximation (LSDA) (dotted lines). Lower panel: calculated GGA phonon dispersions (solid lines) for magnetic fcc Ni compared to inelastic neutron scattering data (solid diamond) and to calculated LSDA dispersions (dotted lines). (Reproduced from DCdG.)
• Figure 5: (a)-(h) Calculated spectral functions $\alpha^2 F(\omega)$ of the electron-phonon interaction (full lines) for the eight elemental metals considered in LMTO_metals. The behavior of the electron-phonon prefactor $\alpha^2(\omega)$ [defined simply as the ratio $\alpha^2 F(\omega)/ F(\omega)$] is shown by dashed lines. Symbols plots present the results of available tunneling experiments. (Reproduced from LMTO_metals.)