Nonlinear couplings in solids from derivatives of first-principles total energy

ORAL  · Invited

Abstract

In the first part of the talk, I will present selected past achievements in the direct computation of nonlinear couplings in solids within density-functional theory (DFT), from the eighties up to now [1-10]. Adiabatic nonlinear couplings are third- or higher-order derivatives of the total energy with respect to applied perturbations of the system. Many different types of perturbations can be considered: atomic displacements (single or collective, like phonons), electric or magnetic fields, lattice deformations, and also spatial gradients thereof, etc. The related couplings (also considering mixing perturbations) deliver Raman cross-section, second-harmonic generation, Grüneisen parameters and thermal expansion, dynamical quadrupoles, flexoelectrity, optical activity, etc. They can be directly accessed within density-functional perturbation theory (DFPT), especially using the so-called 2n+1 theorem. Generalisation to the time-dependent case has also been developed.

The second part of the talk will focus on (isotropic or anisotropic) thermal expansion [11-12], and then on the non-linear (2nd order) electron-phonon interaction needed to compute Debye-Waller (DW) contribution to the renormalization of the band gap [13-14]. For both of these, practical DFT calculations involve variations on the DFPT theme. If computed solely from Grüneisen parameters, the thermal expansion is quite inaccurate at moderate temperatures (e.g. below Debye temperature). Second derivatives of the phonon free energy with respect to lattice deformations are mandatory to obtain excellent agreement (up to about 800K) for a dozen tested materials, including temperature-dependent lattice parameters and angles for materials like monoclinic ZrO2 or triclinic Al2SiO5. The Debye-Waller (DW) contribution to the zero-point renormalization (ZPR) of the electronic band gap comes from the second-order electron-phonon vertex. It is combined with the Fan contribution, coming from two first-order electron-phonon vertices. Both are needed to obtain reasonable agreement with measured ZPR. Actually the DW contribution can be computed from first-order electron-phonon couplings when the rigid-ion approximation is invoked. I will discuss why this is made possible, and show its usefullness beyond the ZPR case.

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Publication: [1] Density-functional approach to nonlinear-response coefficients of solids. X. Gonze and J.-P. Vigneron, Phys. Rev. B 39, 13120 (1989)
[2] Adiabatic density-functional perturbation theory. X. Gonze, Phys. Rev. A52, 1096 (1995).
[3] Density-functional theory of the nonlinear optical susceptibility: Application to cubic semiconductors. A. Dal Corso and F. Mauri and A. Rubio, Phys. Rev. B 53, 15638 (1996)
[4] Anharmonic effects in the phonons of III--V semiconductors: first principles calculations. A. Debernardi, Solid State Communications 113, 1 (2000).
[5] Phonons and related crystal properties from density-functional perturbation theory. S. Baroni, S. de Gironcoli, A. Dal Corso and P. Giannozzi. Rev. Mod. Phys. 73, 515 (2001).
[6] Nonlinear optical susceptibilities, Raman efficiencies, and electro-optic tensors from first-principles density functional perturbation theory. M. Veithen, X. Gonze, and Ph. Ghosez, Phys. Rev. B 71, 125107 (2005)
[7] Electron-phonon beyond Fröhlich: dynamical quadrupoles in polar and covalent solids. G. Brunin et al, Phys. Rev. Lett. 125, 136601 (2020)
[8] Natural optical activity from density-functional perturbation theory. A. Zabalo and M. Stengel. Phys. Rev. Lett. 131, 086902 (2023).
[9] Variational density functional perturbation theory for metals. X. Gonze, S. Rostami and Ch. Tantardini. Phys. Rev. B 109, 014317 (2024).
[10] Ensemble density functional perturbation theory: Spatial dispersion in metals. A. Zabalo and M. Stengel. Phys. Rev. B 109, 245116 (2024).
[11] Approximations in first-principles volumetric thermal expansion determination. S. Rostami and X. Gonze. Phys. Rev. B 110, 014103 (2024).
[12] Anisotropic temperature-dependent lattice parameters and elastic constants from first principles. S. Rostami, M. Giantomassi and X. Gonze. npj Comput. Materials, 11, 271 (2025)
[13] Temperature dependence of the electronic structure of semiconductors and insulators. S. Poncé and Y. Gillet and J. Laflamme Janssen and A. Marini and M. Verstraete and X. Gonze. J. Chem. Phys. 143, 102813 (2015).
[14] Predominance of non-adiabatic effects in zero-point renormalization of the electronic band gap. A. Miglio et al, npj Comput. Materials, 6, 167 (2020).

Presenters

  • Xavier Gonze

    • Universite catholique de Louvain

Authors

  • Xavier Gonze

    • Universite catholique de Louvain