Yannick Gillet

Temperature dependence of the electronic structure of semiconductors and insulators

The renormalization of electronic eigenenergies due to electron-phonon coupling (temperature dependence and zero-point motion effect) is sizable in many materials with light atoms. This effect, often neglected in ab initio calculations, can be computed using the perturbation-based Allen-Heine-Cardona theory in the adiabatic or non-adiabatic harmonic approximation. After a short description of the recent progresses in this field and a brief overview of the theory, we focus on the issue of phonon wavevector sampling convergence, until now poorly understood. Indeed, the renormalization is obtained numerically through a slowly converging q-point integration. For non-zero Born effective charges, we show that a divergence appears in the electron-phonon matrix elements at q → Γ, leading to a divergence of the adiabatic renormalization at band extrema. This problem is exacerbated by the slow convergence of Born effective charges with electronic wavevector sampling, which leaves residual Born effective charges in ab initio calculations on materials that are physically devoid of such charges. Here, we propose a solution that improves this convergence. However, for materials where Born effective charges are physically non-zero, the divergence of the renormalization indicates a breakdown of the adiabatic harmonic approximation, which we assess here by switching to the non-adiabatic harmonic approximation. Also, we study the convergence behavior of the renormalization and develop reliable extrapolation schemes to obtain the converged results. Finally, the adiabatic and non-adiabatic theories, with corrections for the slow Born effective charge convergence problem (and the associated divergence) are applied to the study of five semiconductors and insulators: α-AlN, β-AlN, BN, diamond, and silicon. For these five materials, we present the zero-point renormalization, temperature dependence, phonon-induced lifetime broadening, and the renormalized electronic band structure.

Temperature dependence of electronic eigenenergies in the adiabatic harmonic approximation

The renormalization of electronic eigenenergies due to electron-phonon interactions (temperature dependence and zero-point motion effect) is important in many materials. We address it in the adiabatic harmonic approximation, based on first principles (e.g., density-functional theory), from different points of view: directly from atomic position fluctuations or, alternatively, from Janak’s theorem generalized to the case where the Helmholtz free energy, including the vibrational entropy, is used.We prove their equivalence, based on the usual form of Janak’s theorem and on the dynamical equation. We then also place the Allen-Heine-Cardona (AHC) theory of the renormalization in a first-principles context. The AHC theory relies on the rigid-ion approximation, and naturally leads to a self-energy (Fan) contribution and a Debye-Waller contribution. Such a splitting can also be done for the complete harmonic adiabatic expression, in which the rigid-ion approximation is not required. A numerical study within the density-functional perturbation theory framework allows us to compare the AHC theory with frozen-phonon calculations, with or without the rigid-ion approximation. For the two different numerical approaches without non-rigid-ion terms, the agreement is better than 7 μeV in the case of diamond, which represent an agreement to five significant digits. The magnitude of the non-rigid-ion terms in this case is also presented, distinguishing specific phonon modes contributions to different electronic eigenenergies.

First-principles study of excitonic effects in Raman intensities

The ab initio prediction of Raman intensities for bulk solids usually relies on the hypothesis that the frequency of the incident laser light is much smaller than the band gap. However, when the photon frequency is a sizable fraction of the energy gap, or higher, resonance effects appear. In the case of silicon, when excitonic effects are neglected, the response of the solid to light increases by nearly three orders of magnitude in the range of frequencies between the static limit and the gap. When excitonic effects are taken into account, an additional tenfold increase in the intensity is observed.We include these effects using a finite-difference scheme applied on the dielectric function obtained by solving the Bethe-Salpeter equation. Our results for the Raman susceptibility of silicon show stronger agreement with experimental data compared with previous theoretical studies. For the sampling of the Brillouin zone, a double-grid technique is proposed, resulting in a significant reduction in computational effort.

First-principles investigation of the structural, dynamical, and dielectric properties of kesterite, stannite, and PMCA phases of Cu2ZnSnS4

Cu2ZnSnS4 (CZTS) is a promising material as an absorber in photovoltaic applications. The measured efficiency, however, is far from the theoretically predicted value for the known CZTS phases. To improve the understanding of this discrepancy we investigate the structural, dynamical, and dielectric of the three main phases of CZTS (kesterite, stannite, and PMCA) using density functional perturbation theory (DFPT). The effect of the exchange-correlation functional on the computed properties is analyzed. A qualitative agreement of the theoretical Raman spectrum with measurements is observed. However, none of the phases correspond to the experimental spectrum within the error bar that is usually to be expected for DFPT. This corroborates the need to consider cation disorder and other lattice defects extensively in this material.

Ab Initio Approach to Second-order Resonant Raman Scattering Including Exciton-Phonon Interaction

Raman spectra obtained by the inelastic scattering of light by crystalline solids contain contributions from first-order vibrational processes (e.g. the emission or absorption of one phonon, a quantum of vibration) as well as higher-order processes with at least two phonons being involved. At second order, coupling with the entire phonon spectrum induces a response that may strongly depend on the excitation energy, and reflects complex processes more difficult to interpret. In particular, excitons (i.e. bound electron-hole pairs) may enhance the absorption and emission of light, and couple strongly with phonons in resonance conditions. We design and implement a first-principles methodology to compute second-order Raman scattering, incorporating dielectric responses and phonon eigenstates obtained from density-functional theory and many-body theory. We demonstrate our approach for the case of silicon, relating frequency-dependent relative Raman intensities, that are in excellent agreement with experiment, to different vibrations and regions of the Brillouin zone. We show that exciton-phonon coupling, computed from first principles, indeed strongly affects the spectrum in resonance conditions. The ability to analyze second-order Raman spectra thus provides direct insight into this interaction.

Temperature evolution of the band gap in BiFeO3 traced by resonant Raman scattering

Knowledge of the electronic band structure of multiferroic oxides, crucial for the understanding and tuning of photo-induced effects, remains very limited even in the model and thoroughly studied BiFeO3. Here, we investigate the electronic band structure of BiFeO3 using Raman scattering with twelve different excitation wavelengths ranging from the blue to the near infrared. We show that resonant Raman signatures can be assigned to direct and indirect electronic transitions, as well as in-gap electronic levels, most likely associated to oxygen vacancies. Their temperature evolution establishes that the remarkable and intriguing variation of the optical band-gap can be related to the shrinking of an indirect electronic band-gap, while the energies for direct electronic transitions remains nearly temperature independent.

Efficient on-the-fly interpolation technique for Bethe–Salpeter calculations of optical spectra

Abstract The Bethe–Salpeter formalism represents the most accurate method available nowadays for computing neutral excitation energies and optical spectra of crystalline systems from first principles. Bethe–Salpeter calculations yield very good agreement with experiment but are notoriously difficult to converge with respect to the sampling of the electronic wavevectors. Well-converged spectra therefore require significant computational and memory resources, even by today’s standards. These bottlenecks hinder the investigation of systems of great technological interest. They are also barriers to the study of derived quantities like piezoreflectance, thermoreflectance or resonant Raman intensities. We present a new methodology that decreases the workload needed to reach a given accuracy. It is based on a double-grid on-the-fly interpolation within the Brillouin zone, combined with the Lanczos algorithm. It achieves significant speed-up and reduction of memory requirements. The technique is benchmarked in terms of accuracy on silicon, gallium arsenide and lithium fluoride. The scaling of the performance of the method as a function of the Brillouin Zone point density is much better than a conventional implementation. We also compare our method with other similar techniques proposed in the literature.