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 affect the spectrum in resonance conditions. The ability to analyze second-order Raman spectra thus provides direct insight into this interaction.Comment: 10 pages, 8 figure

Vibrational Effects in X-ray Absorption Spectra of Two-Dimensional Layered Materials

With the examples of the C K-edge in graphite and the B K-edge in hexagonal boron nitride, we demonstrate the impact of vibrational coupling and lattice distortions on the X-ray absorption near-edge structure (XANES) in two-dimensional layered materials. Theoretical XANES spectra are obtained by solving the Bethe–Salpeter equation of many-body perturbation theory, including excitonic effects through the correlated motion of the core hole and excited electron. We show that accounting for zero-point motion is important for the interpretation and understanding of the measured X-ray absorption fine structure in both materials, in particular for describing the σ*-peak structure

First-principles study of second-order Resonance Raman scattering of silicon

In this work, we want to investigate the evolution of the second-order Raman scattering process when the laser frequency is changed. The second-order intensity can be computed from the generalization of the approach used for first-order intensity [Y. Gillet et al, Phys. Rev. B 88, 094305 (2013) and C. Ambrosch-Draxl et al, Phys. Rev. B 65, 064501 (2002)], combining multiple finite difference calculations with supercells generated on different points in the Brillouin Zone. We present the general methodology and the results obtained in the silicon case

First-Principles Study of Frequency-Dependent Resonant Raman Scattering

A resonance phenomenon appears in the Raman response when the exciting light has frequency close to electronic transitions. Unlike for molecules and for graphene, the theoretical prediction of such frequency-dependent Raman response of crystalline systems has remained a challenge. Indeed, many Raman intensity first-principle calculations are nowadays done at vanishing light frequency, using static Density-Functional Perturbation Theory, thus neglecting the frequency dependence and excitonic effects. Recently, we proposed a finite-difference method for the computation of the first-order frequency-dependent Raman intensity [1], with excitonic effects described by the Bethe-Salpeter equation. We found these to be crucial for the accurate description of the experimental enhancement for laser photon energies around the gap. In this work, we generalize this approach to the more complex second-order Raman intensity, with phonon losses coming from the entire Brillouin zone. Interestingly, even without excitonic effects, one is able to capture the main relative changes in the frequency-dependent Raman spectrum at fixed laser frequencies. The excitonic effects are discussed. [1] Y. Gillet, M. Giantomassi, X. Gonze, Phys. Rev. B 88, 094305 (2013)

First-principles study of frequency-dependent Resonant Raman scattering

Raman spectroscopy is a widely used technique for materials characterization. The dependence of the Raman intensity on the frequency of the incident light is well known: a resonance phenomenon appears when the exciting light has frequency close to electronic transitions. Unlike for molecules and for graphene, the theoretical prediction of the frequency-dependent Raman response of crystalline systems has remained a challenge. Indeed, many Raman calculations are nowadays done in the static limit (vanishing light frequency), using Density-Functional Theory and Density-Functional Perturbation Theory, thus neglecting frequency-dependence and excitonic effects. In this work, we present a finite difference method to obtain the frequency-dependent Raman intensity. Excitonic effects, included by solving the Bethe-Salpeter Equation are crucial to describe accurately the enhancement of the absolute first-order Raman intensity of silicon for laser photon energies corresponding to the gap of the material [1]. The approach is then generalized to second-order Raman scattering. The comparison of the simulations with experimental measurements shows that the Random-Phase Approximation (i.e. neglecting excitonic effects) is able to capture the main changes in frequency-dependence relative intensities. [1] Y. Gillet, M. Giantomassi, X. Gonze, Phys. Rev. B 88, 094305 (2013)

Vibrational Effects in X-ray Absorption Spectra of Two-Dimensional Layered Materials

With the examples of the C K-edge in graphite and the B K-edge in hexagonal boron nitride, we demonstrate the impact of vibrational coupling and lattice distortions on the X-ray absorption near-edge structure (XANES) in two-dimensional layered materials. Theoretical XANES spectra are obtained by solving the Bethe–Salpeter equation of many-body perturbation theory, including excitonic effects through the correlated motion of the core hole and excited electron. We show that accounting for zero-point motion is important for the interpretation and understanding of the measured X-ray absorption fine structure in both materials, in particular for describing the σ*-peak structure.Funding agencies:  Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linkoping University [2009 00971]; Knut and Alice Wallenbergs Foundation; Swedish Energy Research [43606-1]; Carl Trygger Foundation [CTS16:303, CTS14:310]; JSPS KA</p

First-Principles Study of Frequency-Dependent Resonant Raman Scattering

A resonance phenomenon appears in the Raman response when the exciting light has frequency close to electronic transitions. Unlike for molecules and for graphene, the theoretical prediction of such frequency-dependent Raman response of crystalline systems has remained a challenge. Indeed, many Raman intensity first-principle calculations are nowadays done at vanishing light frequency, using static Density-Functional Perturbation Theory, thus neglecting the frequency dependence and excitonic effects. During this presentation, I will describe the finite-difference method we propose to compute frequency-dependent Raman intensities. Recently, we used this methodology for the computation of the first-order frequency-dependent Raman intensity [1], with excitonic effects described by the Bethe-Salpeter equation. We found these to be crucial for the accurate description of the experimental enhancement for laser photon energies around the gap. This approach can be generalized to the more complex second-order Raman intensity, with phonon losses coming from the entire Brillouin zone. Interestingly, even without excitonic effects, one is able to capture the main relative changes in the frequency-dependent Raman spectrum at fixed laser frequencies. However, excitonic effects might affect significantly the intensity of specific modes and also lead to a global tenfold increase of absolute intensities. [1] Y. Gillet, M. Giantomassi, X. Gonze, Phys. Rev. B 88, 094305 (2013)

First-principles study of frequency-dependent Resonant Raman scattering

Raman spectroscopy is a widely used technique for materials characterization. The dependence of the Raman intensity on the frequency of the incident light is well known: a resonance phenomenon appears when the exciting light has frequency close to electronic transitions. Unlike for molecules and for graphene, the theoretical prediction of the frequency-dependent Raman response of crystalline systems has remained a challenge. Indeed, many Raman calculations are nowadays done in the static limit (vanishing light frequency), using Density-Functional Theory [1] and Density-Functional Perturbation Theory [2], thus neglecting frequency-dependence and excitonic effects. In this work, we present a finite difference method to obtain the frequency-dependent Raman intensity. Excitonic effects, included by solving the Bethe-Salpeter Equation [3] are crucial to describe accurately the enhancement of the absolute first-order Raman intensity of silicon for laser photon energies corresponding to the gap of the material [4]. The approach is then generalized to second-order Raman scattering in the spirit of Ref. [5]. The comparison of the simulations with experimental measurements [6] shows that the Random-Phase Approximation (i.e. neglecting excitonic effects) is able to capture the main changes in frequency-dependence relative intensities. References [1] R. M. Martin, 'Electronic Structure', Cambridge University Press (2004). [2] M. Veithen, X. Gonze and Ph. Ghosez, Phys. Rev. B 71, 125107 (2005). [3] G. Onida, L. Reining, A. Rubio, Rev. Mod. Phys. 74, 601 (2002). [4] Y. Gillet, M. Giantomassi, X. Gonze, Phys. Rev. B 88, 094305 (2013). [5] C. Ambrosch-Draxl et al, Phys. Rev. B 65, 064501 (2002) [6] J. B. Renucci, R. N. Tyte and M. Cardona. Phys. Rev. B 11, 3885 (1975)