The Fortran Cafe'

The Bethe-Salpeter-Equation (BSE) wine

## Collaboration Team on Electron-vibrational Coupling: Rome Meeting 2015.

15th-16th January 2015 at CNR-ISM

### Program

#### Thursday 15th

 Simon Karl Moser Tunable polaronic conduction in anatase TiO2 Anatase TiO2 has been proposed for many applications from transparent conducting panels to photovoltaic- and photocatalytic- devices, as well as memristors. However, little is known about the dynamics of the photoexcited or doped-in charge carriers in this textbook insulator. In this presentation, we show that the number of conduction electrons in anatase, and their nature, can be controlled by UV light in a reversible way. Oxygen vacancies created in the beam spot liberate electrons which populate the bottom of the conduction band. At low densities, these electrons are dressed by lattice vibrations, and behave as a gas of weakly interaction large polarons. At larger densities, the quasiparticles spatially overlap, lose their identity, and eventually dissolve into a weakly correlated Fermi liquid. Hui Shang First-principles Evidence for Intermediate Hole Polarons in ZnO We performed density functional theory calculations at the hybrid-functional level (HSE06) to investigate the nature of the polaronic states in ZnO. Our calculations confirm that neither small~(i.e., strong coupling) electron nor hole polarons are stable in ZnO, in agreement with previous studies [1]. The binding energy of large polarons~(i.e., weak coupling) was determined by evaluating the renormalization of the band edges due to the zero-point motion of the atoms [2]. However, for intermediate polarons at intermediate coupling strength, the harmonic approximation breaks down, and there is currently no first-principle theory. We use the HSE06 effective masses to calculate the Fr\"ohlich coupling constants~α. Feynman's path integral technique then yields an intermediate hole polaron, whose binding energy of 245~meV and associated peaks in the optical absorption spectrum are consistent with infrared reflection absorption spectroscopy. [1] J. B. Varley {\it et al.}, Phys. Rev. B \textbf{85}, 081109(R)(2012) [2] G. Antonius {\it et al.}, Phys. Rev. Lett. {\bf 112}, 215501 (2014) Samuel Ponce G. Antonius, Y. Gillet, P. Boulanger, J. Laflamme Janssen, A. Marini, M. Cote and X. Gonze 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 then also place the Allen-Heine-Cardona (AHC) theory of the renormalization in a first-principle 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 $\mu$eV in the case of diamond, which represent an agreement to 5 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. Finally, we will present the temperature-dependence of the eigenenergies for $\alpha$-Aluminum Nitride, $\beta$-Aluminium Nitride, Boron Nitride, Diamond and Silicon within the rigid-ion approximation. Alejandro Molina-Sánchez, L. Wirtz, M. Palummo and A. Marini Finite temperature effects on the electronic properties of single-layer MoS2 Research in ultra-thin two-dimensional materials has been booming since the discovery of graphene along with its interesting physical properties. The transition metal dichalcogenides as MoS 2 are gaining considerable attention due to their potential application in photovoltaics and nanoscale transistors. The electronic and optical properties of these layered materials depend greatly on the number of layers. The paradigmatic example is the transition from indirect to direct bandgap when we change from multi-layer to single-layer MoS 2 . Up to now, theoretical studies of the electro-optical properties of MoS 2 single- layer has been based on the frozen-atom approximation. Within this picture, the coupling of the electron to the lattice vibrations is neglected. Important physical effects are missed, as the zero-point motion re-normalization, the temperature dependence of the bandgap, or the phonon-assisted decay of the photo-generated electron-hole pairs, among others. In this work, we study the effects of the electron-phonon interaction in the electronic properties of single-layer MoS 2 . In the framework of the GW method, we calculate the contribution to the self-energy of the electron-phonon coupling. This allows us to calculate the zero-point re-normalization of the quasi-particle energies and to include finite temperature effects. We discuss the bandgap dependence on the temperature, and the change in the linewidth of the Yannick Gillet , M. Giantomassi, S. Kontur, C. Draxl, X. Gonze 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.

#### Friday 16th

 José Lorenzana Pump-Probe of lattice excitations on correlated systems  using impulsive raman TBA Christian Carbogno Rapid and accurate strategies to achieve time- and size convergence in thermal conductivity simulations TBA Matthieu Verstraete Electron phonon coupling in transport: Seebeck coefficients in metals and semiconductors, and some anharmonic effects The ab initio DFPT calculation of electron phonon (EP) coupling matrix elements gives access to many physical properties, governing superconductivity, resistivity, and thermal dependencies of basically everything (in particular band gaps). We present an implementation of the general framework by PB Allen for solving the Boltzmann Transport Equations with EP scattering, with an ansatz which works well for metals. Examples of resistivities and Seebeck coefficicents for simple and less simple metals are given, with some hints at necessary extensions to quasi harmonic and fully anharmonic phonons. Extensions for doped semiconductors are discussed. These have very small densities of states, and often parabolic bands, which simplifies some quantities but complicates brute force numerical approaches. Andrea Marini Dynamical electron-phonon effects: standard perturbation theory versus a dynamical frozen phonon scheme TBA