yambo is an ab initio code for calculating quasiparticle energies and optical properties of electronic systems within the framework of many-body perturbation theory and time-dependent density functional theory. Quasiparticle energies are calculated within the GW approximation for the self-energy. Optical properties are evaluated either by solving the Bethe-Salpeter equation or by using the adiabatic local density approximation. yambo is a plane-wave code that, although particularly suited for calculations of periodic bulk systems, has been applied to a large variety of physical systems. yambo relies on efficient numerical techniques devised to treat systems with reduced dimensionality, or with a large number of degrees of freedom. The code has a user-friendly command-line based interface, flexible I/O procedures and is interfaced to several publicly available density functional ground-state codes. 71.45.Gm, 71.15.Qe

We present converged ab initio calculations of the optical absorption spectra of single-layer, double-layer, and bulk MoS 2 . Both the quasiparticle-energy calculations (on the level of the GW approximation ) and the calculation of the absorption spectra (on the level of the Bethe-Salpeter equation) explicitly include spin-orbit coupling, using the full spinorial Kohn-Sham wave functions as input. Without excitonic effects, the absorption spectra would have the form of a step function, corresponding to the joint density of states of a parabolic band dispersion in two dimensions. This profile is deformed by a pronounced bound excitonic peak below the continuum onset. The peak is split by spin-orbit interaction in the case of single-layer and (mostly) by interlayer interaction in the case of double-layer and bulk MoS 2 . The resulting absorption spectra are thus very similar in the three cases, but the interpretation of the spectra is different. Differences in the spectra can be seen in the shape of the absorption spectra at 3 eV where the spectra of the single and double layers are dominated by a strongly bound exciton.

Transition metal dichalcogenides (TMDs) are emerging as promising two-dimensional (2D) semiconductors for optoelectronic and flexible devices. However, a microscopic explanation of their photophysics, of pivotal importance for the understanding and optimization of device operation, is still lacking. Here, we use femtosecond transient absorption spectroscopy, with pump pulse tunability and broadband probing, to monitor the relaxation dynamics of single-layer MoS2 over the entire visible range, upon photoexcitation of different excitonic transitions. We find that, irrespective of excitation photon energy, the transient absorption spectrum shows the simultaneous bleaching of all excitonic transitions and corresponding red-shifted photoinduced absorption bands. First-principle modeling of the ultrafast optical response reveals that a transient bandgap renormalization, caused by the presence of photoexcited carriers, is primarily responsible for the observed features. Our results demonstrate the strong impact of many-body effects in the transient optical response of TMDs even in the low-excitation-density regime.

We present a reciprocal space analytical method to cut off the long range interactions in supercell calculations for systems that are infinite and periodic in one or two dimensions, generalizing previous work to treat finite systems. The proposed cutoffs are functions in Fourier space, that are used as a multiplicative factor to screen the bare Coulomb interaction. The functions are analytic everywhere except in a subdomain of the Fourier space that depends on the periodic dimensionality. We show that the divergences that lead to the nonanalytical behavior can be exactly canceled when both the ionic and the Hartree potential are properly screened. This technique is exact, fast, and very easy to implement in already existing supercell codes. To illustrate the performance of the scheme, we apply it to the case of the Coulomb interaction in systems with reduced periodicity ͑as one-dimensional chains and layers͒. For these test cases, we address the impact of the cutoff on different relevant quantities for ground and excited state properties, namely: the convergence of the ground state properties, the static polarizability of the system, the quasiparticle corrections in the GW scheme, and the binding energy of the excitonic states in the Bethe-Salpeter equation. The results are very promising and easy to implement in all available first-principles codes.

We show that the optical absorption spectra of boron nitride (BN) nanotubes are dominated by strongly bound excitons. Our first-principles calculations indicate that the binding energy for the first and dominant excitonic peak depends sensitively on the dimensionality of the system, varying from 0.7 eV in bulk hexagonal BN via 2.1 eV in the single sheet of BN to more than 3 eV in the hypothetical 2; 2 tube. The strongly localized nature of this exciton dictates the fast convergence of its binding energy with increasing tube diameter towards the sheet value. The absolute position of the first excitonic peak is almost independent of the tube radius and system dimensionality. This provides an explanation for the observed ''optical gap'' constancy for different tubes and bulk hexagonal BN.

yambo is an open source project aimed at studying excited state properties of condensed matter systems from first principles using many-body methods. As input, yambo requires ground state electronic structure data as computed by density functional theory codes such as Quantum ESPRESSO and Abinit. yambo's capabilities include the calculation of linear response quantities (both independentparticle and including electron-hole interactions), quasi-particle corrections based on the GW formalism, optical absorption, and other spectroscopic quantities. Here we describe recent developments ranging from the inclusion of important but oft-neglected physical effects such as electron-phonon interactions to the implementation of a real-time propagation scheme for simulating linear and nonlinear optical properties. Improvements to numerical algorithms and the user interface are outlined. Particular emphasis is given to the new and efficient parallel structure that makes it possible to exploit modern high performance computing architectures. Finally, we demonstrate the possibility to automate workflows by interfacing with the yambopy and AiiDA software tools. CONTENTS

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.

The coupling with the lattice vibrations is shown to drastically modify the state-of-the-art picture of the excitonic states based on a frozen atom approximation. The zero-point vibrations renormalize the bare energies and optical strengths. Excitons acquire a non-radiative lifetime that decreases with increasing temperature. The optical brightness turns out to be strongly temperature dependent such as to induce bright to dark (and vice versa) transitions. The finite temperature experimental optical absorption spectra of bulk Si and hexagonal BN are successfully explained without using any external parameter. The ab initio description of the excitonic states, obtained by solving the Bethe-Salpeter (BS) equation of Many-Body Perturbation Theory (MBPT), constitutes a well-established approach to interpret the photoexcited properties of bulk materials, surfaces, nanostructures and organic/bio-molecules [1]. Although absorption and photoluminescence (PL) experiments are usually performed at room temperature, in the standard approach the BS equation is solved assuming the atoms frozen in their crystallographic positions, thus neglecting the effect of lattice vibrations. As a consequence excitons turn out to be insensitive to the temperature T and to have an infinite lifetime. This is in stark contrast with the experimental results, where the absorption and emission lines at any temperature show an intrinsic width that reflects the finite lifetime of the underlying excitonic states. Moreover, in bulk semiconductors, it is a well known fact that the absorption line position, width, and intensity show a clear T dependence [2]. In the frozen-atom BS equation this dependence is not described at all. Even in the T → 0 limit, where atoms vibrate to fulfill the uncertainty principle (zero-point vibrations), the calculated absorption spectra is commonly convoluted with some artificial, ad-hoc numerical broadening function chosen to yield the best agreement with the experiment. More generally the finite temperature non-radiative damping, and the energy and optical strength renormalization, define the quantum efficiency of the excitons as photo-emitters, a key parameter in devising materials for optoelectronic applications.