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We calculated the structural, electronic and magnetic properties of FeSe within density-functional theory at the generalized gradient approximation level. First, we studied how the bandwidth of the d-bands at the Fermi energy are renormalized by adding simple corrections: Hubbard U, Hunds J and by introducing long-range magnetic orders. We found that introducing either a striped or a staggered dimer antiferromagnetic order brings the bandwidths -- which are starkly overestimated at the generalized gradient approximation level -- closer to those experimentally observed. Second, for the ferromagnetic, the striped, checkerboard and the staggered dimer antiferromagnetic order, we investigate the change in magnetic formation energy with local magnetic moment of Fe at a pressure up to 6 GPa. The bilinear and biquadratic exchange energies are derived from the Heisenberg model and noncollinear first-principles calculations, respectively. We found a non-trivial behavior of the spin-exchange parameters on the magnetization, and we put forward a field-theory model that rationalizes these results in terms of two-dimensional spin and orbital fluctuations. The character of these fluctuations can be either that of a standard density wave or a topological vortex. Topological vortexes can result in mesoscopic magnetization structures.

We present an extension of the quasiparticle self-consistent $GW$ approximation (QS$GW$) [Phys. Rev. B, 76 165106 (2007)] to include vertex corrections in the screened Coulomb interaction $W$. This is achieved by solving the Bethe-Salpeter equation for the polarization matrix at all $k$-points in the Brillouin zone. We refer to this method as QS$G\hat{W}$. QS$GW$ yields a reasonable and consistent description of the electronic structure and optical response, but systematic errors in several properties appear, notably a tendency to overestimate insulating bandgaps, blue-shift plasmon peaks in the imaginary part of the dielectric function, and underestimate the dielectric constant $\epsilon_{\infty}$. A primary objective of this paper is to assess to what extent including ladder diagrams in $W$ ameliorates systematic errors for insulators in the QS$GW$ approximation. For benchmarking we consider about 40 well understood semiconductors, and also examine a variety of less well characterized nonmagnetic systems, six antiferromagnetic oxides, and the ferrimagnet Fe$_3$O$_4$. We find ladders ameliorate shortcomings in QS$GW$ to a remarkable degree in both the one-body Green's function and the dielectric function for a wide range of insulators. New discrepancies with experiment appear, and a key aim of this paper is to establish to what extent the errors are systematic and can be traced to diagrams missing from the theory. One key finding of this work is to establish a relation between the bandgap and the dielectric constant $\epsilon_{\infty}$. Good description of both properties together provides a much more robust benchmark than either alone. We show how this information can be used to improve our understanding of the one-particle spectral properties in materials systems such as SrTiO$_3$ and FeO., Comment: 47 pages, 28 figures

We present a Floquet scheme for the ab-initio calculation of nonlinear optical properties in extended systems. This entails a reformulation of the real-time approach based on the dynamical Berry-phase polarisation [Attaccalite & Gr\"uning, PRB 88, 1-9 (2013)] and retains the advantage of being non-perturbative in the electric field. The proposed method applies to periodically-driven Hamiltonians and makes use of this symmetry to turn a time-dependent problem into a self-consistent time-independent eigenvalue problem. We implemented this Floquet scheme at the independent particle level and compared it with the real-time approach. Our reformulation reproduces real-time-calculated $2^{nd}$ and $3^{rd}$ order susceptibilities for a number of bulk and two-dimensional materials, while reducing the associated computational cost by one or two orders of magnitude.

Convergence with respect to the size of the k-points sampling-grid of the Brillouin zone is the main bottleneck in the calculation of optical spectra of periodic crystals via the Bethe-Salpeter equation (BSE). We tackle this challenge by proposing a double grid approach to k-sampling compatible with the effective Lanczos-based Haydock iterative solution. Our method relies on a coarse k-grid that drives the computational cost, while a dense k-grid is responsible for capturing excitonic effects, albeit in an approximated way. Importantly, the fine k-grid requires minimal extra computation due to the simplicity of our approach, which also makes the latter straightforward to implement. We performed tests on bulk Si, bulk GaAs and monolayer MoS2, all of which produced spectra in good agreement with data reported elsewhere. This framework has the potential of enabling the calculation of optical spectra in semiconducting systems where the efficiency of the Haydock scheme alone is not enough to achieve a computationally tractable solution of the BSE, e.g., large-scale systems with very stringent k-sampling requirements for achieving convergence., Comment: 31 pages, 7 figures

The optical response functions and band structures of LiCoO$_2$ are studied at different levels of approximation, from density functional theory (DFT) in the generalized gradient approximation (GGA) to quasiparticle self-consistent QS$GW$ (with $G$ for Green's function and $W$ for screened Coulomb interaction) without and with ladder diagrams (QS$G\hat W$) and the Bethe Salpeter Equation (BSE) approach. The QS$GW$ method is found to strongly overestimate the band gap and electron-hole or excitonic effects are found to be important. They lower the quasiparticle gap by only about 11~\% but the lowest energy peaks in absorption are found to be excitonic in nature. The contributions from different band to band transitions and the relation of excitons to band-to-band transitions are analyzed. The excitons are found to be strongly localized. A comparison to experimental data is presented., Comment: 12 pages, 10 figures

We explore the electronic band structure of free standing monolayers of chromium trihalides, CrX\textsubscript{3}{, X= Cl, Br, I}, within an advanced \emph{ab-initio} theoretical approach based in the use of Green's function functionals. We compare the local density approximation with the quasi-particle self-consistent \emph{GW} approximation (QS\emph{GW}) and its self-consistent extension (QS$G\widehat{W}$) by solving the particle-hole ladder Bethe-Salpeter equations to improve the effective interaction \emph{W}. We show that at all levels of theory, the valence band consistently changes shape in the sequence Cl{\textrightarrow}Br{\textrightarrow}I, and the valence band maximum shifts from the M point to the $\Gamma$ point. However, the details of the transition, the one-particle bandgap, and the eigenfunctions change considerably going up the ladder to higher levels of theory. The eigenfunctions become more directional, and at the M point there is a strong anisotropy in the effective mass. Also the dynamic and momentum dependent self energy shows that QS$G\widehat{W}$ adds to the localization of the systems in comparison to the QS\emph{GW} thereby leading to a narrower band and reduced amount of halogens in the valence band manifold.

We present an approach to calculate the electronic structure for a range of materials using the quasiparticle self-consistent GW method with vertex corrections included in the screened Coulomb interaction W. This is achieved by solving the Bethe-Salpeter equation for the polarization matrix at all k-points in the Brillouin zone. We refer to this method as QSGW^. We show that including ladder diagrams in W can greatly reduce the band gap overestimation of RPA-based QSGW. The resultant discrepency of the calculated band gap in this method is then attributed mostly to the fact that electron-phonon contributions to W are neglected; which would allow one to then obtain an estimate for the size of this effect. We present results for a range of systems from simple sp semiconductors to the strongly correlated systems NiO and CoO. Results for systems where the RPA-based QSGW band gap is larger than expected are investigated, and an estimate for the Frolich contribution to the gap is included in a few polar compounds where QSGW can overestimate the gap by as much as 2 eV. The improvement over QSGW for the dielectric constants is also presented, Comment: More up to date version

The temperature renormalization of the bulk band structure of a topological crystalline insulator, SnTe, is calculated using first principles methods. We explicitly include the effect of thermal-expansion-induced modification of electronic states and their band inversion on electron-phonon interaction. We show that the direct gap decreases with temperature, as both thermal expansion and electron-phonon interaction drive SnTe towards the phase transition to a topologically trivial phase as temperature increases. The band gap renormalization due to electron-phonon interaction exhibits a non-linear dependence on temperature as the material approaches the phase transition, while the lifetimes of the conduction band states near the band edge show a non-monotonic behavior with temperature. These effects should have important implications on bulk electronic and thermoelectric transport in SnTe and other topological insulators., Comment: 10 pages, 8 figures. Accepted for publication in Phys. Rev. B on June 8, 2020

PbTe is a leading thermoelectric material at intermediate temperatures, largely thanks to its low lattice thermal conductivity. However, its efficiency is too low to compete with other forms of power generation. This efficiency can be effectively enhanced by designing nanostructures capable of scattering phonons over a wide range of length scales to reduce the lattice thermal conductivity. The presence of grain boundaries can reduce the thermal conductivity to $\sim 0.5$ Wm$^{-1}$K$^{-1}$ for small vacancy concentrations and grain sizes. However, grains anneal at finite temperature, and equilibrium and metastable grain size distributions determine the extent of the reduction in thermal conductivity. In the present work, we propose a phase-field model informed by molecular dynamics simulations to study the annealing process in PbTe and how it is affected by the presence of grain boundaries and voids. We find that the thermal conductivity of PbTe is reduced by up to 35\% in the porous material at low temperatures. We observe that a phase transition at a finite density of voids governs the kinetics of impeding grain growth by Zener pinning.

We calculate the electronic structure of the narrow gap semiconductors PbTe, SnTe and GeTe in the cubic phase using density functional theory (DFT) and the $G_0W_0$ method. Within DFT, we show that the band ordering obtained with a conventional semilocal exchange-correlation approximation is correct for SnTe and GeTe but wrong for PbTe. The correct band ordering at the high-symmetry point L is recovered adding $G_0W_0$ quasiparticle corrections. However, one-shot $G_0W_0$ produces artifacts in the band structure due to the wrong orbital character of the DFT single-particle states at the band edges close to L. We show that in order to correct these artifacts it is enough to consider the off-diagonal elements of the $G_0W_0$ self-energy corresponding to these states. We also investigate the pressure dependence of the band gap for these materials and the possibility of a transition from a trivial to a non-trivial topology of the band structure. For PbTe, we predict the band crossover and topological transition to occur at around 4.8 GPa. For GeTe, we estimate the topological transition to occur at 1.9 GPa in the constrained cubic phase, a pressure lower than the one of the structural phase transition from rombohedral to cubic. SnTe is a crystalline topological insulator at ambient pressure, and the transition into a trivial topology would take place under a volume expansion of approximately $10\%$., Comment: 8 pages, 4 figures

Second Harmonic Generation (SHG) of single-layer monochalcogenides, such as GaSe and InSe, has been recently reported [2D Mater. 5 (2018) 025019; J. Am. Chem. Soc. 2015, 137, 79947997] to be extremely strong with respect to bulk and multilayer forms. To clarify the origin of this strong SHG signal, we perform first-principles real-time simulations of linear and non-linear optical properties of these two-dimensional semiconducting materials. The simulations, based on ab-initio many-body theory, accurately treat the electron-hole correlation and capture excitonic effects that are deemed important to correctly predict the optical properties of such systems. We find indeed that, as observed for other 2D systems, the SHG intensity is redistributed at excitonic resonances. The obtained theoretical SHG intensity is an order of magnitude smaller than that reported at the experimental level. This result is in substantial agreement with previously published simulations which neglected the electron-hole correlation, demonstrating that many-body interactions are not at the origin of the strong SHG measured. We then show that the experimental data can be reconciled with the theoretical prediction when a single layer model, rather than a bulk one, is used to extract the SHG coefficient from the experimental data., Comment: 8 pages, 4 figures

VO$_{2}$ is a model material system which exhibits a metal to insulator transition at 67$^\circ$C. This holds potential for future ultrafast switching in memory devices, but typically requires a purely electronic process to avoid the slow lattice response. The role of lattice vibrations is thus important, but it is not well understood and it has been a long-standing source of controversy. We use a combination of ultrafast spectroscopy and ab initio quantum calculations to unveil the mechanism responsible for the transition. We identify an atypical Peierls vibrational mode which acts as a trigger for the transition. This rules out the long standing paradigm of a purely electronic Mott transition in VO$_{2}$; however, we found a new electron-phonon pathway for a purely reversible electronic transition in a true bi-stable fashion under specific conditions. This transition is very atypical, as it involves purely charge-like excitations and requires only small nuclear displacement. Our findings will prompt the design of future ultrafast electro-resistive non-volatile memory devices., Comment: 13 pages, 3 figures

We calculate the two-photon absorption in bulk and single layer hexagonal boron nitride (hBN) both by an ab-initio real-time Bethe-Salpeter approach and by a the real-space solution of the excitonic problem in tight-binding formalism. The two-photon absorption obeys different selection rules from those governing linear optics and therefore provides complementary information on the electronic excitations of hBN. Combining the results from the simulations with a symmetry analysis we show that two-photon absorption is able to probe the lowest energy $1s$ states in the single layer hBN and the lowest dark degenerate dark states of bulk hBN. This deviation from the "usual" selection rules based on the continuous hydrogenic model is explained within a simple model that accounts for the crystalline symmetry. The same model can be applied to other two-dimensional materials with the same point-group symmetry, such as the transition metal chalcogenides. We also discuss the selection rules related to the inversion symmetry of the bulk layer stacking., Comment: 13 pages, 4 figures

For many 2D materials, optical and Raman spectra are richly structured, and convey information on a range of parameters including nanosheet size and defect content. By contrast, the equivalent spectra for h-BN are relatively simple, with both the absorption and Raman spectra consisting of a single feature each, disclosing relatively little information. Here, the ability to size-select liquid-exfoliated h-BN nanosheets has allowed us to comprehensively study the dependence of h-BN optical spectra on nanosheet dimensions. We find the optical extinction coefficient spectrum to vary systematically with nanosheet lateral size due to the presence of light scattering. Conversely, once light scattering has been decoupled to give the optical absorbance spectra, we find the size dependence to be mostly removed save for a weak but well-defined variation in energy of peak absorbance with nanosheet thickness. This finding is corroborated by our ab initio GW and Bethe-Salpeter equation calculations, which include electron correlations and quasiparticle self-consistency (QSGW). In addition, while we find the position of the sole h-BN Raman line to be invariant with nanosheet dimensions, the linewidth appears to vary weakly with nanosheet thickness. These size-dependent spectroscopic properties can be used as metrics to estimate nanosheet thickness from spectroscopic data., Comment: Accepted in Chemistry Materials (In press)

We present an approach to calculate the optical absorption spectra that combines the quasiparticle self-consistent GW method [Phys. Rev. B, 76 165106 (2007)] for the electronic structure with the solution of the ladder approximation to the Bethe-Salpeter equation for the macroscopic dielectric function. The solution of the Bethe-Salpeter equation has been implemented within an all-electron framework, using a linear muffin-tin orbital basis set, with the contribution from the non-local self-energy to the transition dipole moments (in the optical limit) evaluated explicitly. This approach addresses those systems whose electronic structure is poorly described within the standard perturbative GW approaches with as a starting point density-functional theory calculations. The merits of this approach have been exemplified by calculating optical absorption spectra of a strongly correlated transition metal oxide, NiO, and a narrow gap semiconductor, Ge. In both cases, the calculated spectrum is in good agreement with the experiment. It is also shown that for systems whose electronic structure is well-described within the standard perturbative GW, such as Si, LiF and h-BN, the performance of the present approach is in general comparable to the standard GW plus Bethe-Salpeter equation. It is argued that both vertex corrections to the electronic screening and the electron-phonon interaction are responsible for the observed systematic overestimation of the fundamental bandgap and spectrum onset., Comment: 16 pages, 9 figures

We introduce a hybrid method for dielectric-metal composites that describes the dynamics of the metallic system classically whilst retaining a quantum description of the dielectric. The time-dependent dipole moment of the classical system is mimicked by the introduction of projected equations of motion (PEOM) and the coupling between the two systems is achieved through an effective dipole-dipole interaction. To benchmark this method, we model a test system (semiconducting quantum dot-metal nanoparticle hybrid). We begin by examining the energy absorption rate, showing agreement between the PEOM method and the analytical rotating wave approximation (RWA) solution. We then investigate population inversion and show that the PEOM method provides an accurate model for the interaction under ultrashort pulse excitation where the traditional RWA breaks down.

The treatment of the Random-Phase Approximation Hamiltonians, encountered in different frameworks, like Time-Dependent Density Functional Theory or Bethe-Salpeter equation, is complicated by their non-Hermicity. Compared to their Hermitian Hamiltonian counterparts, computational methods for the treatment of non-Hermitian Hamiltonians are often less efficient and less stable, sometimes leading to the breakdown of the method. Recently [Gr\"uning et al. Nano Lett. {\bf 8}, 2820 (2009)], we have identified that such Hamiltonians are usually pseudo-Hermitian. Exploiting this property, we have implemented an algorithm of the Lanczos type for random-Phase Approximation Hamiltonians that benefits from the same stability and computational load as its Hermitian counterpart, and applied it to the study of the optical response of carbon nanotubes. We present here the related theoretical grounds and technical details, and study the performance of the algorithm for the calculation of the optical absorption of a molecule within the Bethe-Salpeter equation framework., Comment: 10 pages, 9 figures, accepted by Computational Materials Science

Quasiparticle calculations are performed to investigate the electronic band structures of various polymorphs of Hf and Zr oxides. The corrections with respect to density-functional-theory results are found to depend only weakly on the crystal structure. Based on these bulk calculations as well as those for bulk Si, the effect of quasiparticle corrections is also investigated for the band offsets at the interface between these oxides and Si assuming that the lineup of the potential at the interface is reproduced correctly within density-functional theory. On the one hand, the valence band offsets are practically unchanged with a correction of a few tenths of eV. On the other hand, conduction band offsets are raised by 1.3--1.5 eV. When applied to existing calculations for the offsets at the density-functional-theory level, our quasiparticle corrections provide results in good agreement with the experiment., Comment: 1 figure, submitted to PRB

{\tt yambo} is an {\it 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. {\tt 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. {\tt 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., Comment: This paper describes the features of the Yambo code, whose source is available under the GPL license at www.yambo-code.org

Within the Tamm-Dancoff approximation ab initio approaches describe excitons as packets of electron-hole pairs propagating only forward in time. However, we show that in nanoscale materials excitons and plasmons hybridize, creating exciton--plasmon states where the electron-hole pairs oscillate back and forth in time. Then, as exemplified by the trans-azobenzene molecule and carbon nanotubes, the Tamm-Dancoff approximation yields errors as large as the accuracy claimed in ab initio calculations. Instead, we propose a general and efficient approach that avoids the Tamm--Dancoff approximation, and correctly describes excitons, plasmons and exciton-plasmon states.