The GW approximation for the self-energy operator is used to calculate the corrections to band structures obtained within the local-density approximation (LDA). To that end we derive rigorous expressions for the quasiparticle energies and wave functions, being also valid for the exact self-energy. A detailed analysis of the state and energy dependence of the nonlocal exchange-correlation contributions to the quasiparticle energies is given and compared to the approximative self-energies used within the LDA. The self-energy and the dielectric response matrix are evaluated in plane-wave representation. We demonstrate that the wave functions obtained from the empirical pseudopotential model (EPM) are sufficient to compute the final energy bands to within 0.1–0.2 eV. The merit of the EPM wave functions is a fast convergence and the possibility to calculate exchange-correlation self-energies for band structures which are determined in a localized basis. These wave functions incorporate all structural details contained in the ab initio wave functions. As far as the dynamics of the dielectric response is concerned a new generalized plasmon-pole concept for the dielectric matrix is introduced which fulfills all important sum rules and possesses the right analytical properties also for the off-diagonal elements. This new scheme provides a significant improvement in computational efficiency. Explicit results are given for germanium.

In the last five years a large number of new high-temperature superconductors have been predicted and experimentally discovered among hydrogen-rich crystals, at pressures, which are way too high to meet any practical application. In this paper, we report the computational prediction of a hydride superconductor, $\mathrm{La}{\mathrm{BH}}_8$, with a $T_{\text{c}}$ of 126 K at a pressure of 50 GPa, thermodynamically stable above 100 GPa, and dynamically stable down to 40 GPa, an unprecedentedly low pressure for high-$T_{\text{c}}$ hydrides. $\mathrm{La}{\mathrm{BH}}_8$ can be seen as a ternary sodalite-like hydride, in which a metallic hydrogen sublattice is stabilized by the chemical pressure exerted by the La-B scaffolding, which achieves a more efficient packing of atoms than in binary sodalite hydrides thanks to the combination of elements with very different sizes. The proposed aufbau principle may be exploited to design high-$T_{\text{c}}$ hydrides that survive at even lower pressure, through a careful choice of the elements.

We introduce a versatile method to compute electronic steady-state properties of strongly correlated extended quantum systems out of equilibrium. The approach is based on dynamical mean-field theory (DMFT), in which the original system is mapped onto an auxiliary nonequilibrium impurity problem imbedded in a Markovian environment. The steady-state Green's function of the auxiliary system is solved by full diagonalization of the corresponding Lindblad equation. The approach can be regarded as the nontrivial extension of the exact-diagonalization-based DMFT to the nonequilibrium case. As a first application, we consider an interacting Hubbard layer attached to two metallic leads and present results for the steady-state current and the nonequilibrium density of states.

We present a numerical method for the study of correlated quantum impurity problems out of equilibrium, which is particularly suited to address steady-state properties within dynamical mean field theory. The approach, recently introduced by Arrigoni et al. [Phys. Rev. Lett. 110, 086403 (2013)], is based upon a mapping of the original impurity problem onto an auxiliary open quantum system, consisting of the interacting impurity coupled to bath sites as well as to a Markovian environment. The dynamics of the auxiliary system is governed by a Lindblad master equation whose parameters are used to optimize the mapping. The accuracy of the results can be readily estimated and systematically improved by increasing the number of auxiliary bath sites, or by introducing a linear correction. Here, we focus on a detailed discussion of the proposed approach including technical remarks. To solve for the Green's functions of the auxiliary impurity problem, a non-Hermitian Lanczos diagonalization is applied. As a benchmark, results for the steady-state current-voltage characteristics of the single-impurity Anderson model are presented. Furthermore, the bias dependence of the single-particle spectral function and the splitting of the Kondo resonance are discussed. In its present form, the method is fast, efficient, and features a controlled accuracy.