Nonmonotonic band gap evolution in bent phosphorene nanosheets

Nonmonotonic bending-induced changes of fundamental band gaps and quasiparticle energies are observed for realistic nanoscale phosphorene nanosheets. Calculations using stochastic many-body perturbation theory (sGW) show that even slight curvature causes significant changes in the electronic properties. For small bending radii (< 4 nm) the band-gap changes from direct to indirect. The response of phosphorene to deformation is strongly anisotropic (different for zig-zag vs. armchair bending) due to an interplay of exchange and correlation effects. Overall, our results show that fundamental band gaps of phosphorene sheets can be manipulated by as much as 0.7 eV depending on the bending direction.Comment: 23 pages, 5 figures, 3 table

Embedding vertex corrections in GW self-energy: theory, implementation, and outlook

The vertex function ($\Gamma$) within the Green's function formalism encapsulates information about all higher-order electron-electron interaction beyond those mediated by density fluctuations. Herein, we present an efficient approach that embeds vertex corrections in the one-shot $GW$ correlation self-energy for isolated and periodic systems. The vertex-corrected self-energy is constructed through the proposed separation-propagation-recombination procedure: the electronic Hilbert space is separated into an active space and its orthogonal complement denoted as the "rest"; the active component is propagated by a space-specific effective Hamiltonian different from the rest. The vertex corrections are introduced by a rescaled time-dependent non-local exchange interaction. The direct $\Gamma$ correction to the self-energy is further updated by adjusting the rescaling factor in a self-consistent post-processing circle. Our embedding method is tested mainly on donor-acceptor charge-transfer systems. The embedded vertex effects consistently and significantly correct the quasiparticle energies of the gap-edge states. The fundamental gap is generally improved by 1-3 eV upon the one-shot $GW$ approximation. Furthermore, we provide an outlook for applications of (embedded) vertex corrections in calculations of extended solids

Spatial Decay and Limits of Quantum Solute-Solvent Interactions

Molecular excitations in the liquid phase environment are significantly renormalized by the surrounding solvent molecules. Herein, we employ the many-body Green's function approach (in the GW approximation) to investigate the solvation effects on the ionization energy of phenol in various solvents with distinct polarizability. The many-body effects among the investigated solvents differ by up to 0.4 eV, and this difference is not simply owed to the macroscopic solvent polarizability. Utilizing orbital localization and projection, we define an electronic subspace for a fragment, i.e., a solvation shell, in the solvent environment. The resulting fragment correlation self-energy is shown to decay with respect to the intermolecular distance and vanish at ~9 angstroms. This decaying pattern is independent of the ionization state and the solvent type. The 9-angstrom cut-off distance defines an effective interacting volume, within which we find the quasiparticle energy shift per solvent molecule is directly related to the polarizability of the solvent molecules. Finally, we propose a simple solvation model for computing the quasiparticle energies of solvated systems

On the unimportance of memory for the time non-local components of the Kadanoff-Baym equations

The generalized Kadanoff-Baym ansatz (GKBA) is an approximation to the Kadanoff-Baym equations (KBE), that neglects certain memory effects that contribute to the Green's function at non-equal times. Here we present arguments and numerical results to demonstrate the practical insignificance of the quantities neglected when deriving the GKBA at conditions at which KBE and GKBA are appropriate. We provide a mathematical proof that places a scaling bound on the neglected terms, further reinforcing that these terms are typically small in comparison to terms that are kept in the GKBA. We perform calculations in a range of models, including different system sizes and filling fractions, as well as experimentally relevant non-equilibrium excitations. We find that both the GKBA and KBE capture the dynamics of interacting systems with moderate and even strong interactions well. We explicitly compute terms neglected in the GKBA approximation and show, in the scenarios tested here, that they are orders of magnitude smaller than the terms that are accounted for, i.e., they offer only a small correction when included in the full Kadanoff-Baym equations.Comment: 14 pages, 3 figures, Supplemental information with 10 figure

Dynamic Mode Decomposition for Extrapolating Non-equilibrium Green's Functions Dynamics

The HF-GKBA offers an approximate numerical procedure for propagating the two-time non-equilibrium Green's function(NEGF). Here we compare the HF-GKBA to exact results for a variety of systems with long and short-range interactions, different two-body interaction strengths and various non-equilibrium preparations. We find excellent agreement between the HF-GKBA and exact time evolution in models when more realistic long-range exponentially decaying interactions are considered. This agreement persists for long times and for intermediate to strong interaction strengths. In large systems, HF-GKBA becomes prohibitively expensive for long-time evolutions. For this reason, look at the use of dynamical mode decomposition(DMD) to reconstruct long-time NEGF trajectories from a sample of the initial trajectory. Using no more than 16\% of the total time evolution we reconstruct the total trajectory with high fidelity. Our results show the potential for DMD to be used in conjunction with HF-GKBA to calculate long time trajectories in large-scale systems

Improved ground-state electronic structure and optical dielectric constants with a semilocal exchange functional

A recently published generalized gradient approximation functional within density functional theory (DFT) has shown, in a few paradigm tests, an improved KS orbital description over standard (semi) local approximations. The characteristic feature of this functional is an enhancement factor that diverges like s ln(s) for large reduced density gradients s which leads to unusual properties. We explore the improved orbital description of this functional more thoroughly by computing the electronic band structure, band gaps, and the optical dielectric constants in semiconductors, Mott insulators, and ionic crystals. Compared to standard semilocal functionals, we observe improvement in both the band gaps and the optical dielectric constants. In particular, the results are similar to those obtained with orbital functionals or by perturbation theory methods in that it opens band gaps in systems described as metallic by standard (semi) local density functionals, e. g., Ge, alpha-Sn, and CdO.Funding Agencies|Deutsche Forschungsgemeinschaft (DFG) [STE1105/8-1, SFB840, B1]; Swedish Research Council [621-2011-4249]; VR</p