Towards fully automatized GW band structure calculations: What we can learn from 60.000 self-energy evaluations

We analyze a data set comprising 370 GW band structures composed of 61716 quasiparticle (QP) energies of two-dimensional (2D) materials spanning 14 crystal structures and 52 elements. The data results from PAW plane wave based one-shot G$_0$W$_0$@PBE calculations with full frequency integration. We investigate the distribution of key quantities like the QP self-energy corrections and renormalization factor $Z$ and explore their dependence on chemical composition and magnetic state. The linear QP approximation is identified as a significant error source and propose schemes for controlling and drastically reducing this error at low computational cost. We analyze the reliability of the $1/N_\text{PW}$ basis set extrapolation and find that is well-founded with narrow distributions of $r^2$ peaked very close to 1. Finally, we explore the validity of the scissors operator approximation concluding that it is generally not valid for reasonable error tolerances. Our work represents a step towards the development of automatized workflows for high-throughput G$_0$W$_0$ band structure calculations for solids.Comment: 11 pages, 9 figures, 1 tabl

Discovering new two-dimensional topological insulators from computational screening

We have performed a computational screening of topological two-dimensional (2D) materials from the Computational 2D Materials Database (C2DB) employing density functional theory. A full \textit{ab initio} scheme for calculating hybrid Wannier functions directly from the Kohn-Sham orbitals has been implemented and the method was used to extract $\mathbb{Z}_2$ indices, Chern numbers and Mirror Chern numbers of 3331 2D systems including both experimentally known and hypothetical 2D materials. We have found a total of 46 quantum spin Hall insulators, 7 quantum anomalous Hall insulators and 9 crystalline topological insulators that are all predicted to be dynamically stable. Roughly one third of these were known prior to the screening. The most interesting of the novel topological insulators are investigated in more detail. We show that the calculated topological indices of the quantum anomalous Hall insulators are highly sensitive to the approximation used for the exchange-correlation functional and reliable predictions of the topological properties of these materials thus require methods beyond density functional theory. We also performed $GW$ calculations, which yield a gap of 0.65 eV for the quantum spin Hall insulator PdSe$_2$ in the MoS$_2$ crystal structure. This is significantly higher than any known 2D topological insulator and three times larger than the Kohn-Sham gap.Comment: 12 page

Scanning Quantum Dot Microscopy

Interactions between atomic and molecular objects are to a large extent defined by the nanoscale electrostatic potentials which these objects produce. We introduce a scanning probe technique that enables three-dimensional imaging of local electrostatic potential fields with sub-nanometer resolution. Registering single electron charging events of a molecular quantum dot attached to the tip of a (qPlus tuning fork) atomic force microscope operated at 5 K, we quantitatively measure the quadrupole field of a single molecule and the dipole field of a single metal adatom, both adsorbed on a clean metal surface. Because of its high sensitivity, the technique can record electrostatic potentials at large distances from their sources, which above all will help to image complex samples with increased surface roughness.Comment: main text: 5 pages, 4 figures, supplementary information file: 4 pages, 2 figure