The GW approximation in electronic structure theory has become a widespread tool for predicting electronic excitations in chemical compounds and materials. In the realm of theoretical spectroscopy, the GW method provides access to charged excitations as measured in direct or inverse photoemission spectroscopy. The number of GW calculations in the past two decades has exploded with increased computing power and modern codes. The success of GW can be attributed to many factors: favorable scaling with respect to system size, a formal interpretation for charged excitation energies, the importance of dynamical screening in real systems, and its practical combination with other theories. In this review, we provide an overview of these formal and practical considerations. We expand, in detail, on the choices presented to the scientist performing GW calculations for the first time. We also give an introduction to the many-body theory behind GW , a review of modern applications like molecules and surfaces, and a perspective on methods which go beyond conventional GW calculations. This review addresses chemists, physicists and material scientists with an interest in theoretical spectroscopy. It is intended for newcomers to GW calculations but can also serve as an alternative perspective for experts and an up-to-date source of computational techniques.

Owing to its remarkable electronic and transport properties, graphene has great potential of replacing silicon for next-generation electronics and optoelectronics; but its zero bandgap associated with Dirac fermions prevents such applications. Among numerous attempts to create semiconducting graphene, periodic patterning using defects, passivation, doping, nanoscale perforation, etc., is particularly promising and has been realized experimentally. However, despite extensive theoretical investigations, the precise role of periodic modulations on electronic structures of graphene remains elusive. Here we employ both the tight-binding modeling and first-principles electronic structure calculations to show that the appearance of bandgap in patterned graphene has a geometric symmetry origin. Thus the analytic rule of gap-opening by patterning graphene is derived, which indicates that if a modified graphene is a semiconductor, its two corresponding carbon nanotubes, whose chiral vectors equal graphene's supercell lattice vectors, are both semimetals.

Magnetic impurities have a dramatic effect on superconductivity by breaking the time-reversal symmetry and inducing so-called Yu–Shiba–Rusinov (YSR) low energy bound states within the superconducting gap. The spatial extent of YSR states is greatly enhanced in two-dimensional (2D) systems, which should facilitate the formation of coupled states. Here, we observe YSR states on single cobalt phthalocyanine (CoPC) molecules on a 2D superconductor NbSe2 using low-temperature scanning tunneling microscopy (STM) and spectroscopy. We use STM lateral manipulation to create controlled CoPc dimers and demonstrate the formation of coupled YSR states. The experimental results are corroborated by theoretical analysis of the coupled states in lattice and continuum models.

Excitonic effects are crucial to optical properties, and the exciton binding energy E(b) in technologically important semiconductors varies from merely a few meV to about 100 meV. This large variation, however, is not well understood. We investigate the relationship between the electronic band structures and exciton binding energies in semiconductors, employing first-principles calculations based on the density functional theory and the many-body perturbation theory using Green's functions. Our results clearly show that E(b) increases as the localization of valence electrons increases due to the reduced electronic screening. Furthermore, E(b) increases in ionic semiconductors such as ZnO because, contrary to the simple two-level coupling model, it has both conduction and valence band edge states strongly localized on anion sites, leading to an enhanced electron-hole interaction. These trends are quantized by electronic structures obtained from the density functional theory; thus, our approach can be applied to understand the excitonic effects in complex semiconducting materials.

We investigate the spectral evolution in different metal phthalocyanine molecules on NbSe2 surface using scanning tunnelling microscopy (STM) as a function of the coupling with the substrate. For manganese phthalocyanine (MnPc), we demonstrate a smooth spectral crossover from Yu-Shiba-Rusinov (YSR) bound states to spin-flip excitations. This has not been observed previously and it is in contrast to simple theoretical expectations. We corroborate the experimental findings using numerical renormalization group calculations. Our results provide fundamental new insight on the behavior of atomic scale magnetic/SC hybrid systems, which is important, for example, for engineered topological superconductors and spin logic devices.