We reveal a strongly anisotropic excitonic landscape in monolayer and bulk-like CrSBr using optical absorption spectroscopy and GW-Bethe-Salpeter equation ab initio calculations. The direct absorptive determination of the lowest bright optical onsets i.e. X_0^a and X_0^b excitons for the two in-plane polarization eigenaxes yield an in-plane optical gap anisotropy of 470 ± 15 meV. This is the highest observed value for any material in the near-infrared-to-visible spectral region to the best of our knowledge. Energetically above, we identify multiple strongly polarized excitons spanning 1.25 eV to 3.1 eV selectively aligned along the two orthogonal axes. A resonance X^-, located 24 meV below the X_0^b progressively transfers oscillator strength to X_b^0, a behavior consistent with a coupled trion (Fermi-polarion)/exciton pair. Our experiments also provide polarization-resolved broadband dielectric functions of CrSBr. These results establish CrSBr as a strongly polarization-selective excitonic system and highlight its potential for polarization-selective optoelectronics enabled with its large optical-gap anisotropy.

We investigate the adsorption geometry, binding energetics, and electronic structure of the polycyclic aromatic hydrocarbons benzene, naphthalene, and anthracene on a monolayer of MoS 2 using first-principles calculations. Structural relaxations are performed within density functional theory (DFT) including corrections for van der Waals interactions. Quasiparticle electronic structures are subsequently obtained using many-body perturbation theory employing the GW approximation. All three molecules preferentially adsorb flat above sulfur sites of the MoS 2 surface and form type-I heterojunctions with MoS 2 . Only anthracene exhibits weak hybridization with the MoS 2 valence band maximum (VBM) and VBM-1, leading to a slight reduction of the MoS 2 valence band splitting. The HOMO-LUMO (highest occupied molecular orbital, lowest unoccupied molecular orbital) gaps of the molecules are substantially reduced by the dielectric screening of the MoS 2 substrate. These results highlight the asymmetric role of screening and hybridization in MoS 2 -organic hybrid systems and provide insight into band alignment and electronic structure engineering for molecularly functionalized two-dimensional semiconductors.

The optical properties of layered materials are dominated by intralayer excitons; especially for layered antiferromagnets the layer-to-layer charge hopping, and therefore interlayer excitons, are spin forbidden. An external magnetic field, however, can continuously drive the magnetic order towards layer-to-layer ferromagnetic, which opens spin-allowed charge-transfer channels between the layers. Here, we elaborate how their admixture changes the composition and nature of the excitons, leading to an extension over many layers, and causing a quadratic redshift with respect to the external magnetic field in CrSBr. We present a minimal four-band model to elucidate the interplay between the various interaction and coupling mechanisms which is able to reproduce the findings of our GW–Bethe-Salpeter equation calculations as a function of magnetic field. Our model is generally valid for any coupled layers with different spin directions and the insights help to systematically address excitons and to predict their optical signatures in such systems. Published by the American Physical Society 2025

The van der Waals magnetic semiconductor CrSBr combines multistable magnetic order with strong light–matter coupling, enabling optical access to a rich and reconfigurable layered magnetic domain structure. A purely optical, non-destructive, and non-contact readout of layered magnetic configurations is realized here by magneto-reflectance measurements and interpreted using an optical multilayer model. The magnetic state is tunable by applied magnetic fields and by interfacing CrSBr with the antiferromagnet MnPS_3. Applying an external magnetic field along the easy axis drives the hysteretic antiferromagnetic–to–ferromagnetic transition, which is not universally binary but instead develops through a cascade of intermediate magnetic configurations whose multiplicity and stability scale systematically with layer thickness and can be tailored by magnetic interfaces. The intertwined optical and magnetic properties of CrSBr provide a readout mechanism for information encoded in and processed through its magnetic configuration that is compatible with modern on- and off-chip photonic and electronic technologies. These properties identify CrSBr as a promising platform for intelligent matter and for spin-optoelectronics, in particular for neuromorphic architectures that can learn and evolve in response to changing environments.

The interaction between electrons and phonons leads to a renormalization of the electronic band structure and the associated band gap. In solids this renormalization can be calculated from first principles using the supercell-based frozen phonon method or the perturbation-based Allen-Heine-Cardona theory. Each approach relies on certain assumptions and can become computationally expensive. In this work we present an ab initio implementation that aims to increase the accuracy and the efficiency of such calculations by combining the nonadiabatic Allen-Heine-Cardona theory and supercell calculations. Additionally, the benefits of a localized basis set of Gaussian orbitals are exploited. Due to its computational complexity the Debye-Waller component of Allen-Heine-Cardona theory is usually treated on a rigid-ion approximation level using a version of the acoustic sum rule. In our implementation the evaluation of the Debye-Waller component is straightforward and contributions beyond the rigid-ion approximation from several shells of nearest neighbors can easily be included. We use bulk silicon and diamond as test systems and find a good agreement with the literature on the level of the rigid-ion approximation. Beyond that we calculate the contributions up to third-nearest neighbors and find that these contributions are small with up to about 5% of the rigid-ion contribution but not necessarily negligible. For silicon the calculated zero-point renormalization of the direct (indirect) band gap is -43.5 meV (-54.9 meV). At high temperature, the band gaps shrink at a rate of -0.17 and -0.27 meV/K, respectively. For diamond we find a zero-point renormalization of -405.2 meV (-313.7 meV) for the direct (indirect) band gap. The reduction at high temperature is -0.46 and -0.37 meV/K, respectively.

We present preliminary results of theoretical in vestigation of mono- and multi-layers of graphene (G), hexag onal boron nitride (hBN) and/or their combinations, functional ized with hydrogen, which are prospective for photovoltaic (PV) applications. Controlled hydrogenation of the above lay ered systems allows to simultaneously tune 2D electron gap of the materials, create strong covalent interlayer bonding or bond the multilayers to a substrate. The functionalized nano materials under investigation demonstrate not only chemical stability and natural hardness, but they are also compatible with standard growth technologies used in photovoltaics. Such mul tilayers can be used as transparent solar cell windows, an inter facial layer, e.g., in a form of a tunnel junction, an electrode, 2D semiconducting material and other. In particular, gra phene/hBN heterosystems considered, allow tailoring of struc tural, electronic and bonding properties by controlled dose of hydrogen. Their promising PV applications as well as already existing experimental implementations will be discussed in the end.

Point defects in hexagonal boron nitride (hBN) are often discussed as single-photon emitters for quantum technologies. Understanding the dependence of electronic and optical properties on the geometry might help to identify the atomic structure of the defects and is also crucial in order to make these emitters applicable. Here, we (constrained) density functional theory to obtain optimal geometries of the electronic ground state and the first excited state and then refine quasiparticle energies and optical excitation energies using a GW and Bethe-Salpeter equation (BSE) based approach. All three defect systems host transitions between deep-lying defect states. We find the lowest defect exciton of CBCN at -4 eV and of the other two defects at <^>2 eV with significant Stokes shifts of 0.15 and 0.79 eV, respectively. Finally, we investigate the effects of the Tamm-Dancoff approximation and show that it can have a significant influence on hBN defect excitons calculated from BSE.

The optical properties of the layered magnet CrSBr are dominated by intralayer excitons: the antiferromagnetic order between the layers makes layer-to-layer charge hopping, and therefore interlayer excitons, spin-forbidden. An external magnetic field, however, continuously drives the magnetic order towards layer-to-layer ferromagnetic, which opens spin-allowed charge-transfer channels between the layers. Here we elaborate how their admixture changes the composition and nature of the excitons, leading to an extension over many layers, and causes a quadratic red-shift with respect to the external magnetic field. We address these effects by ab-initio $GW$-BSE calculations as a function of magnetic field and cast the data into a minimal four-band model to elucidate the interplay between the various interaction and coupling mechanisms. Our findings should be generally valid for antiferromagnetic layered magnets with and without external magnetic fields, and moreover for any couple of layers with different spin directions. Our insights help to systematically address excitons and predict their optical signatures in such systems.

The electronic and optical properties of layered materials, such as transition metal dichalcogenides, can be strongly affected by their dielectric environment-this phenomenon is also known as the image charge effect. In multilayers, the stacked crystal structure implies a layer-dependent variation of the image charge effect. However, this variation and its implications on the interlayer coupling are heretofore not well understood. Here, we show that the variation of dielectric screening effects in layered materials can be described by a macroscopic dielectric continuum model within classical electrostatics. We present an efficient method that incorporates this effect in electronic structure calculations. The present method is based on semi-empirical tight-binding and amenable to use for large-scale systems. By applying this method to multilayer MoS2, we find an energetic decoupling of the surface layer-at the K point of the Brillouin zone-which leads to the formation of a surface-layer band gap. More generally, our calculations reveal that the image charge effect can cause spatial modulation of the interlayer coupling by changing the band alignment between the layers.

Two-dimensional (2D) materials have revealed many fascinating physical and chemical properties. Due to the quantum confinement and enhanced many-body effects especially the optical properties are altered compared to their bulk counterparts. The optics of 2D materials can easily be modified by various means, e.g. the substrate, doping, strain, stacking, electric or magnetic fields. In this review we focus on the theoretical description of the excited states and optical properties of 2D semiconductors paying particular attention to the current challenges and future opportunities. While the presented methodology is completely general and applicable to any 2D material, we discuss results for the transition metal dichalcogenides, their heterostructures, and some novel materials from the computational 2D materials database.

The vertex function F(1, 2; 3) within Hedin's equations constitutes a long-standing challenge to electronic -structure theory. We propose an explicit expression for F as a function of space and time. This ansatz fulfils the equation of motion within reasonable approximations. The equation of motion is controlled by the screened Coulomb interaction W and the Green's function G. Concerning W we find that its dynamics (here approximated by plasmons) is crucial for obtaining a realistic F. Concerning G the renormalization of the quasiparticle peak and the split-off satellites are important. In combination these effects can be approximated by simple expressions that can easily be incorporated in the determination of the screening and the electronic self-energy. Similar to previous literature we find significant cancellation of such vertex corrections and electronic self-consistency. In the case of silicon as a prototypical semiconductor material we obtain realistic results for the optical spectrum, the electronic spectral function, and the fundamental band gap.

The optical and electronic properties of multilayer transition metal dichalcogenides differ significantly from their monolayer counterparts due to interlayer interactions. The separation of individual layers can be tuned in a controlled way by applying pressure. Here, we use a diamond anvil cell to compress bilayers of 2H-MoS2 in the gigapascal range. By measuring optical transmission spectra, we find that increasing pressure leads to a decrease in the energy splitting between the A and the interlayer exciton. Comparing our experimental findings with ab initio calculations, we conclude that the observed changes are not due to the commonly assumed hydrostatic compression. This effect is attributed to the MoS2 bilayer adhering to the diamond, which reduces the in-plane compression. Moreover, we demonstrate that the distinct real-space distributions and resulting contributions from the valence band account for the different pressure dependencies of the inter- and intralayer excitons in compressed MoS2 bilayers.

Correlated quantum phenomena in one-dimensional (1D) systems that exhibit competing electronic and magnetic order are of strong interest for the study of fundamental interactions and excitations, such as Tomonaga-Luttinger liquids and topological orders and defects with properties completely different from the quasiparticles expected in their higher-dimensional counterparts. However, clean 1D electronic systems are difficult to realize experimentally, particularly for magnetically ordered systems. Here, we show that the van der Waals layered magnetic semiconductor CrSBr behaves like a quasi-1D material embedded in a magnetically ordered environment. The strong 1D electronic character originates from the Cr-S chains and the combination of weak interlayer hybridization and anisotropy in effective mass and dielectric screening, with an effective electron mass ratio of mXe/mYe ∼ 50. This extreme anisotropy experimentally manifests in strong electron-phonon and exciton-phonon interactions, a Peierls-like structural instability, and a Fano resonance from a van Hove singularity of similar strength to that of metallic carbon nanotubes. Moreover, because of the reduced dimensionality and interlayer coupling, CrSBr hosts spectrally narrow (1 meV) excitons of high binding energy and oscillator strength that inherit the 1D character. Overall, CrSBr is best understood as a stack of weakly hybridized monolayers and appears to be an experimentally attractive candidate for the study of exotic exciton and 1D-correlated many-body physics in the presence of magnetic order.

While the optical band gap of pristine hexagonal boron nitride (hBN) is about 6 eV, emissions from defects in the visible regime with single-photon characteristics have been observed in experiment for a long time. To tackle the question which kind of defects are responsible for these emissions, many ab initio studies have been conducted. Most of them are on the level of density-functional theory (DFT). While DFT provides an efficient method to obtain band dispersion and optimal structure, it lacks the ability to calculate the quasiparticle energy levels correctly. In this work, we employ an efficient approximation of the GW theory to calculate quasiparticle energy levels of small atomic defects: Two carbon substitutions CN and CB, the nitrogen vacancy VN, and the divacancy VNB. Optical spectra are calculated by solving the Bethe-Salpeter equation. The defect systems which are examined in this work allow for transitions between intrinsic states of hBN and deep defect states which lie inside the band gap, resulting in bright excitons at ???2 eV.

The assembly of single-molecule devices with the help of the manipulation capability of scanning probe microscopes offers many opportunities for quantum- and nanotechnology. A key challenge is fabricating device structures that can overcome their attraction to the underlying surface and thus protrude from the two-dimensional flatlands of the surface. In my talk, I will report the fabrication of such a structure: we use the tip of a scanning probe microscope to lift a large planar aromatic molecule into an upright, standing geometry on a pedestal of two metal adatoms. This atypical upright orientation of the single molecule, whose stability can be understood as the result of a fine balance between chemical and dispersion forces, enables the system to function as a quantum dot and an on-demand coherent single-electron field emitter. If attached to the tip of the microscope, the standing molecule can also be applied as a sensitive quantum dot sensor. We anticipate that other metastable adsorbate configurations might also be accessible, thereby opening up the third dimension for the design of functional nanostructures on surfaces. Finally, we have made first steps into the direction of an autonomous robotic nanofabrication of single-molecule devices.

Subsystem Density-Functional Theory and its extension to excited states, namely, subsystem Time-Dependent Density-Functional Theory, have been proven to be efficient and accurate fragmentation approaches for ground and excited states. In the present study we extend this approach to the subsystem-based description of total systems by means of GW and the Bethe-Salpeter equation (BSE). For this, we derive the working equations starting from a subsystem-based partitioning of the screened-Coulomb interaction for an arbitrary number of subsystems. Making use of certain approximations, we develop a parameter-free approach in which environmental screening contributions are effectively included for each subsystem. We demonstrate the applicability of these approximations by comparing quasi-particle energies and excitation energies from subsystem-based GW/BSE calculations to the supermolecular reference. Furthermore, we demonstrate the computational efficiency and the usefulness of this method for the description of photoinduced processes in complex chemical environments.

A route towards covalent functionalization of chemically inert 2H-MoS2 exploiting sulfur vacancies is explored by means of (TD)DFT and GW/BSE calculations. Functionalization via nitrogen incorporation at sulfur vacancies is shown to result in more stable covalent binding than via thiol incorporation. In this way, defective monolayer MoS2 is repaired and the quasiparticle band structure as well as the remarkable optical properties of pristine MoS2 are restored. Hence, defect-free functionalization with various molecules is possible. Our results for covalently attached azobenzene, as a prominent photo-switch, pave the way to create photoresponsive two-dimensional (2D) materials.

Excitons with nonzero momenta and their energy dependence are important for time dependent phenomena such as transport properties or the coupling to external or internal fields, for example in electron energy loss spectroscopy. In this paper we calculate the momentum dependent energy landscape of excitons in rubrene single crystals. We show that singlet excitons exhibit a dispersion that is qualitatively similar to the electronic valence and conduction bands, namely a relatively large bandwidth along $\mathrm{\ensuremath{\Gamma}}$--Y and much flatter bands along $\mathrm{\ensuremath{\Gamma}}$--X and $\mathrm{\ensuremath{\Gamma}}$--Z. However, the absolute value of the bandwidths is significantly weaker than for both electronic bands. Triplet excitons, on the other hand, show much less dispersion and the exciton bands are much flatter than their singlet counterparts.