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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., Comment: 9 pages, 3 figures

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-MoS$_2$ 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 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 MoS$_2$ bilayer adhering to the diamond, which reduces 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 MoS$_2$ bilayers., Comment: 8 pages, 5 figures

Correlated quantum phenomena in one-dimensional (1D) systems that exhibit competing electronic and magnetic order are of strong interest for studying 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 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 $m^e_X/m^e_Y \sim 50$. 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 of metallic carbon nanotubes. Moreover, due to 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., Comment: main: 16 pages, 5 figures; SI: 15 pages, 9 figures

The effect of a magnetic field on the optical absorption in semiconductors has been measured experimentally and modeled theoretically for various systems in previous decades. We present a new first-principles approach to systematically determine the response of excitons to magnetic fields, i.e. exciton $g$ factors. By utilizing the $GW$-Bethe-Salpeter equation methodology we show that $g$ factors extracted from the Zeeman shift of electronic bands are strongly renormalized by many-body effects which we trace back to the extent of the excitons in reciprocal space. We apply our approach to monolayers of transition metal dichalcogenides (MoS$_2$, MoSe$_2$, MoTe$_2$, WS$_2$, and WSe$_2$) with strongly bound excitons for which $g$ factors are weakened by about 30%.

Even if individual two-dimensional materials own various interesting and unexpected properties, the stacking of such layers leads to van der Waals solids which unite the characteristics of two dimensions with novel features originating from the interlayer interactions. In this topical review, we cover fabrication and characterization of van der Waals heterosructures with a focus on heterobilayers made of monolayers of semiconducting transition metal dichalcogenides. Experimental and theoretical techniques to investigate those heterobilayers are introduced. Most recent findings focusing on different transition metal dichalcogenides heterostructures are presented and possible optical transitions between different valleys, appearance of moire patterns and signatures of moire excitons are discussed. The fascinating and fast growing research on van der Waals hetero-bilayers provide promising insights required for their application as emerging quantum-nano materials., Comment: 14 pages, 6 figures

We perform absorption and photoluminescence spectroscopy of trions in hBN-encapsulated WSe$_2$, WS$_2$, MoSe$_2$, and MoS$_2$ monolayers, depending on temperature. The different trends for W- and Mo-based materials are excellently reproduced considering a Fermi-Dirac distribution of bright and dark trions. We find a dark trion, $\rm{X_D^-}$ 19 meV $\textit{below}$ the lowest bright trion, $\rm{X}_1^-$ in WSe$_2$ and WS$_2$. In MoSe$_2$, $\rm{X_D^-}$ lies 6 meV $\textit{above}$ $\rm{X}_1^-$, while $\rm{X_D^-}$ and $\rm{X}_1^-$ almost coincide in MoS$_2$. Our results agree with GW-BSE $\textit{ab-initio}$ calculations and quantitatively explain the optical response of doped monolayers with temperature., Comment: 16 pages including supporting information, 4 figures in the main text, 10 figures in the supporting information

We present an extension of the tunneling theory for scanning tunneling microcopy (STM) to include different types of vibrational-electronic couplings responsible for inelastic contributions to the tunnel current in the strong-coupling limit. It allows for a better understanding of more complex scanning tunneling spectra of molecules on a metallic substrate in separating elastic and inelastic contributions. The starting point is the exact solution of the spectral functions for the electronic active local orbitals in the absence of the STM tip. This includes electron-phonon coupling in the coupled system comprising the molecule and the substrate to arbitrary order including the anti-adiabatic strong coupling regime as well as the Kondo effect on a free electron spin of the molecule. The tunneling current is derived in second order of the tunneling matrix element which is expanded in powers of the relevant vibrational displacements. We use the results of an ab-initio calculation for the single-particle electronic properties as an adapted material-specific input for a numerical renormalization group approach for accurately determining the electronic properties of a NTCDA molecule on Ag(111) as a challenging sample system for our theory. Our analysis shows that the mismatch between the ab-initio many-body calculation of the tunnel current in the absence of any electron-phonon coupling to the experiment scanning tunneling spectra can be resolved by including two mechanisms: (i) a strong unconventional Holstein term on the local substrate orbital leads to reduction of the Kondo temperature and (ii) a different electron-vibrational coupling to the tunneling matrix element is responsible for inelastic steps in the $dI/dV$ curve at finite frequencies., Comment: 34 pages, 26 figure

The research field of two dimensional (2D) materials strongly relies on optical microscopy characterization tools to identify atomically thin materials and to determine their number of layers. Moreover, optical microscopy-based techniques opened the door to study the optical properties of these nanomaterials. We presented a comprehensive study of the differential reflectance spectra of 2D semiconducting transition metal dichalcogenides (TMDCs), MoS2, MoSe2, WS2, and WSe2, with thickness ranging from one layer up to six layers. We analyzed the thickness-dependent energy of the different excitonic features, indicating the change in the band structure of the different TMDC materials with the number of layers. Our work provided a route to employ differential reflectance spectroscopy for determining the number of layers of MoS2, MoSe2, WS2, and WSe2., Comment: Main text (3 Figures) and Supp. Info. (23 Figures)

Since their discovery single-layer semiconducting transition metal dichalcogenides have attracted much attention thanks to their outstanding optical and mechanical properties. Strain engineering in these two-dimensional materials aims to tune their bandgap energy and to modify their optoelectronic properties by the application of external strain. In this paper we demonstrate that biaxial strain, both tensile and compressive, can be applied and released in a timescale of a few seconds in a reproducible way on transition metal dichalcogenides monolayers deposited on polymeric substrates. We can control the amount of biaxial strain applied by letting the substrate expand or compress. To do this we change the substrate temperature and choose materials with a large thermal expansion coefficient. After the investigation of the substrate-dependent strain transfer, we performed micro-differential spectroscopy of four transition metal dichalcogenides monolayers (MoS2, MoSe2, WS2, WSe2) under the application of biaxial strain and measured their optical properties. For tensile strain we observe a redshift of the bandgap that reaches a value as large as 95 meV/% in the case of single-layer WS2 deposited on polypropylene. The observed bandgap shifts as a function of substrate extension/compression follow the order MoSe2 < MoS2 < WSe2 < WS2. Theoretical calculations of these four materials under biaxial strain predict the same trend for the material-dependent rates of the shift and reproduce well the features observed in the measured reflectance spectra., Comment: 10 pages, 5 figures, 2 tables, supporting information

Trion states of three correlated particles (e.g., two electrons and one hole) are essential to understand the optical spectra of doped or gated nanostructures, like carbon nanotubes or transition-metal dichalcogenides. We develop a theoretical many-body description for such correlated states using an ab-initio approach. It can be regarded as an extension of the widely used $GW$ method and Bethe-Salpeter equation, thus allowing for a direct comparison with excitons. We apply this method to a semiconducting (8,0) carbon nanotube, and find that the lowest optically active trions are red-shifted by $\sim 130$ meV compared to the excitons, confirming experimental findings for similar tubes. Moreover, our method provides detailed insights in the physical nature of trion states. In the prototypical carbon nanotube we find a variety of different excitations, discuss the spectra, energy compositions, and correlated wave functions., Comment: main text, supplement

We investigate the adsorption of a single tetracyanoethylene (TCNE) molecule on the silver (001) surface. Adsorption structures, electronic properties, and scanning tunneling microscopy (STM) images are calculated within density-functional theory. Adsorption occurs most favorably in on-top configuration, with the C=C double bond directly above a silver atom and the four N atoms bound to four neighboring Ag atoms. The lowest unoccupied molecular orbital of TCNE becomes occupied due to electron transfer from the substrate. This state dominates the electronic spectrum and the STM image at moderately negative bias. We discuss and employ a spatial extrapolation technique for the calculation of STM and scanning tunneling spectroscopy (STS) images. Our calculated images are in good agreement with experimental data.

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 figures

Optical excitations of molecular systems can be modified by their physical environment. We analyze the underlying mechanisms within many-body perturbation theory, which is particularly suited to study non-local polarizability effects on the electronic structure. Here we focus on the example of a semiconducting carbon nanotube, which observes redshifts of its excitons when the tube is touched by another nanotube or other physisorbates. We show that the redshifts mostly result from the polarizability of the attached ad-system. Electronic coupling may enhance the redshifts, but depends very sensitively on the structural details of the contact.

The dynamics of a molecular junction consisting of a PTCDA molecule between the tip of a scanning tunneling microscope and a Ag(111) surface have been investigated experimentally and theoretically. Repeated switching of a PTCDA molecule between two conductance states is studied by low-temperature scanning tunneling microscopy for the first time, and is found to be dependent on the tip-substrate distance and the applied bias. Using a minimal model Hamiltonian approach combined with density-functional calculations, the switching is shown to be related to the scattering of electrons tunneling through the junction, which progressively excite the relevant chemical bond. Depending on the direction in which the molecule switches, different molecular orbitals are shown to dominate the transport and thus the vibrational heating process. This in turn can dramatically affect the switching rate, leading to non-monotonic behavior with respect to bias under certain conditions. In this work, rather than simply assuming a constant density of states as in previous works, it was modeled by Lorentzians. This allows for the successful description of this non-monotonic behavior of the switching rate, thus demonstrating the importance of modeling the density of states realistically., Comment: 20 pages, 6 figures, 1 table

We discuss an efficient approach to excited electronic states within ab-initio many-body perturbation theory (MBPT). Quasiparticle corrections to density-functional theory result from the difference between metallic and non-metallic dielectric screening. They are evaluated as a small perturbation to the DFT-LDA band structure, rather than fully calculating the self energy and evaluating its difference from the exchange-correlation potential. The dielectric screening is desribed by a model, which applies to bulk crystals, as well as, to systems of reduced dimension, like molecules, surfaces, interfaces, and more. The approach also describes electron-hole interaction. The resulting electronic and optical spectra are slightly less accurate but much faster to calculate than a full MBPT calculation. We discuss results for bulk silicon and argon, for the Si(111)-(2x1) surface, the SiH4 molecule, an argon-aluminum interface, and liquid argon.

Using a scanning tunneling microscope we have measured the quantum conductance through a PTCDA molecule for different configurations of the tip-molecule-surface junction. A peculiar conductance resonance arises at the Fermi level for certain tip to surface distances. We have relaxed the molecular junction coordinates and calculated transport by means of the Landauer/Keldysh approach. The zero bias transmission calculated for fixed tip positions in lateral dimensions but different tip substrate distances show a clear shift and sharpening of the molecular chemisorption level on increasing the STM-surface distance, in agreement with experiment., Comment: accepted for publication in Applied Physics A

Two state-of-the-art computational approaches: quantum Monte Carlo (QMC), based on accurate total energies, and GW with exciton effects (GW-BSE), based on perturbation theory are employed to calculate ionization potentials, electron affinities, and first excited singlet and triplet energies for the silane and methane molecules. Results are in excellent agreement between these dramatically different approaches and with available experiment. The optically forbidden triplet excitation in silane is predicted to lie roughly 1 eV higher than previously reported. For methane, the impact of geometry relaxation is shown to be $\sim$ 2 eV for excited states. Further, in the GW-BSE method, we demonstrate that inclusion of off-diagonal matrix elements in the self-energy operator is crucial for an accurate picture., Comment: Accepted to Physical Review Letters (11/15/00)