The electronic and optical properties of quasi-one-dimensional transition-metal trichalcogenides remain largely unexplored beyond the mean-field approximation, and it is not clear how they evolve as the crystal is thinned. By performing first-principles many-body perturbation theory calculations, we determine the quasiparticle band structures and the polarization-resolved optical response of ZrS 3 in the bulk, bilayer, and monolayer limits, using a hierarchy of methods (hybrid DFT, G W , and the Bethe-Salpeter equation). We find that all three systems are indirect-gap semiconductors with a quasidirect character, the direct-indirect splitting being δ ≈ 0.10 – 0.13 eV and nearly independent of both the level of theory and the dimensionality. The mean-field gaps are almost insensitive to thickness, whereas the quasiparticle corrections increase the gap by ≈ 0.9 eV from bulk to monolayer. The effective exact-exchange fraction reproducing the G W gap scales as α ∼ ɛ ∞ − 1 , increasing from ≈ 0.19 to ≈ 0.33 , so that no single hybrid functional describes the full dimensional series. The optical onset blueshifts monotonically ( ≈ 2.4 → 2.8 → 3.0 eV ) and the near-edge absorption is strongly dichroic. A change in light polarization does not simply shift the excitonic resonance ( ≈ 0.09 eV ); it also reorganizes the underlying excitonic wave function, selecting distinct band channels and k -space regions. A real-space, participation-ratio analysis resolves moderately delocalized, Wannier-Mott-like excitons templated along the covalent chains. They are predominantly sulfur-derived (75%–88% of the density on sulfur for the chain-polarized bulk states), which identifies them as ( S 2 ) 2 − disulfide excitations rather than S → Zr charge-transfer states, while in the bilayer the electron delocalizes across both layers, the real-space imprint of interlayer screening. These results provide a consistent reference for the quasiparticle and excitonic energy scales of ZrS 3 from the bulk to the few-layer limit.
The electronic and optical properties of quasi-one-dimensional transition-metal trichalcogenides remain largely unexplored beyond the mean-field approximation, and it is not clear how they evolve as the crystal is thinned. By performing first-principles many-body perturbation theory calculations, we determine the quasiparticle band structures and the polarization-resolved optical response of ZrS 3 in the bulk, bilayer, and monolayer limits, using a hierarchy of methods (hybrid DFT, G W , and the Bethe-Salpeter equation). We find that all three systems are indirect-gap semiconductors with a quasidirect character, the direct-indirect splitting being δ ≈ 0.10 – 0.13 eV and nearly independent of both the level of theory and the dimensionality. The mean-field gaps are almost insensitive to thickness, whereas the quasiparticle corrections increase the gap by ≈ 0.9 eV from bulk to monolayer. The effective exact-exchange fraction reproducing the G W gap scales as α ∼ ɛ ∞ − 1 , increasing from ≈ 0.19 to ≈ 0.33 , so that no single hybrid functional describes the full dimensional series. The optical onset blueshifts monotonically ( ≈ 2.4 → 2.8 → 3.0 eV ) and the near-edge absorption is strongly dichroic. A change in light polarization does not simply shift the excitonic resonance ( ≈ 0.09 eV ); it also reorganizes the underlying excitonic wave function, selecting distinct band channels and k -space regions. A real-space, participation-ratio analysis resolves moderately delocalized, Wannier-Mott-like excitons templated along the covalent chains. They are predominantly sulfur-derived (75%–88% of the density on sulfur for the chain-polarized bulk states), which identifies them as ( S 2 ) 2 − disulfide excitations rather than S → Zr charge-transfer states, while in the bilayer the electron delocalizes across both layers, the real-space imprint of interlayer screening. These results provide a consistent reference for the quasiparticle and excitonic energy scales of ZrS 3 from the bulk to the few-layer limit.
A systematically converging series of ab initio, postdensity functional, size-consistent, electron-correlated approximations is desired for predictive computing of electronic band structures of insulating, semiconducting, and metallic solids. A series that meets all of these desiderata (except the applicability to metals) is ab initio many-body Green’s function theory based on Gaussian-type orbital (GTO) basis sets. Here, its leading-order approximation, the second-order Green’s function (GF2) method in the diagonal and frequency-independent approximations with the aug-cc-pVDZ basis set, is applied to the fundamental band gaps of three semiconductors (diamond, silicon, and silicon carbide in the zincblende structure) using cluster models. Corrections are made to the basis set incompleteness errors by the explicit correlation (F12) ansatz (GF2-F12) for the valence band edges. The crystals are modeled as surface-passivated clusters of increasing sizes, whose wave functions are expanded by up to 2709 GTO basis functions. Immense computational costs of these calculations are overcome by the highly scalable stochastic algorithm of the Monte Carlo GF2-F12 method, whose operation cost per state increases only as a cubic power of system size, which has a tiny memory footprint and easily achieves near-perfect parallel efficiency on thousands of CPUs or on hundreds of GPUs. The correlated, F12-corrected highest-occupied and lowest-unoccupied molecular orbital energy (HOMO–LUMO) gap is 5.78 ± 0.07 eV for C 87 H 76 as compared with the experimental value of the fundamental (indirect) band gap of bulk diamond at 5.48 eV. The correlated, F12-corrected HOMO–LUMO gaps for Si 75 H 76 and Si 32 C 43 H 76 are 2.56 ± 0.15 and 3.50 ± 0.12 eV, respectively, which are expected to decrease further with increasing cluster sizes. The experimental fundamental (indirect) band gaps of bulk silicon and silicon carbide are 1.17 and 2.42 eV, respectively.
We develop an analytical procedure to retrieve fundamental material parameters of monolayer transition-metal dichalcogenides from optical and magneto-optical exciton spectra, based on the solvable modified Kratzer model. The proposed retrieval procedure naturally consists of two complementary stages. In the first stage, explicit inversion formulas determine the quasiparticle bandgap, effective screening parameter, and energy scaling factor directly from the experimentally measured energies of the three lowest excitonic states, from which the screening length is subsequently obtained. In the second stage, an analytical expression for the magnetic-field dependence of the exciton energies independently yields the reduced exciton mass, from which the surrounding dielectric constant is then calculated. Once the complete set of material parameters has been retrieved, the framework analytically predicts the diamagnetic coefficients, exciton radii, and complete magnetoexciton spectra without introducing additional fitting parameters or matrix diagonalization. The method is applied to a broad range of experimental samples for WSe2, WS2, MoS2, MoSe2, and MoTe2 monolayers embedded in different dielectric environments. The retrieved material parameters are in good agreement with independent experimental measurements and previous Rytova--Keldysh (RK) calculations, while the predicted excitonic properties accurately reproduce available magneto-optical observations. The proposed analytical theory provides an efficient, physically transparent alternative to conventional numerical fitting procedures and offers an effective tool for the rapid characterization of two-dimensional semiconductors via excitonic spectroscopy.
The three-band $p\text{\ensuremath{-}}d$ model of strongly correlated electrons interacting with optical phonons via diagonal and off-diagonal electron-phonon interactions is considered within the cluster perturbation theory. In the beginning, the exact diagonalization of the Hamiltonian of a CuO4 cluster results in the construction of local polaronic eigenstates $\left|p\right\ensuremath{\rangle}$ with hole numbers nh=0,1,2 per unit cell. The intercluster hoppings and interactions are exactly written in terms of Hubbard operators ${X}_{f}^{pq}=\left|p\right\ensuremath{\rangle}\ensuremath{\langle}q|$ determined via the multielectron polaronic eigenstates $\left|p\right\ensuremath{\rangle}$ at site f. The Fermi-type single-electron quasiparticle dispersion and spectral weight are calculated for the undoped antiferromagnetic parent insulator like La2CuO4. The quasiparticle dispersion of Hubbard polarons is determined by a hybridization of the Hubbard fermion subbands with local Franck-Condon resonances so the main polaronic effect of the quasiparticle band structure is a splitting of the Hubbard bands on the number of Hubbard polaron subbands. Increasing of the EPI constant results in an increase of splitting, decrease of the subband width, transfer of the spectral weight to high-energy multiphonon excitations, and subsequent localization of the charge carriers. Herewith, the effect of such renormalization for the conduction band and the valence one differs depending on the ratio of the diagonal and off-diagonal EPI. In the framework of the GTB method, the Franck-Condon broadening of the spectral function of polaronic excitations is also reproduced for strongly correlated systems with strong electron-phonon interaction.
We study the effects of electron-electron interactions on the charge excitation spectrum of the spinful Su-Schrieffer-Heeger (SSH) model, a prototype of a one-dimensional bulk obstructed topological insulator. In view of recent progress in the fabrication of dopant-based quantum simulators we focus on experimentally detectable signatures of interacting topology in finite lattices. To this end we use Lanczos-based exact diagonalization to calculate the single-particle spectral function in real space which generalizes the local density of states to interacting systems. Its spatial and spectral resolution allows for the direct investigation and identification of edge states. By studying the noninteracting limit, we demonstrate that the topological in-gap states on the boundary are robust against both finite-size effects as well as random bond and onsite disorder which suggests the feasibility of simulating the SSH model in engineered dopant arrays in silicon. While edge excitations become zero-energy spinlike for any finite interaction strength, our analysis of the spectral function shows that the single-particle charge excitations are gapped out on the boundary. Despite the loss of topological protection, we find that these edge excitations are quasiparticlelike as long as they remain within the bulk gap. Above a critical interaction strength of ${U}_{c}\ensuremath{\approx}5t$ these quasiparticles on the boundary lose their coherence which is explained by the merging of edge and bulk states. This is in contrast to the many-body edge excitations which survive the limit of strong coupling, as established in the literature. Our findings show that for moderate repulsive interactions the nontrivial phase of the interacting SSH model can be detected through remnant signatures of topological single-particle states using single-particle local measurement techniques such as scanning tunneling spectroscopy.
Polarons—quantum particles dressed by a cloud of bath excitations—arise whenever a particle interacts strongly with its host medium. Electron and hole polarons, formed when carriers bind to a phonon cloud through electron-phonon (e-ph) interactions, govern charge transport in transition metal oxides, organic semiconductors, and halide perovskites. The concept generalizes to exciton-phonon interactions, giving rise to exciton polarons that produce the large Stokes shifts and broad photoluminescence (PL) lineshapes central to light-emitting applications. A predictive treatment of polarons has remained elusive. Numerically exact methods such as diagrammatic Monte Carlo (DMC) have been restricted to simplified model Hamiltonians, while first-principles approaches based on density functional theory provide material-specific e-ph interactions but treat the e-ph correlation approximately. This thesis bridges that gap by developing first-principles diagrammatic Monte Carlo (FPDMC), which stochastically sums all e-ph Feynman diagrams using accurate ab-initio interactions, yielding numerically exact polaron properties in real materials. Two methodological advances make FPDMC possible. A matrix-product formalism sums over electronic band indices exactly, alleviating the multi-band sign problem in realistic band structures. A data-driven compression of e-ph interactions based on singular-value decomposition (SVD) in the Wannier basis then accelerates the method by more than 10³×. The SVD compression also reveals a hidden low-dimensional structure of quantum interactions, maintaining accuracy across charge transport, spin relaxation, band renormalization, and superconductivity calculations. Extending this philosophy to phonon-phonon interactions via a permanent CP (PCP) decomposition yields 10³–10⁴× compression of anharmonic force constants and orders-of-magnitude speedups in thermal conductivity calculations. Applying FPDMC, we study polarons in LiF, SrTiO₃, and TiO₂, finding excellent agreement with experimental mobilities and resolving the contrasting small- and large-polaron transport in the two TiO₂ polymorphs. To make the microscopic picture concrete, we introduce an e-ph correlation function that visualizes lattice distortion and polaron orbital character. Extending FPDMC to exciton polarons, we obtain first-principles exciton-phonon interactions from finite-momentum Bethe-Salpeter equation calculations and derive a Fermi-golden-rule PL theory. Applied to CrBr₃, FPDMC predicts a broad PL spectrum agreeing with experiment in both peak position and lineshape.
Many-body GW-Bethe-Salpeter equation calculations are essential for accurate simulations of electronic structure and optical properties in modern low-dimensional nanomaterials. However, these methods are computationally demanding and can exhibit localized numerical instabilities or convergence failures that are difficult to detect within high-throughput workflows. We introduce an agent-guided multi-fidelity framework for correcting GW-Bethe-Salpeter excited-state landscapes in strained MoS2-WS2 bilayers. Across stacking registries, strain branches and reciprocal-space samplings, the workflow identifies spike-like excursions, near-zero-gap collapse and cross-fidelity inconsistencies associated with fragile long-wavelength dielectric screening. A structural agent evaluates calculations by assigning confidence weights and selectively using a small number of high-accuracy reference points. Machine learning models then transfer information across related systems and apply Gaussian process corrections to recover improved quasiparticle gaps and exciton binding energies, with calibrated uncertainty estimates. The approach corrects numerically induced artifacts without erasing physical strain dependence and substantially improves agreement with higher-fidelity references relative to a no-agent baseline. These results show that reliable surrogate learning for excited-state materials requires explicit diagnosis of numerical fragility, not direct interpolation of raw first-principles data points. The proposed framework is readily transferable to other optoelectronic nanomaterials characterized by strong quantum confinement, such as quantum dots, nanoribbons, layered two-dimensional semiconductors, and hybrid perovskite nanostructures.