Abstract Ga 2 O 3 has garnered substantial interest owing to its promising applications in power electronics and optoelectronics. Herein, the electronic properties of N-doped κ -Ga 2 O 3 are explored through density functional theory calculations. A variety of N-doped complex defects are examined, including <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>N</mml:mtext> </mml:mrow> <mml:mrow> <mml:mtext>O</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> (N-doped κ -Ga 2 O 3 ), N O V O (N-doped κ -Ga 2 O 3 with O vacancy), N O V Ga (N-doped κ -Ga 2 O 3 with Ga vacancy), N O O i (N-doped κ -Ga 2 O 3 with O interstitial), N O Ga i (N-doped κ -Ga 2 O 3 with Ga interstitial), alongside nitrogen substituting gallium at tetrahedral ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>N</mml:mtext> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mtext>Ga</mml:mtext> </mml:mrow> <mml:mo>,</mml:mo> <mml:mrow> <mml:mtext>tetra</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> ) and octahedral ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>N</mml:mtext> </mml:mrow> <mml:mrow> <mml:mrow> <mml:mtext>Ga</mml:mtext> </mml:mrow> <mml:mo>,</mml:mo> <mml:mrow> <mml:mtext>octa</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> ) sites. Analysis of their formation energies reveals that N O predominates under both Ga-rich and O-rich environments, functioning as a shallow acceptor. Intriguingly, under Ga-rich conditions, there exists a pronounced preference for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>N</mml:mtext> </mml:mrow> <mml:mrow> <mml:mtext>O</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>V</mml:mtext> </mml:mrow> <mml:mrow> <mml:mtext>O</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:mtext> </mml:mtext> </mml:mrow> </mml:mrow> </mml:math> defects over other acceptor-like deep defects, implying that such complexes may obstruct the attainment of p-type conductivity in κ -Ga 2 O 3 due to extensive compensation by oxygen vacancies. Moreover, it is demonstrated that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>N</mml:mtext> </mml:mrow> <mml:mrow> <mml:mtext>O</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>V</mml:mtext> </mml:mrow> <mml:mrow> <mml:mtext>O</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:mtext> </mml:mtext> </mml:mrow> </mml:mrow> </mml:math> complexes can elicit red luminescence, arising from oxygen vacancies coupled with holes localized at acceptor sites introduced by N doping. The intricate electronic structure of κ -Ga 2 O 3 with these complex defects is elucidated through comprehensive analyses of the density of states and electronic band structures. Complementary examinations of electron localization and real-space wavefunctions further illuminate the influence of these defects on the κ -Ga 2 O

Abstract In this work, we introduce a selective and scalable extension of&amp;#xD;the multi-step Rayleigh–Schrödinger and Brillouin–Wigner (RSBW) perturbative&amp;#xD;scheme (see Ref. [5]) , designed to efficiently access the low-energy spectrum&amp;#xD;of molecular systems. The method proceeds by combining successive effective&amp;#xD;Hamiltonian diagonalizations inspired by second-order Rayleigh–Schrödinger&amp;#xD;perturbation theory, with a Brillouin–Wigner correction applied to individually&amp;#xD;optimized states using an updated partitioning of the Hamiltonian. At each&amp;#xD;step, a candidate zeroth-order state is identified and progressively decoupled&amp;#xD;from the remaining higher-lying states, thereby enabling a well-conditioned&amp;#xD;Brillouin–Wigner expansion for the energy correction. In contrast to previous&amp;#xD;approaches, the method selectively targets a small number of low-lying&amp;#xD;states, significantly reducing the numerical overhead while maintaining chemical&amp;#xD;accuracy. The robustness of the method is demonstrated on the LiH and&amp;#xD;H4 molecules, where accurate excitation energies are obtained for the lowest&amp;#xD;singlet states using compact model spaces, confirming its potential for realistic&amp;#xD;applications.

Abstract The electronic structure of solids can routinely be calculated by standard methods like density functional theory. However, in complicated situations like interfaces, grain boundaries or contact geometries one needs to resort to more simplified models of the electronic structure. Tight-binding models are using a reduced set of orbitals and aim to approximate the electronic structure by short range hopping processes. For example, maximally localized Wannier functions are often used for that purpose. However, their accuracy is limited by the need to disentangle the electronic bands. Here, we develop and investigate a different procedure to obtain tight-binding models inspired by machine-learning techniques. The model parameters are optimized in such a way as to reproduce ab-initio band structure data as accurately as possible using an as small as possible number of model parameters. The procedure is shown to result in models with smaller ranges and fewer orbitals than maximally localized Wannier functions but same or even better accuracy. We argue that such a procedure is more useful for automated construction of tight-binding models particularly for large-scale materials calculations.

Abstract Transition metal dichalcogenides (TMDs) are layered materials obtained by stacking two-dimensional sheets weakly bonded by van der Waals interactions. In bulk TMD, band dispersions are observed in the direction normal to the sheet plane (z-direction) due to the hybridization of out-of-plane orbitals but no kz -dispersion is expected at the single-layer limit. Using angle-resolved photoemission spectroscopy, we precisely address the two-dimensional to three-dimensional crossover of the electronic band structure of large area epitaxial WSe2 thin films. Increasing number of discrete electronic states appears in given kz -ranges while increasing the number of layers. The continuous bulk dispersion is nearly retrieved for 6-sheet films. These results are reproduced by calculations going from a relatively simple tight-binding model to a sophisticated KKR-Green’s function calculation.

Abstract This work is a theoretical investigation of the influence of next-nearest-neighbor (NNN) couplings on the electronic properties of blue phosphorus (buk-P) within the multi-orbital tight-binding (MOTB). The objective is to enhance the quantitative accuracy of the tight-binding model of buk-P. We intend to identify and discuss how distant hopping parameters up to the fifth intralayer nearest-neighbors (5NN) and second interlayer nearest-neighbors (2NN) affect the energy dispersion of two-dimensional configurations. We demonstrate that the inclusion of more long-range neighbors is necessary to accurately describe the electronic band levels. In the monolayer, the maximal deviation of the 5NN MOTB result from the 2NN MOTB computation is approximately ≈ 100 meV for the conduction band at the Г–K direction and approximately ≈ 80 meV for the valence band at the Г point, a trend that is also observed in the AA bilayer. This consistency strongly suggests that the 5NN are the primary contributors to this transition. However, in both systems, the introduction of the 5NN significantly improves the overall valence band (conduction band) picture with first-principles interpretations (the conduction band minimum shifts from the Γ–K in the 2NN description to the Γ–M region in the 5NN model), and their energies occur at the Γ–K (Γ–M) region. Our models accurately reproduce the most effective self-energy computations based on the GW approach, showing an indirect energy band gap of approximately Eg ≈ 3.00 (1.44) eV for the monolayer (AA bilayer). To our knowledge, this study is the first to explore the influence of NNN interactions on the energy dispersion bands of buk-P modeled by several valence-state 5NN in-plane and 2NN out-of-plane hopping MOTB approximations. These insights are important for exploring the potential of buk-P in advanced applications, particularly in fields such as quantum computing and optoelectronic devices, where precise control over electronic states is essential.

Abstract The ‘egg-box effect’ is a known challenge in density functional theory (DFT) calculations which arises from the discretisation of continuous quantities, e.g. the electron density. This effect is observed when the system is moved relative to the underlying computational grid and causes an unphysical change in the system’s total energy, violating translational invariance. The pattern of energy change with translation is reminiscent of an egg-box. This effect can cause unphysical results such as geometry relaxations finding incorrect crystal symmetries or imaginary phonon modes in vibrational calculations. The egg-box effect can be mitigated by using finer grids for all continuous quantities, but this greatly increases computational cost. For plane-wave DFT the effect’s origin is the evaluation of the exchange and correlation (XC) energy ( E XC ). We present a novel technique for estimating the violation of translational invariance in E XC , using a Fourier interpolation scheme, providing an estimate of the uncertainty. Our results also show that the numerical behaviour of the XC approximations is strongly linked to the magnitude of the violation of the translation invariance. The more numerically ill behaved XC functionals, such as the more advanced meta-generalised-gradient approximations functionals, exhibit changes in E XC (due to violation of translation invariance) that are orders of magnitude worse than less advanced functionals. Performing this analysis at an early stage of a workflow can inform the user about the expected accuracy of subsequent calculations. Further, our results demonstrate that by selectively computing E XC and its corresponding potential ( V XC ) on a finer grid, the egg-box effect can be significantly reduced. Coupled with our uncertainty quantification method, egg-box related inaccuracies can be avoided more conveniently and efficiently than just increasing grid resolution until inaccuracies appear suppressed. This work offers a promising pathway towards mitigating the egg-box effect in a diverse range of materials modelling applications.

Abstract We report on results from an experiment at the European x-ray free electron laser where we measured the x-ray Thomson scattering (XRTS) spectrum of single crystal silicon with ultrahigh resolution. Compared to similar previous experiments, we consider a more complex scattering setup, in which the scattering vector changes orientation through the crystal lattice. In doing so, we are able to observe strong geometric dependencies in the inelastic scattering spectrum of silicon at low scattering angles. Furthermore, the high quality of the experimental data allows us to benchmark state-of-the-art TDDFT calculations, and demonstrate TDDFT’s ability to accurately predict these geometric dependencies. Finally, we note that this experimental data was collected at a much faster rate than another recently reported dataset using the same setup, demonstrating that ultrahigh resolution XRTS data can be collected in more general experimental scenarios.

Abstract Thanks to their favorable electronic and optical properties, sodium–potassium-antimonides are an emerging class of crystals used as photocathodes in particle accelerators. The persisting challenges related to the synthesis and characterization of these materials demand support from theory and make the study of computationally predicted polymorphs particularly relevant to identifying the structure, composition, and properties of the samples. Using first-principles methods based on density-functional theory and many-body perturbation theory, the electronic and optical properties of cubic NaK2Sb and hexagonal Na2KSb are studied. Both systems, experimentally reported in the hexagonal and cubic phase, respectively, exhibit an indirect fundamental gap that is energetically very close to the direct band gap at Γ of magnitude 0.81 eV for NaK2Sb and 0.70 eV for Na2KSb. In the band structure of both materials, Sb p-states dominate the valence region with minor contributions from the alkali p-states, while the alkali s-states mainly contribute at lower energies. The optical spectra of both crystals are not subject to sizeable excitonic effects, except for a redshift of the excitation energies of 50–100 meV and some redistribution of the oscillator strength beyond the lowest-energy peak in the near-infrared region. Our results indicate that computationally predicted cubic NaK2Sb and hexagonal Na2KSb have favorable characteristics as photocathodes and, as such, their presence in polycrystalline samples is not detrimental for this application.

Abstract The recently proposed machine learning-based physically-constrained nonlocal (MPN) kinetic energy density functional (KEDF) can be used for simple metals and their alloys (Sun and Chen 2024 Phys. Rev. B 109 115135). However, the MPN KEDF does not perform well for semiconductors. Here we propose a multi-channel MPN (CPN) KEDF, which extends the MPN KEDF to semiconductors by integrating information collected from multiple channels, with each channel featuring a specific length scale in real space. The CPN KEDF is systematically tested on silicon and binary semiconductors. We find that the multi-channel design for KEDF is beneficial for machine-learning-based models in capturing the characteristics of semiconductors, particularly in handling covalent bonds. In particular, the CPN5 KEDF, which utilizes five channels, demonstrates excellent accuracy across all tested systems. These results offer a new path for generating KEDFs for semiconductors.

Abstract Twisted multilayer structures are considered a helpful framework for exploring strongly correlated many-particle systems, where phenomena of physics correlation emerge. Here, we present the Trotter–Suzuki tight-binding time propagation method for computing the density of states (DOS) in a 30° twisted bilayer graphene (TBG). This method solves the time-dependent Schrödinger equation by decomposing Hamiltonian matrices to derive the correlation function. The Fourier transform of this correlation function yields the DOS of the system up to ≈ 1000 000 atoms. Our calculation proves that geometry makes an outstanding contribution to our final results. Additionally, applying additional gate voltage induces shifts in Van Hove singularities, potentially leading to the emergence of new states at the Fermi energy level. The results demonstrate that TBG systems can be easily adjusted and modified for further investigation of optoelectronic features.