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The fundamental energy gap of a periodic solid distinguishes insulators from metals and characterizes low-energy single-electron excitations. However, the gap in the band structure of the exact multiplicative Kohn–Sham (KS) potential substantially underestimates the fundamental gap, a major limitation of KS densityfunctional theory. Here, we give a simple proof of a theorem: In generalized KS theory (GKS), the band gap of an extended system equals the fundamental gap for the approximate functional if the GKS potential operator is continuous and the density change is delocalized when an electron or hole is added. Our theorem explains how GKS band gaps from metageneralized gradient approximations (meta-GGAs) and hybrid functionals can be more realistic than those from GGAs or even from the exact KS potential. The theorem also follows from earlier work. The band edges in the GKS one-electron spectrum are also related to measurable energies. A linear chain of hydrogen molecules, solid aluminum arsenide, and solid argon provide numerical illustrations.

Dye-doped polymer films of Poly(methyl methacrylate) PMMA have been prepared with the use of the conventional solution cast technique. Natural dye has been extracted from environmentally friendly material of green tea (GT) leaves. Obvious Fourier transform infrared (FTIR) spectra for the GT extract were observed, showing absorption bands at 3401 cm−1, 1628 cm−1, and 1029 cm−1, corresponding to O–H/N–H, C=O, and C–O groups, respectively. The shift and decrease in the intensity of the FTIR bands in the doped PMMA sample have been investigated to confirm the complex formation between the GT dye and PMMA polymer. Different types of electronic transition could be seen in the absorption spectra of the dye-doped samples. For the PMMA sample incorporated with 28 mL of GT dye, distinguishable intense peak around 670 nm appeared, which opens new frontiers in the green chemistry field that are particularly suitable for laser technology and optoelectronic applications. The main result of this study showed that the doping of the PMMA polymer with green tea dye exhibited a strong absorption peak around 670 nm in the visible range. The absorption edge was found to be shifted towards the lower photon energy for the doped samples. Optical dielectric loss and Tauc’s model were used to estimate the optical band gaps of the samples and to specify the transition types between the valence band (VB) and conduction band (CB), respectively. A small band gap of around 2.6 eV for the dye-doped PMMA films was observed. From the scientific and engineering viewpoints, this topic has been found to be very important and relevant. The amorphous nature of the doped samples was found and ascribed to the increase of Urbach energy. The Urbach energy has been correlated to the analysis of X-ray diffraction (XRD) to display the structure-properties relationships.

We present designs of 2D, isotropic, disordered, photonic materials of arbitrary size with complete band gaps blocking all directions and polarizations. The designs with the largest band gaps are obtained by a constrained optimization method that starts from a hyperuniform disordered point pattern, an array of points whose number variance within a spherical sampling window grows more slowly than the volume. We argue that hyperuniformity, combined with uniform local topology and short-range geometric order, can explain how complete photonic band gaps are possible without long-range translational order. We note the ramifications for electronic and phononic band gaps in disordered materials.

2D Ruddlesden–Popper halide perovskites, which incorporate hydrophobic organic interlayers to considerably improve environmental stability and optical properties diversity, have attracted substantial research attention for optoelectronic applications. The burgeoning broad emission arising from exciton self‐trapping of 2D perovskites shows a strong dependence on a deformable structure. Here, the pressure‐induced broadband emission of layered (001) Pb‐Br perovskite with a large Stokes shift in the visible region is observed by finely improving lattice distortion to increase exciton–phonon coupling under hydrostatic pressure. Band gap narrows ≈0.5 eV under modest pressure, mainly due to the large compressibility of the orientational organic layer, confirming that the bulky organic cations notably influence the structure and, in turn, the various properties of materials. Sequential amorphization of the organic and inorganic layer is confirmed by high pressure Raman and X‐ray diffraction measurements, suggesting the particularity of layered crystal structures. The mechanism constructed here offers a new route for tuning the optical properties of 2D perovskites. The optical properties of 2D halide perovskite (C6H5C2H4NH3)2PbBr4 are significantly modified by lattice compression. A pressure‐induced new broadband emission with a large Stokes shift is observed in 2D Pb‐Br perovskite by improving lattice distortion to increase exciton–phonon coupling, promoting its current and future optoelectronic device applications through improved materials‐by‐design.

We show that slightly polydisperse disordered 2D foams can be used as a self-assembled template for isotropic photonic band gap (PBG) materials for transverse electric (TE) polarization. Calculations based on in-house experimental and simulated foam structures demonstrate that, at sufficient refractive index contrast, a dry foam organization with threefold nodes and long slender Plateau borders is especially advantageous to open a large PBG. A transition from dry to wet foam structure rapidly closes the PBG mainly by formation of bigger fourfold nodes, filling the PBG with defect modes. By tuning the foam area fraction, we find an optimal quantity of dielectric material, which maximizes the PBG in experimental systems. The obtained results have a potential to be extended to 3D foams to produce a next generation of self-assembled disordered PBG materials, enabling fabrication of cheap and scalable photonic devices.

In addition to its traditional application in white pigments, nanocrystalline titania (TiO2) has optoelectronic and photocatalytic properties (strongly dependent on crystallinity, particle size, and surface structure) that grant this naturally occurring oxide new technological applications. Sol-gel is one of the most widely used methods to synthesize TiO2 films and NPs, but the products obtained (mostly oxy-hydrated amorphous phases) require severe heat-treatments to promote crystallization, in which control over size and shape is difficult to achieve. In this work, we obtained new photocatalytic materials based on amorphous titania and measured their electronic band gap. Two case studies are reported that show the enormous potential of amorphous titania as bactericide or photocatalyst. In the first, amorphous sol-gel TiO2 thin films doped with N (TiO2−xNx, x = 0.75) were designed to exhibit a photonic band gap in the visible region. The identification of Ti-O-N and N-Ti-O bindings was achieved by XPS. The photonic band gaps were found to be 3.18 eV for a-TiO2 and 2.99 eV for N-doped a-TiO2. In the second study, amorphous titania and amine-functionalized amorphous titania nanoparticles were synthetized using a novel base-catalysed sol-gel methodology. All the synthesized amorphous TiO2 nanoparticles exhibit bactericide performance (E. coli, ASTME 2149-13).

Despite the excellent merits of lead perovskite solar cells, their instability and toxicity still present a bottleneck for practical applications. Bismuth perovskite has emerged as a candidate for photovoltaic (PV) applications, because it not only has a low toxicity but is also stable in air. However, the power conversion efficiency (PCE) remains an unsolved problem. We performed band gap tuning experiments to improve the efficiency. The absorption of ABi 3 I 10 structure films was extended within the visible region, and the optical band gap was decreased considerably compared to that for Cs 3 Bi 2 I 9 . Furthermore, we explained the correlation between the structure and the optical properties via a first-principles study. A device employing CsBi 3 I 10 as a photoactive layer exhibits a PCE of 1.51% and an excellent ambient stability over 30 days.

In this work, we have explored a novel application of one–dimensional (1D) photonic crystals (PCs) as a biomarker for the detection of organic materials in wastewater. The high concentration of organic materials may lead to adverse impact on human life. In order to save human life from these adverse effects, we have investigated the bio-alcohol sensing properties of a 1D multilayer periodic structure (AB)N/C/(AB)N capable of detecting organic materials in wastewater. The proposed structure works on the principle to detect a very small change in the refractive index of the wastewater sample under investigation by means of producing a shift in the position of the defect mode inside the photonic band gap (PBG) of the proposed structure. The transfer matrix method (TMM) has been used to investigate the transmission properties of the proposed design with the help of MATLAB software. We have also studied the effect of changes in the defect layer’s thickness, the volume fraction of the nanocomposite material and the incident angle on the sensitivity of our proposed bio-alcohol sensing design. Our bio-alcohol sensor shows a high sensitivity value of 500 nm/RIU and a low detection limit value of 1 × 10−5 RIU. The figure of merit and quality factor values of our bio-alcohol sensor are 5 × 103 and 5.236 × 103, respectively. The damping rate of the design is ξ=95.4927×10−5.

Band gap engineering of atomically thin two-dimensional (2D) materials has attracted a huge amount of interest as a key aspect to the application of these materials in nanooptoelectronics and nanophotonics. Low-loss electron energy loss spectroscopy has been employed to perform a direct measurement of the band gap in atomically thin MoxW(1−x)S2 nanoflakes. The results show a bowing effect with the alloying degree, which fits previous studies focused on excitonic transitions. Additional properties regarding the Van Hove singularities in the density of states of these materials, as well as high energy excitonic transition, have been analysed as well.

To address the recombination problem of photogenerated electrons and holes during photocatalysis, strategies to design composite photocatalysts with heterojunction structures have been widely adopted. In order to explore the electron transfer pathway and photocatalytic mechanism of the PtS2/WSe2 heterostructure, the band structure, electronic properties and catalytic activity of the structure were systematically calculated by density functional theory (DFT). We designed two models consisting of PtS2 and WSe2 monolayers to find more stable structures through adsorption energy calculations. In this work, MUlliken charge analysis and differential charge density confirmed the heterojunction as an S-scheme heterojunction. Due to the height difference between the Fermi levels of the two pristine semiconductors, electrons flow from WSe2 to PtS2 to form a built-in electric field and band bending. The properties of the S-scheme heterojunction allow the heterostructure to possess a suitable band gap without losing the redox ability, thereby ensuring that the PtS2/WSe2 heterostructure can spontaneously undergo HER and OER processes of water splitting. Copyright © 2025 by Authors, Published by BCREC Publishing Group. This is an open access article under the CC BY-SA License (https://creativecommons.org/licenses/by-sa/4.0).