We investigate the properties of the vortex singularities in two-component exciton-polariton condensates in semiconductor microcavities in the presence of transverse-electric\char21{}transverse-magnetic (TE\char21{}TM) splitting of the lower polariton branch. This splitting does not change qualitatively the basic (lemon and star) geometry of half-quantum vortices (HQVs), but results in warping of both the polarization field and the supercurrent streamlines around these entities. The TE\char21{}TM splitting has a pronounced effect on the HQV energies and interactions, as well as on the properties of integer vortices, especially on the energy of the hedgehog polarization vortex. The energy of this vortex can become smaller than the energies of HQVs. This leads to modification of the Berezinskii-Kosterlitz-Thouless transition from the proliferation of half-vortices to the proliferation of hedgehog-based vortex molecules.

We show that the conclusions of recent paper by Flayac et al. [Phys. Rev. B 81, 045318 (2010)] concerning the stability of half-quantum vortices are misleading. We demonstrate the existence of static half-quantum vortices in exciton-polariton condensates and calculate the warping of their texture produced by transverse-electric-transverse-magnetic splitting of polariton band.

In this study, opal–magnetite photocatalysts based on SiO₂ artificial opal crystals infiltrated with different concentrations of Fe₃O₄ nanoparticles (NPs) were synthesized using a combination of lateral infiltration and co-assembly methods. By adjusting the concentration of Fe₃O₄ NPs in the SiO₂ opal crystal, the energy band gap (Eg) was tuned to enable efficient degradation of methylene blue (MB) under visible light (410 nm and 575 nm). The photocatalytic process involved two stages: MB adsorption on the surface due to charge differences in the composite film and subsequent degradation through oxidative radicals on the catalyst’s surface. The developed material exhibited potential for applications in water remediation.