From first-principles calculations, the magnetism and electronic structures of bilayer bismuth (stannum) films at the monolayer CrI₃ (CrBr₃) interface are studied.

The electronic properties and interfacial contact of the graphene-based heterostructure graphene/CrSiTe ₃ (Gr/CrSiTe ₃ ) are modulated by tuning the interfacial distance, along with application of an external electric field.

It is challenging to realize the quantum anomalous Hall effect (QAHE) at high operating temperatures using the two-dimensional (2D) Dirac surface states of three-dimensional (3D) topological insulators (TIs). Given the small non-trivial gap induced by adsorbing ferromagnetic (FM) CrI₃ monolayer (ML) on the surface of Bi₂Se₃ films, we here propose another TI and FM semiconductor interfaced system to enhance the gap by inserting CrI₃ ML between the first top (bottom) quintuple layers (QL) and sub-top (sub-bottom) QL of Bi₂Se₃ films symmetrically. The 2D non-trivial phase emerges in the Bi₂Se₃ films with five or more QLs and the gap is enlarged to 30 meV in 1QL-Bi₂Se₃/CrI₃/4QL-Bi₂Se₃/CrI₃/1QL-Bi₂Se₃, which can be understood by the enhanced magnetic proximity effect. The topological non-triviality is confirmed by the nonzero Chern number and the existence of chiral edge state. Our finding will provide useful guidance to optimize the Bi₂Se₃–CrI₃ interface system for realizing QAHE at relatively high operating temperatures.

As there is a strong spectral link among the three color channels of a color image, a color image model based on four-dimensional algebra ensures an intrinsic link among the channels and creates an approach for color image compression. We propose a theory of singular value decomposition of split quaternion matrices using a special 2×2 real representation matrix structure and provide an effective and efficient algorithm to deal with the color image compression problem. Numerical examples show that under the same compression conditions, the proposed algorithm outperforms the quaternion color image compression method and traditional three-color channel compression method in terms of fidelity, measured by peak signal-to-noise ratio and structural similarity. It has been proven to be a highly competitive method, with a balance of efficiency and performance that makes it a standout choice.