Frequency-dependent Faraday and Kerr rotation in anisotropic nonsymmorphic Dirac semimetals in a magnetic field

We calculate the frequency-dependent longitudinal and Hall conductivities and the Faraday and Kerr rotation angles for a single sheet of anisotropic Dirac semimetal protected by nonsymmorphic symmetry in the presence of a perpendicular magnetic field. While the magnetic field causes a rotation of the plane of polarization of the light, the anisotropy causes the appearance of an elliptically polarized component in an initially linearly polarized beam. The two effects can be combined in a single complex Faraday rotation angle. At the zero-frequency limit, we find a finite value of the Faraday rotation angle, which is given by $2\alpha_F$, where $\alpha_F$ is the effective fine structure constant associated with the velocity of the linearly dispersing Dirac fermions. We also find a logarithmic enhancement of the Faraday (and Kerr) rotation angles as the frequency of the light approaches the absorption edge associated with the magnetic field-induced gap. While the enhancement is reduced by impurity scattering, it remains significant for an attainable level of material purity. These results indicate that two-dimensional Dirac materials protected by nonsymmorphic symmetry are responsive to weak magnetic fields and can be used as platforms for magneto-optic applications, such as the realization of polarization-rotating devices.Comment: 24 pages, 7 Figure

Exotic Superconducting Properties in Topological Nodal Semimetal PbTaSe2_2

We report the electronic properties of superconductivity in the topological nodal-line semimetal PbTaSe$_2$. Angle-resolved photoemission measurements accompanied by band calculations confirmed the nodal-line band structure in the normal state of single crystalline PbTaSe$_2$. Resistivity, magnetic-susceptibility and specific heat measurements have also been performed on high-quality single crystals. We observed upward features and large anisotropy in upper critical field ($H_{c2}$) measured in-plane (H//\textbf{ab}) and out-plane (H//\textbf{c}), respectively. Especially, $H_{c2}$ measured in H//\textbf{ab} shows sudden upward features rather than a signal of saturation in ultralow temperatures. The specific heat measurements under magnetic field reveal a full superconducting gap with no gapless nodes. These behaviors in this clean noncentrosymmetric superconductor is possibly related to the underlying exotic physics, providing important clue for realization of topological superconductivity.Comment: 6 pages, 5 figures,1 table;Accepted for publication on PR

Air pollution concentration fuzzy evaluation based on evidence theory and the K-nearest neighbor algorithm

Background: Air pollution, characterized by complex spatiotemporal dynamics and inherent uncertainty, poses significant challenges in accurate air quality prediction, and current methodologies often fail to adequately address these complexities.Objective: This study presents a novel fuzzy modeling approach for estimating air pollution concentrations.Methods: This fuzzy evaluation method integrates an improved evidence theory with comprehensive weighting and the K-nearest neighbor (KNN) interval distance within the framework of the matter-element extension model. This involves generating the basic probability assignment (BPA) based on interval similarity, performing sequential fusion using the Dempster–Shafer evidence theory, enhancing the fusion results via comprehensive weighting, and conducting fuzzy evaluation of air pollution concentrations using the matter-element extension KNN interval distance.Results: Our method achieved significant improvements in monitoring air pollution concentrations, incorporating spatiotemporal factors and pollutant concentrations more effectively than existing methods. Implementing sequential fusion and subjective–objective weighting reduced the error rate by 38% relative to alternative methods.Discussion: Fusion of multi-source air pollution data via this method effectively mitigates inherent uncertainty and enhances the accuracy of the KNN method. It produces more comprehensive air pollution concentration fusion results, improving accuracy by considering spatiotemporal correlation, toxicity, and pollution levels. Compared to traditional air-quality indices, our approach achieves greater accuracy and better interpretability, making it possible to develop more effective air quality management strategies. Future research should focus on expanding the dataset to include more diverse geographical and meteorological conditions, further refining the model to integrate external factors like meteorological data and regional industrial activity, and improving computational efficiency for real-time applications