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The $\rho(T)$ curve is traditionally employed to discern metallic, semiconductor, and insulating behaviors in materials, with any deviations often interpreted as indicative of phase transitions. However, does this interpretation hold under the influence of a magnetic field? Our research addresses this critical question by reevaluating the $\rho(T)$ curve in the presence of magnetic field. We uncover that metal-insulator shifts and reentrant metallic states may not indicate true phase transitions but rather originate from the scaling behavior of magnetoresistance, influenced by magnetic field and temperature through a power-law dependence. Employing advanced first-principles calculations and the Boltzmann method, we analyzed the magnetoresistance of SiP$_2$ and NbP across a range of conditions, successfully explaining not only the reentrant behavior observed in experiments but also resolving the discrepancies in magnetoresistance behavior reported by different research groups. These findings challenge the conventional use of the $\rho(T)$ curve as a straightforward indicator of phase transitions under magnetic conditions, highlighting the essential need to exclude typical magnetoresistance effects due to the Lorentz force before confirming such transitions. This novel insight reshapes our understanding of complex material properties in magnetic fields and sets a new precedent for the interpretation of transport phenomena in condensed matter physics., Comment: 3 figures, 6 pages

The origin of anomalous resistivity peak and accompanied sign reversal of Hall resistivity of ZrTe$_5$ has been under debate for a long time. Although various theoretical models have been proposed to account for these intriguing transport properties, a systematic study from first principles view is still lacking. In this work, we present a first principles calculation combined with Boltzmann transport theory to investigate the transport properties in narrow-gap semiconductors at different temperatures and doping densities within the relaxation time approximation. Regarding the sensitive temperature-dependent chemical potential and relaxation time of semiconductors, we take proper approximation to simulate these two variables, and then comprehensively study the transport properties of ZrTe$_5$ both in the absence and presence of an applied magnetic field. Without introducing topological phases and correlation interactions, we qualitatively reproduced crucial features observed in experiments, including zero-field resistivity anomaly, nonlinear Hall resistivity with sign reversal, and non-saturating magnetoresistance at high temperatures. Our calculation allows a systematic interpretation of the observed properties in terms of multi-carrier and Fermi surface geometry. Our method can be extended to other narrow-gap semiconductors and further pave the way to explore interesting and novel transport properties of this field., Comment: 12 pages, 7 figures

The Hall effect has been a fascinating topic ever since its discovery, resulting in exploration of entire family of this intriguing phenomena. As the field of topology develops and novel materials emerge endlessly over the past few decades, researchers have been passionately debating the origins of various Hall effects. Differentiating between the ordinary Hall effect and extraordinary transport properties, like the anomalous Hall effect, can be quite challenging, especially in high-conductivity materials, including those with topological origins. In this study, we conduct a systematic and comprehensive analysis of Hall effects by combining the semiclassical Boltzmann transport theory with first principles calculations within the relaxation time approximation. We first highlight some striking similarities between the ordinary Hall effect and certain anomalous Hall effects, such as nonlinear dependency on magnetic field and potential sign reversal of the Hall resistivity. We then demonstrate that the Hall resistivity can be scaled with temperature and magnetic field as well, analogue to the Kohler's rule which scales the longitudinal resistivity under the relaxation time approximation. We then apply this Kohler's rule for Hall resistivity to two representative materials: ZrSiS and PtTe$_2$ with reasonable agreement with experimental measurement. Moreover, our methodology has been proven to be applicable to the planar Hall effects of bismuth, of perfect agreements with experimental observations. Our research on the scaling behavior of Hall resistivity addresses a significant gap in this field and provides a comprehensive framework for a deeper understanding of the Hall resistance family, and thus has potential to propel the field forward and spark further investigations into the fascinating world of Hall effects., Comment: 12 pages, 4 figures

Unusual magnetotransport behaviors such as temperature dependent negative magnetoresistance(MR) and bowtie-shaped MR have puzzled us for a long time. Although several mechanisms have been proposed to explain them, the absence of comprehensive quantitative calculations has made these explanations less convincing. In our work, we introduce a methodology to study the magnetotransport behaviors in magnetic materials. This approach integrates anomalous Hall conductivity induced by Berry curvature, with a multi-band ordinary conductivity tensor, employing a combination of first-principles calculations and semi-classical Boltzmann transport theory. Our method incorporates both the temperature dependency of relaxation time and anomalous Hall conductivity, as well as the field dependency of anomalous Hall conductivity. We initially test this approach on two-band models and then apply it to a Weyl semimetal \CSS. The results, which align well with experimental observations in terms of magnetic field and temperature dependencies, demonstrate the efficacy of our approach. Additionally, we have investigated the distinct behaviors of magnetoresistance (MR) and Hall resistivities across various types of magnetic materials. This methodology provides a comprehensive and efficient means to understand the underlying mechanisms of the unusual behaviors observed in magneto-transport measurements in magnetic materials., Comment: 6 pages, 4 figures

Recent advancements in large language models (LLMs) have demonstrated remarkable abilities in handling a variety of natural language processing (NLP) downstream tasks, even on mathematical tasks requiring multi-step reasoning. In this report, we introduce the KwaiYiiMath which enhances the mathematical reasoning abilities of KwaiYiiBase1, by applying Supervised Fine-Tuning (SFT) and Reinforced Learning from Human Feedback (RLHF), including on both English and Chinese mathematical tasks. Meanwhile, we also constructed a small-scale Chinese primary school mathematics test set (named KMath), consisting of 188 examples to evaluate the correctness of the problem-solving process generated by the models. Empirical studies demonstrate that KwaiYiiMath can achieve state-of-the-art (SOTA) performance on GSM8k, CMath, and KMath compared with the similar size models, respectively., Comment: technical report. arXiv admin note: text overlap with arXiv:2306.16636 by other authors

We investigate, based on the coupled dipole model, collective properties of dense Sr ensembles trapped in a three-dimensional (3D) optical lattice in the presence of dipole-dipole interactions induced on the 5$s5p^{3}$P$_{0}\to5s4d^{3}$D$_{1}$ transition. Our results reveal that the collective scattering properties, such as the scattered light intensity, frequency shift and linewidth, strongly depend on the interatomic distance and the atom number in the lattice. Moreover, the emission intensity is strongly dependent on the atomic distribution in lattices, the laser polarization and the detection position. The results not only offer the understanding of collective behaviors of lattice-trapped ensembles with an atom number equivalent to the experimental scale, but also provide an excellent platform for exploring many-body physics, thereby, opening a new window for applications like quantum information processing and quantum simulation.

We thank G.P. Mikitik and Yu.V. Sharlai for contributing this note and the cordial exchange about it. First and foremost, we note that the aim of our paper is to report a methodology to diagnose topological (semi)metals using magnetic quantum oscillations. Thus far, such diagnosis has been based on the phase offset of quantum oscillations, which is extracted from a "Landau fan plot". A thorough analysis of the Onsager-Lifshitz-Roth quantization rules has shown that the famous $\pi$-phase shift can equally well arise from orbital- or spin magnetic moments in topologically trivial systems with strong spin-orbit coupling or small effective masses. Therefore, the "Landau fan plot" does not by itself constitute a proof of a topologically nontrivial Fermi surface. In the paper at hand, we report an improved analysis method that exploits the strong energy-dependence of the effective mass in linearly dispersing bands. This leads to a characteristic temperature dependence of the oscillation frequency which is a strong indicator of nontrivial topology, even for multi-band metals with complex Fermi surfaces. Three materials, Cd$_3$As$_2$, Bi$_2$O$_2$Se and LaRhIn$_5$ served as test cases for this method. Linear band dispersions were detected for Cd$_3$As$_2$, as well as the $F$ $\approx$ 7 T pocket in LaRhIn$_5$., Comment: Response to Matter arising for Nature Communications 12, 6213 (2021)