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The discovery of advanced materials is the cornerstone of human technological development and progress. The structures of materials and their corresponding properties are essentially the result of a complex interplay of multiple degrees of freedom such as lattice, charge, spin, symmetry, and topology. This poses significant challenges for the inverse design methods of materials. Humans have long explored new materials through a large number of experiments and proposed corresponding theoretical systems to predict new material properties and structures. With the improvement of computational power, researchers have gradually developed various electronic structure calculation methods, particularly such as the one based density functional theory, as well as high-throughput computational methods. Recently, the rapid development of artificial intelligence technology in the field of computer science has enabled the effective characterization of the implicit association between material properties and structures, thus opening up an efficient paradigm for the inverse design of functional materials. A significant progress has been made in inverse design of materials based on generative and discriminative models, attracting widespread attention from researchers. Considering this rapid technological progress, in this survey, we look back on the latest advancements in AI-driven inverse design of materials by introducing the background, key findings, and mainstream technological development routes. In addition, we summarize the remaining issues for future directions. This survey provides the latest overview of AI-driven inverse design of materials, which can serve as a useful resource for researchers., Comment: 43 pages, 5 figures, 2 tables

Increased training parameters have enabled large pre-trained models to excel in various downstream tasks. Nevertheless, the extensive computational requirements associated with these models hinder their widespread adoption within the community. We focus on Knowledge Distillation (KD), where a compact student model is trained to mimic a larger teacher model, facilitating the transfer of knowledge of large models. In contrast to much of the previous work, we scale up the parameters of the student model during training, to benefit from overparameterization without increasing the inference latency. In particular, we propose a tensor decomposition strategy that effectively over-parameterizes the relatively small student model through an efficient and nearly lossless decomposition of its parameter matrices into higher-dimensional tensors. To ensure efficiency, we further introduce a tensor constraint loss to align the high-dimensional tensors between the student and teacher models. Comprehensive experiments validate the significant performance enhancement by our approach in various KD tasks, covering computer vision and natural language processing areas. Our code is available at https://github.com/intell-sci-comput/OPDF., Comment: 38th Conference on Neural Information Processing Systems (NeurIPS 2024)

In this study, we introduce a novel implementation of density functional theory integrated with single-site dynamical mean-field theory to investigate the complex properties of strongly correlated materials. This comprehensive first-principles many-body computational toolkit, termed $\texttt{Zen}$, utilizes the Vienna $\textit{ab initio}$ simulation package and the $\texttt{Quantum ESPRESSO}$ code to perform density functional theory calculations and generate band structures for realistic materials. The challenges associated with correlated electron systems are addressed through two distinct yet complementary quantum impurity solvers: the natural orbitals renormalization group solver for zero temperature and the hybridization expansion continuous-time quantum Monte Carlo solver for finite temperature. Additionally, this newly developed toolkit incorporates several valuable post-processing tools, such as $\texttt{ACFlow}$, which employs the maximum entropy method and the stochastic pole expansion method for the analytic continuation of Matsubara Green's functions and self-energy functions. To validate the performance of this toolkit, we examine three representative cases: the correlated metal SrVO$_{3}$, the nickel-based unconventional superconductor La$_{3}$Ni$_{2}$O$_{7}$, and the wide-gap Mott insulator MnO. The results obtained demonstrate strong agreement with experimental findings and previously available theoretical results. Notably, we successfully elucidate the quasiparticle peak and band renormalization in SrVO$_{3}$, the dominance of Hund correlation in La$_{3}$Ni$_{2}$O$_{7}$, and the pressure-driven insulator-metal transition as well as the high-spin to low-spin transition in MnO. These findings suggest that $\texttt{Zen}$ is proficient in accurately describing the electronic structures of $d$-electron correlated materials., Comment: 14 pages, 8 figures, 1 table

The time-reversal symmetry is thought to be a necessary condition for realizing valley Hall effect. If the time-reversal symmetry is broken, whether the valley Hall effect can be realized has not been explored. In this letter, based on symmetry analysis and the first-principles electronic structure calculations, we demonstrate that the vally Hall effect without time-reversal symmetry can be realized in two-dimensional altermagnetic materials Fe$_2$WSe$_4$ and Fe$_2$WS$_4$. Due to crystal symmetry required, the vally Hall effect without time-reversal symmetry is called crystal vally Hall effect. In addition, under uniaxial strain, both monolayer Fe$_2$WSe$_4$ and Fe$_2$WS$_4$ can realize piezomagnetic effect. Under biaxial compressive stress, both monolayer Fe$_2$WSe$_4$ and Fe$_2$WS$_4$ will transform from altermagnetic semiconductor phase to bipolarized topological Weyl semimetal phase. Our work not only provides a new direction for exploring the novel valley Hall effect, but also provides a good platform for exploring altermagnetic semiconductors and altermagnetic topological phase transitions., Comment: 6 pages,4 figures

Symmetry protected topology has been studied extensively in the past twenty years, but the topology protected by spin symmetry has just begun to be studied. In this work, based on spin symmetry analysis, we propose that a class of Weyl nodal line semimetals is protected by the spin symmetry. Then, by the first-principles electronic structure calculations, we predict that both altermagnetic $\rm Nb_2FeB_2$ and $\rm Ta_2FeB_2$ are node-network semimetals protected by the spin symmetry. Moreover, both altermagnetic $\rm Nb_2FeB_2$ and $\rm Ta_2FeB_2$ have nodal rings protected by the mirror symmetry and Dirac points protected by nonsymmorphic spin symmetry. Furthermore, both altermagnetic $\rm Nb_2FeB_2$ and $\rm Ta_2FeB_2$ transform node-network semimetal phase into Weyl semimetal phase when considering spin-orbit coupling. Therefore, our work not only enriches the topological phases protected by spin symmetry, but also provides an excellent material platform to investigate the exotic physical properties of multiple altermagnetic topological semimetal phases in experiment., Comment: 6 pages, 4 figures

The discovery of new superconducting materials, particularly those exhibiting high critical temperature ($T_c$), has been a vibrant area of study within the field of condensed matter physics. Conventional approaches primarily rely on physical intuition to search for potential superconductors within the existing databases. However, the known materials only scratch the surface of the extensive array of possibilities within the realm of materials. Here, we develop an AI search engine that integrates deep model pre-training and fine-tuning techniques, diffusion models, and physics-based approaches (e.g., first-principles electronic structure calculation) for discovery of high-$T_c$ superconductors. Utilizing this AI search engine, we have obtained 74 dynamically stable materials with critical temperatures predicted by the AI model to be $T_c \geq$ 15 K based on a very small set of samples. Notably, these materials are not contained in any existing dataset. Furthermore, we analyze trends in our dataset and individual materials including B$_4$CN$_3$ and B$_5$CN$_2$ whose $T_c$s are 24.08 K and 15.93 K, respectively. We demonstrate that AI technique can discover a set of new high-$T_c$ superconductors, outline its potential for accelerating discovery of the materials with targeted properties., Comment: 11 pages, 7 figures, 4 tables

Low-energy excitations may manifest intricate behaviors of correlated electron systems and provide essential insights into the dynamics of quantum states and phase transitions. We study a two-orbital Hubbard model featuring the so-called holon-doublon low-energy excitations in the Mott insulating narrow band in the orbital-selective Mott phase (OSMP). We employ an improved dynamical mean-field theory (DMFT) technique to calculate the spectral functions at zero temperature. We show that the holon-doublon bound state is not the sole component of the low-energy excitations. Instead, it should be a bound state composed of a Kondo-like state in the wide band and a doublon in the narrow band, named inter-band Kondo-like (IBK) bound states. Notably, as the bandwidths of the two bands approach each other, we find anomalous IBK bound-state excitations in the metallic {\em wide} band., Comment: 5 pages, 4 figures

High-$T_c$ superconductivity (SC) was recently found in the bilayer material La$_3$Ni$_2$O$_7$ (La327) under high pressures. We study the bilayer two-orbital Hubbard model derived from the band structure of the La327. The model is solved by cluster dynamical mean-field theory (CDMFT) with natural orbitals renormalization group (NORG) as impurity solver at zero temperature, considering only normal states. With hole doping, we have observed sequentially the Mott insulator (Mott), pseudogap (PG), non-Fermi liquid (NFL), and Fermi liquid (FL) phases, with quantum correlations decreasing. The ground state of the La327 is in the NFL phase with Hund spin correlation, which transmits the Ni-$3d_{z^2}$ ($z$) orbital inter-layer AFM correlation to the Ni-$3d_{x^2-y^2}$ orbitals. When the $\sigma$-bonding state of the $z$ orbitals ($z+$) is no longer fully filled, the inter-layer antiferromagnetic (AFM) correlations weaken rapidly. At low pressures, the fully filled $z+$ band supports a strong inter-layer AFM correlations, potentially favoring short-range spin density wave (SDW) and suppressing SC. Hole doping at low pressures may achieve a similar effect to high pressures, under which the $z+$ band intersects with the Fermi level, and consequently the spin correlations weaken remarkably, potentially suppressing the possible short-range SDW and favoring SC., Comment: 8 pages, 9 figures

By preforming DFT+DMFT calculations, we systematically investigate the correlated electronic structure in the newly discovered monolayer-trilayer (ML-TL) phase of La$_3$Ni$_2$O$_7$ (1313-La327). Our calculated Fermi surfaces are in good agreement with the angle-resolved photoemission spectroscopy (ARPES) results. We find that 1313-La327 is a multiorbital correlated metal. An orbital-selective Mott behavior is found in ML. The ML Ni-3$d_{z^2}$ orbitals exhibit a Mott behavior, while the ML Ni-3$d_{x^2-y^2}$ orbitals are metallic due to self-doping. And the ML also shows features of heavy fermions, which indicates that there may be Kondo physics in 1313-La327. We also find a large static local spin susceptibility of ML Ni, suggesting that there is large spin fluctuation in 1313-La327. The TL Ni-$e_g$ orbitals possess similar electronic correlation to those in La$_4$Ni$_3$O$_{10}$ (La4310). The $e_g$ orbitals of the outer-layer Ni in TL (TL-outer Ni) show non-Fermi liquid behaviors. Besides, large weight of high-spin states are found in TL-outer Ni and ML Ni, implying Hundness. Under 16 GPa, a Lifshitz transition is revealed by our calculations and a La-related band crosses the Fermi level. Our work provides a theoretical reference for studying other potential mixed-stacked nickelate superconductors., Comment: 7 pages, 3 figures, 3 tables

Magnetism and topology are two major areas of condensed matter physics. The combination of magnetism and topology gives rise to more novel physical effects, which have attracted strongly theoretical and experimental attention. Recently, the concept of altermagnetism has been introduced, characterized by a dual nature: real-space antiferromagnetism and reciprocal-space anisotropic spin polarization. The amalgamation of altermagnetism with topology may lead to the emergence of previously unobserved topological phases and the associated physical effects. In this study, utilizing a four-band lattice model that incorporates altermagnetism and spin group symmetry, we demonstrate that type-I, type-II, and type-III bipolarized Weyl semimetals can exist in altermagnetic systems. Through the first-principles electronic structure calculations, we predict four ideal two-dimensional type-I altermagnetic bipolarized Weyl semimetals Fe$_2$WTe$_4$ and Fe$_2$MoZ$_4$ (Z=S,Se,Te). More significantly, we introduce the quantum crystal valley Hall effect, a phenomenon achievable in three of these materials namely Fe$_2$WTe$_4$, Fe$_2$MoS$_4$, and Fe$_2$MoTe$_4$, when spin-orbit coupling is considered. Furthermore, these materials have the potential to transition from a quantum crystal valley Hall phase to a Chern insulator phase under strain. In contrast, Fe$_2$MoSe$_4$ remains to be a Weyl semimetal under spin-orbit coupling but is distinguished by possessing only a single pair of Weyl points. Additionally, the position, polarization, and number of Weyl points in Fe$_2$WTe$_4$ and Fe$_2$MoZ$_4$ can be manipulated by adjusting the direction of the N\'eel vector. Consequently, Fe$_2$WTe$_4$ and Fe$_2$MoZ$_4$ emerge as promising experimental platforms for investigating the distinctive physical attributes of various altermagnetic topological phases., Comment: 7 pages, 5 figures

The tensor network algorithm, a family of prevalent numerical methods for quantum many-body problems, aptly captures the entanglement properties intrinsic to quantum systems, enabling precise representation of quantum states. However, its computational cost is notably high, particularly in calculating physical observables like correlation functions. To surmount the computational challenge and enhance efficiency, we propose integrating the Green's function Monte Carlo (GFMC) method with the projected entangled pair state (PEPS) ansatz. This approach combines the high-efficiency characteristics of Monte Carlo with the sign-free nature of tensor network states and proves effective in addressing the computational bottleneck. To showcase its prowess, we apply this hybrid approach to investigate the antiferromagnetic $J_1$-$J_2$ Heisenberg model on the square lattice, a model notorious for its sign problem in quantum Monte Carlo simulations. Our results reveal a substantial improvement in the accuracy of ground-state energy when utilizing a preliminary PEPS as the guiding wave function for GFMC. By calculating the structure factor and spin-spin correlation functions, we further characterize the phase diagram, identifying a possible columnar valence-bond state phase within the intermediate parameter range of $0.52 < J_2/J_1 < 0.58$. This comprehensive study underscores the efficacy of our combined approach, demonstrating its ability to accurately simulate frustrated quantum spin systems while ensuring computational efficiency., Comment: 11 pages, 15 figures

A recent experimental study announced the emergence of superconductivity in La$_3$Ni$_2$O$_7$ under pressure, with the highest observed superconducting transition temperature ($T_c$) reaching approximately 80 K beyond 14 GPa. While extensive studies have been devoted to the electronic correlations and potential superconducting pairing mechanisms, there lack investigations into the phonon properties and electron phonon coupling. Using density functional theory in conjunction with Wannier interpolation techniques, we study the phonon properties and electron phonon interactions in La$_3$Ni$_2$O$_7$ under 29.5 GPa. Our findings reveal that the electron phonon coupling is insufficient to solely explain the observed high superconducting $T_c$ $\sim$ 80 K in La$_3$Ni$_2$O$_7$. And the calculated strong Fermi surface nesting may explain the experimental observed charge density wave transition in La$_3$Ni$_2$O$_7$. Our calculations substantiate La$_3$Ni$_2$O$_7$ is an unconventional superconductor., Comment: 5 pages, 4 figures

We propose two novel two-dimensional (2D) topological materials, (PtN$_4$)$_3$C$_{32}$ and (MnN$_4$)$_3$C$_{32}$, with a special geometry that we named as kagome-in-honeycomb (KIH) lattice structure, to illustrate the coexistence of the paradigmatic states of kagome physics, Dirac fermions and flat bands, that are difficult to be simultaneously observed in three-dimensional realistic systems. In such system, MN$_4$(M=Pt or Mn) moieties are embedded in honeycomb graphene sheet according to kagome lattice structure, thereby resulting in a KIH lattice. Using the first-principles calculations, we have systemically studied the structural, electronic, and topological properties of these two materials. In the absence of spin-orbit coupling (SOC), they both exhibit the coexistence of Dirac/quadratic-crossing cone and flat band near the Fermi level. When SOC is included, a sizable topological gap is opened at the Dirac/quadratic-crossing nodal point. For nonmagnetic (PtN$_4$)$_3$C$_{32}$, the system is converted into a $\mathbb{Z}_2$ topological quantum spin Hall insulator defined on a curved Fermi level, while for ferromagnetic (MnN$_4$)$_3$C$_{32}$, the material is changed from a half-semi-metal to a quantum anomalous Hall insulator with nonzero Chern number and nontrivial chiral edge states. Our findings not only predict a new family of 2D quantum materials, but also provide an experimentally feasible platform to explore the emergent kagome physics, topological quantum Hall physics, strongly correlated phenomena, and theirs fascinating applications., Comment: 6 figures. arXiv admin note: text overlap with arXiv:2207.03703

High temperature superconductivity was recently found in the bilayer nickelate $\rm{La}_3 \rm{Ni}_2 \rm{O}_7$ (La327), followed by the discovery of superconductivity in the trilayer $\rm{La}_4 \rm{Ni}_3 \rm{O}_{10}$ (La4310), under high pressure. Through studying the electronic correlation of La4310 with DFT+DMFT, and further comparing it with that of La327, we find that the $e_g$ orbitals of the outer-layer Ni cations in La4310 have a similar (but slightly weaker) electronic correlation to those in La327, in which the electrons behave as a non-Fermi liquid with Hund correlation and linear-in-temperature scattering rate. Our results suggest that the experimentally observed ``strange metal'' behavior may be explained by the Hund spin correlation featuring high spin states and spin-orbital separation. In contrast, the electrons in the inner-layer Ni cations in La4310 behave as a Fermi liquid. The weaker electronic correlation in La4310 is attributed to more hole-doping, which may explain its lower superconducting transition temperature., Comment: 6 pages, 4 figures

Spin-orbit coupling is a key to realize many novel physical effects in condensed matter physics, but the mechanism to achieve strong spin-orbit coupling effect in light element antiferromagnetic compounds has not been explored. In this work, based on symmetry analysis and the first-principles electronic structure calculations, we demonstrate that strong spin-orbit coupling effect can be realized in light element altermagnetic materials, and propose a mechanism for realizing the corresponding effective spin-orbit coupling. This mechanism reveals the cooperative effect of crystal symmetry, electron occupation, electronegativity, electron correlation, and intrinsic spin-orbit coupling. Our work not only promotes the understanding of light element compounds with strong spin-orbit coupling effect, but also provides an alternative for realizing light element compounds with an effective strong spin-orbit coupling., Comment: 5 pages, 4 figures

Altermagnetism is a new magnetic phase with k-dependent spin polarization and may exist in an insulating state with a high N\'eel temperature. This provides a new opportunity to obtain both spin and electric polarization in one material. Here, based on symmetry analysis and the first-principles electronic structures calculations, we predict that LiFe2F6 is a d-wave altermagnetic and charge-ordering-mediated ferroelectric material. Moreover, the LiFe2F6 transforms into a ferrimagnetic and ferroelectric phase with strong magnetoelectric coupling under biaxial compressive strain. Interestingly, the spins of the valence band and the conduction band are opposite in ferrimagnetic LiFe2F6, which facilitates a simultaneous spin-triplet excitonic insulator phase. More importantly, the spin-triplet excitons with spin 1 and -1 can be switched by electric fields in ferrimagnetic LiFe2F6 due to strong magnetoelectric coupling. Due to the abundance of novel physical properties, LiFe2F6 will certainly attract a wide range of theoretical and experimental interest., Comment: 6 pages, 4 figures

By means of density functional theory plus dynamical mean-field theory (DFT+DMFT), we investigate the correlated electronic structures of La$_3$Ni$_2$O$_7$ under high pressure. Our calculations show that La$_3$Ni$_2$O$_7$ is a multi-orbital Hund metal. Both the 3$d_{z^2}$ and 3$d_{x^2 - y^2}$ orbitals of Ni are close to be half filled and contribute the bands across the Fermi level. Band renormalization and orbital selective electronic correlation are observed. Through imaginary-time correlation functions, the discovery of high-spin configuration, spin-frozen phase, and spin-orbital separation shows that the system is in a frozen moment phase at high temperatures above 290 K and is a Fermi liquid at low temperatures, which is further comfirmed by the calculated spin, orbital, and charge susceptibilities under high temperatures. Our study uncovers Hundness in La$_3$Ni$_2$O$_7$ under high pressure., Comment: 6 pages, 5 figures, 2 tables

Altermagnetism, a new magnetic phase, has been theoretically proposed and experimentally verified to be distinct from ferromagnetism and antiferromagnetism. Although altermagnets have been found to possess many exotic physical properties, the limited availability of known altermagnetic materials hinders the study of such properties. Hence, discovering more types of altermagnetic materials with different properties is crucial for a comprehensive understanding of altermagnetism and thus facilitating new applications in the next generation information technologies, e.g., storage devices and high-sensitivity sensors. Since each altermagnetic material has a unique crystal structure, we propose an automated discovery approach empowered by an AI search engine that employs a pre-trained graph neural network to learn the intrinsic features of the material crystal structure, followed by fine-tuning a classifier with limited positive samples to predict the altermagnetism probability of a given material candidate. Finally, we successfully discovered 50 new altermagnetic materials that cover metals, semiconductors, and insulators confirmed by the first-principles electronic structure calculations. The wide range of electronic structural characteristics reveals that various novel physical properties manifest in these newly discovered altermagnetic materials, e.g., anomalous Hall effect, anomalous Kerr effect, and topological property. Noteworthy, we discovered 4 $i$-wave altermagnetic materials for the first time. Overall, the AI search engine performs much better than human experts and suggests a set of new altermagnetic materials with unique properties, outlining its potential for accelerated discovery of the materials with targeted properties., Comment: 46 pages; 23 figures; 4 tables

Exploring various topological states (TS) and topological phase transitions (TPT) has attracted great attention in condensed matter physics. However, so far, there is rarely a typical material system that can be used as a platform to study the TS and TPT as the system transforms from one-dimensional (1D) nanoribbons to two-dimensional (2D) sheet then to three-dimensional (3D) bulk. Here, we first propose that some typical TS in 1D, 2D, and 3D systems can be realized in a tight-binding (TB) model. Following the TB model and further based on first-principles electronic structure calculations, we demonstrate that the structurally stable (4,0) carbon nanotube derivatives are an ideal platform to explore the semiconductor/nodal-point semimetal states in 1D nanoribbons [1D-(4,0)-C16H4 and 1D-(4,0)-C32H4], nodal-ring semimetal state in 2D sheet [2D-(4,0)-C16], and nodal-cage semimetal state in 3D bulk [3D-(4,0)-C16]. Furthermore, we calculate the characteristic band structures and the edge/surface states of 2D-(4,0)-C16 and 3D-(4,0)-C16 to confirm their nontrivial topological properties. Our work not only provides new excellent 2D and 3D members for the topological carbon material family, but also serves as an ideal template for the study of TS and TPT with the change of system dimension., Comment: 17 pages, 7 figures

Possible high-$T_c$ superconductivity (SC) has been found experimentally in the bilayer material La$_3$Ni$_2$O$_7$ under high pressure recently, in which the Ni-$3d_{3z^2-r^2}$ and $3d_{x^2-y^2}$ orbitals are expected to play a key role in the electronic structure and the SC. Here we study the two-orbital electron correlations and the nature of the SC using the bilayer two-orbital Hubbard model downfolded from the band structure of La3Ni2O7 in the framework of the dynamical mean-field theory. We find that each of the two orbitals forms $s_\pm$-wave SC pairing. Because of the nonlocal inter-orbital hoppings, the two-orbital SCs are concomitant and they transition to Mott insulating states simultaneously when tuning the system to half filling. The Hund's coupling induced local inter-orbital spin coupling enhances the electron correlations pronouncedly and is crucial to the SC., Comment: 5 pages, 5 figures

Neural-network quantum states (NQSs), variationally optimized by combining traditional methods and deep learning techniques, is a new way to find quantum many-body ground states and gradually becomes a competitor of traditional variational methods. However, there are still some difficulties in the optimization of NQSs, such as local minima, slow convergence, and sign structure optimization. Here, we split a quantum many-body variational wave function into a multiplication of a real-valued amplitude neural network and a sign structure, and focus on the optimization of the amplitude network while keeping the sign structure fixed. The amplitude network is a convolutional neural network (CNN) with residual blocks, namely a ResNet. Our method is tested on three typical quantum many-body systems. The obtained ground state energies are lower than or comparable to those from traditional variational Monte Carlo (VMC) methods and density matrix renormalization group (DMRG). Surprisingly, for the frustrated Heisenberg $J_1$-$J_2$ model, our results are better than those of the complex-valued CNN in the literature, implying that the sign structure of the complex-valued NQS is difficult to be optimized. We will study the optimization of the sign structure of NQSs in the future., Comment: 9 pages, 3 figures, 4 tables, published version

Very recently, a report on possible room-temperature superconductivity in N-doped lutetium hydrides near 1 GPa pressure has drawn lots of attentions. To date, the superconductivity is not confirmed under relatively low pressure in subsequent studies. Based on the density functional theory first-principles calculations, we extensively investigate the influence of charge doping on the stability and superconductivity of LuH$_3$ at ambient pressure. Although electron doping can not stabilize LuH$_3$, we find that the room-pressure stability of LuH$_3$ can be achieved by doping holes with concentrations in between 0.15-0.30 holes/cell. Moreover, our calculations reveal a positive dependence of superconducting transition temperature on the number of doped holes, with the highest value close to 54 K. These findings suggest that realizing superconductivity in hole-doped LuH$_3$ at ambient pressure is not impossible, although the transition temperature is still far away from the room temperature., Comment: 6 pages, 6 figures

The infinite-layer cuprate $A$CuO$_2$ ($A=$ Ca, Sr, Ba) has the simplest crystal structure among numerous cuprate superconductors and can serve a prototypical system to explore the unconventional superconductivity. Based on the first-principles electronic structure calculations, we have studied the electronic and magnetic properties of the infinite-layer cuprate SrCuO$_{2}$ from a phonon perspective. We find that interesting fluctuations of charges, electrical dipoles, and local magnetic moments can be induced by the zero-point vibrations of phonon modes in SrCuO$_{2}$ upon the hole doping. Among all optical phonon modes of SrCuO$_{2}$ in the antiferromagnetic N\'{e}el state, only the $A_{1}$$_g$ mode that involves the full-breathing O vibrations along the Cu-O bonds can cause significant fluctuations of local magnetic moments on O atoms and dramatic charge redistributions between Cu and O atoms. Notably, due to the zero-point vibration of the $A_{1g}$ mode, both the charge fluctuations on Cu and the electrical dipoles on O show a dome-like evolution with increasing hole doping, quite similar to the experimentally observed behavior of the superconducting $T_c$; in comparison, the fluctuations of local magnetic moments on O display a monotonic enhancement along with the hole doping. Further analyses indicate that around the optimal doping, there exist a large softening in the frequency of the $A_{1g}$ phonon mode and a van Hove singularity in the electronic structure close to the Fermi level, suggesting potential electron-phonon coupling. Our work reveals the important role of the full-breathing O phonon mode playing in the infinite-layer SrCuO$_{2}$, which may provide new insights in understanding the cuprate superconductivity., Comment: 7 pages, 4 figures, 1 table

We investigate the electronic and phonon properties of hydrogen sulfide (SH$_3$) under ultrahigh pressure to elucidate the origin of its high-T$_c$ superconductivity. Contrary to the prevailing belief that the metalized S-H $\sigma$ bond is responsible, our analysis, based on the anisotropic Migdal-Eliashberg equation and the crystal orbital Hamilton population (COHP) calculation, reveals that the H-H $\sigma$-antibonding states play a dominant role in the large electron-phonon coupling that leads to the superconducting pairing in SH$_3$. Furthermore, by partially restricting the vibration of S atoms, we demonstrate that the S-H bonds provide subsidiary contributions to the pairing interaction. These findings shed light on the importance of the previously overlooked H-H $\sigma^*$ bonds in driving high-T$_c$ superconductivity in SH$_3$ and offer insights into the relationship between metallic H-H covalent antibonding and high-T$_c$ superconductivity in other hydrogen-rich materials under high pressure., Comment: 11 pages, 9 figures, 59 references

Using the natural orbitals renormalization group, we studied the problem of a localized spin- 1/2 impurity coupled to two helical liquids via the Kondo interaction in a quantum spin Hall insulator, based on the Kane-Mele model defined in a finite zigzag graphene nanoribbon. We investigated the influence of the Kondo couplings with the helical liquids on both the static and dynamic properties of the ground state. The number and distinct spatial structures of the active natural orbitals (ANOs), which play essential roles in constructing the ground-state wave function, were first analyzed. Our numerical results indicate that two ANOs emerge, equal to the number of helical liquids. Specifically, at the coupling symmetry point, both ANOs are fully active with their spatial structures being respectively constituted by the different helical liquids. In comparison, when deviating from the symmetry point, only one ANO remains fully active, which is dominantly constructed by the helical liquid with the larger Kondo coupling. Local screening of the impurity, described by the impurity spin polarization and susceptibility, was further studied. It shows that at the coupling symmetry point, the impurity is maximally polarized and the spin susceptibility reaches the maximum. On the contrary, the impurity tends to be screened without polarization when the Kondo couplings deviate well from the symmetry point. The Kondo screening cloud, manifested by the spin correlation between the impurity and the conduction electrons, was finally explored. It is demonstrated that the Kondo cloud is mainly formed by the helical liquid with the larger Kondo coupling to the impurity. On the other hand, the spin-orbital coupling breaks the symmetry in spatial distribution of the spin correlation, leading to anisotropy in the Kondo cloud.

It is rarely reported that collinear antiferromagnetic (AFM) metals can have anomalous Hall effect (AHE). In this letter, based on symmetry analysis and the first-principles electronic structure calculations, we predict that two existing collinear antiferromagnets Nb$_{2}$FeB$_{2}$ and Ta$_{2}$FeB$_{2}$, whose N\'eel temperatures are above room temperature, have very large AHE with anomalous Hall conductance (AHC) -100 $\Omega^{-1}$ cm$^{-1}$ and $-54\Omega^{-1}$ cm$^{-1}$, respectively. We further complete the symmetry resquirements for realizing the AHE in collinear antiferromagnetism.

Finding intrinsic carbon superconductor is an interesting topic. Based on density functional first-principles calculations, we first study the phonon-mediated superconductivity in a cubic metallic carbon allotrope, namely sc-C$_{20}$, which has been synthesized in experiment. The electron-phonon coupling is accurately computed with Wannier interpolation method. By solving the Eliashberg equations, we predict that sc-C$_{20}$ is an intrinsic carbon superconductor, without introducing any guest atoms or doping, whose transition temperature is determined to be about 24 K. Our findings enrich the family of carbon-based superconductors., Comment: 4 pages, 5 figures

Applying pressure around megabar is indispensable in the synthesis of high-temperature superconducting hydrides, such as SH$_3$ and LaH$_{10}$. Stabilizing the high-pressure phase of hydride around ambient condition is a severe challenge. Based on the density-functional theory calculations, we give the first example that the structure of hydride CaBH$_5$ predicted above 280 GPa, can maintain its dynamical stability with pressure down to 1 GPa, by modulating the charge transfer from metal atoms to hydrogen atoms via the replacement of Ca with alkali metal atoms e.g. Cs, in which the [BH$_5$]$^{2-}$ anion shrinks along $c$ axis and expands in the $ab$ plane, experiencing an anisotropic virtual high pressure. This mechanism, namely charge transfer modulated virtual high pressure effect, plays a vital role in enhancing the structural stability and leading to the reemergence of ambient-pressure-forbidden [BH$_5$]$^{2-}$ anion around 1 GPa in CsBH$_5$. Moreover, we find that CsBH$_5$ is a strongly coupled superconductor, with transition temperature as high as 98 K, well above the liquid-nitrogen temperature. Our findings provide a novel mechanism to reduce the critical pressure required by hydrogen-rich compound without changing its crystal structure, and also shed light on searching ambient-pressure high-temperature superconductivity in metal borohydrides., Comment: accepted for publication as a Letter in Phys. Rev. B

Quantum materials with tunable correlated and/or topological electronic states, such as the electronic Kagome lattice, provide an ideal platform to study the exotic quantum properties. However, the real-space investigations on the correlated electronic Kagome lattice have been rarely reported. Herein, we report on the electronic Kagome lattice emerging in the correlated charge-density-wave (CDW) state of 1T-TaS$_2$ at ~200 K via variable-temperature scanning tunneling microscopy (VT-STM). This emergent Kagome lattice can be considered a fractional electron-filling superstructure with reduced translational and rotational symmetries, confirmed by STM measurements and density functional theory simulations. The characteristic band structure and density of states of this electronic Kagome lattice are further explored based on theoretical calculations. Our results demonstrate a self-organized electronic Kagome lattice from the correlated CDW state via the effective tuning parameter of temperature and provide a platform to directly explore the interplay of correlated electrons and topological physics., Comment: 20 pages, 4figures

The intrinsic ferromagnetic (FM) axion insulators and Weyl semimetals (WSMs) with only single pair of Weyl points have drawn intensive attention but so far remain rare and elusive in real materials. Here, we propose a new class of Mn\emph{X}$_{2}$\emph{B}$_{2}$\emph{T}$_{6}$-B (\emph{X}=Ge, Sn, or Pb; \emph{B}=Sb or Bi; \emph{T}=Se or Te) family that is the stable structural form of this system. We find that the Mn\emph{X}$_{2}$\emph{B}$_{2}$\emph{T}$_{6}$-B family has not only the intrinsic FM axion insulators MnGe$_{2}$Bi$_{2}$Te$_{6}$-B, MnSn$_{2}$Bi$_{2}$Te$_{6}$-B, and MnPb$_{2}$Bi$_{2}$Te$_{6}$-B, but also the intrinsic WSM MnSn$_{2}$Sb$_{2}$Te$_{6}$-B with only a single pair of Weyl points. Thus, the Mn\emph{X}$_{2}$\emph{B}$_{2}$\emph{T}$_{6}$-B family can provide an ideal platform to explore the exotic topological magnetoelectric effect and the intrinsic properties related to Weyl points., Comment: 6 pages, 5 figures

Recent experiments have reported that inserting metal atoms or small molecules in between the FeSe layers of $\beta$-FeSe can significantly enhance the superconducting transition temperature. Here, based on first-principles electronic structure calculations, we propose a stable compound SnOFeSe by alternatively stacking the SnO and $\beta$-FeSe layers. The predicted SnOFeSe has the same tetragonal structure as the well-known FeAs-based compound LaOFeAs, meanwhile their electronic structures in the nonmagnetic state are quite similar. The magnetic ground state of SnOFeSe is predicted to be the dimer antiferromagnetic (AFM) state, which is energetically only 2.77 (2.15) meV/Fe lower than the trimer (dimer-trimer-dimer-trimer) AFM state, indicating that strong magnetic fluctuations might be induced via slight modulation. Interestingly, SnOFeSe is at the verge of metal-insulator transition in these low-energy magnetic states, hence bridging the metallic parent compounds of iron-based superconductors and the insulating ones of cuprate superconductors. With the reduced dimensionality, monolayer SnOFeSe also shows great similarities in the electronic and magnetic properties to its bulk phase. Given that SnOFeSe is adjacent to magnetic frustration and resembles LaOFeAs in both crystal and electronic structures, we suggest that SnOFeSe is a possible superconductor parent compound, which may provide a promising platform to study the interplay between magnetism and unconventional superconductivity in FeSe-derived materials., Comment: 8 pages, 7 figures, 2 tables

The natural orbitals renormalization group (NORG) has previously been proposed as an efficient numerical method for solving zero-temperature properties of multisite and multiorbital quantum impurity systems. Here, we implement the NORG as an impurity solver for dynamical mean-field theory (DMFT). In comparison with the exact diagonalization method, the NORG method can treat much more bath sites in an impurity model to which the DMFT maps a lattice model and can find accurate zero-temperature Matsubara and low-frequency retarded Green's functions. We demonstrate the effectiveness of this method on a two-orbital Hubbard model on the Bethe lattice and find successfully the orbital selective Mott transition with a Kondo resonance peak in the wide band and two holon-doublon bound state excitation peaks in the narrow band., Comment: 7 pages, 6 figures

Recent experiment reported the self-passivated electride Hf2S with excellent stability and continuous electrocatalytic ability [S. H. Kang et al., Sci. Adv. 6, eaba7416 (2020)]. Starting from its 2H-type layered structure, we have studied the electronic, magnetic, and transport properties of the electride Hf2S in the monolayer and multilayer forms by combining first-principles electronic structure calculations and Kubo formula approach. Our calculations indicate that these thin films of Hf2S electride are both dynamically and thermodynamically stable. Astonishingly, the calculations further show that the outmost Hf atoms and the surface electron gas of the Hf2S multilayers are spin polarized, while the inner Hf atoms and the electron gas in the interlayer regions remain nonmagnetic. Due to the magnetic surface, the multilayer Hf2S exhibits many unusual transport properties such as the surface anomalous Hall effect and the electric-field-induced layer Hall effect. Our theoretical predictions on Hf2S call for future experimental verification., Comment: 5 pages, 5 figures, 34 references

We propose two novel two-dimensional topological Dirac materials, planar PtN4C2 and Pt2N8C6, which exhibit graphene-like electronic structures with linearly dispersive Dirac-cone states exactly at the Fermi level. Moreover, the Dirac cone is anisotropic, resulting in anisotropic Fermi velocities and making it possible to realize orientation-dependent quantum devices. Using the first-principles electronic structure calculations, we have systemically studied the structural, electronic, and topological properties. We find that spin-orbit coupling opens a sizable topological band gap so that the materials can be classified as quantum spin Hall insulators as well as quantum valley Hall insulators. Helical edge states that reside in the insulating band gap connecting the bulk conduction and valence bands are observed. Our work not only expands the Dirac cone material family, but also provides a new avenue to searching for more two-dimensional topological quantum spin and valley Hall insulators., Comment: 6 pages, 4 figures

Unconventional Weyl semimetals have attracted intensive research interest in condensed matter physics and materials science, but they are very rare in two dimensions. In this work, based on symmetry analysis and the first-principles electronic structure calculations, we predict that the Si/Bi van der Waals heterostructure is a two-dimensional unconventional quadratic double Weyl semimetal with strong spin-orbit coupling (SOC). Although unprotected by the C3v double group symmetry of the heterostructure, the two-dimensional quadratic double Weyl semimetal is stable for compressive strains up to 6.64%. The system transforms into a trivial semimetal with further increasing strain, where the phase boundary is a two-dimensional triple degenerate semimetal state. Furthermore, the Kane-Mele tight-binding model calculations show that the quadratic double Weyl phase is derived from the competition between the Rashba SOC and the proximity-effect-enhanced intrinsic SOC. On the other hand, by breaking mirror symmetry, the quadratic double Weyl semimetal transforms into a quantum spin Hall insulator as well as a quantum valley Hall insulator phase. Thus, the Si/Bi heterostructure is an excellent platform for studying the exotic physics of two-dimensional double Weyl semimetal and other novel topological phases., Comment: 6 pages, 5 figures

So far, experimentally realized quantum anomalous Hall (QAH) insulators all exhibit ferromagnetic order and the QAH effect only occurs at very low temperatures. On the other hand, up to now the QAH effect in antiferromagnetic (AFM) materials has never been reported. In this letter, we realize the QAH effect by proposing a four-band lattice model with static AFM order, which indicates that the QAH effect can be found in AFM materials. Then, as a prototype, we demonstrate that a monolayer CrO can be switched from an AFM Weyl semimetal to an AFM QAH insulator by applying strain, based on symmetry analysis and the first-principles electronic structure calculations. Our work not only proposes a new scenario to search for QAH insulators in materials, but also reveals a way to considerably increase the critical temperature of the QAH phase.

A main task in condensed-matter physics is to recognize, classify, and characterize phases of matter and the corresponding phase transitions, for which machine learning provides a new class of research tools due to the remarkable development in computing power and algorithms. Despite much exploration in this new field, usually different methods and techniques are needed for different scenarios. Here, we present SimCLP: a simple framework for contrastive learning phases of matter, which is inspired by the recent development in contrastive learning of visual representations. We demonstrate the success of this framework on several representative systems, including classical and quantum, single-particle and many-body, conventional and topological. SimCLP is flexible and free of usual burdens such as manual feature engineering and prior knowledge. The only prerequisite is to prepare enough state configurations. Furthermore, it can generate representation vectors and labels and hence help tackle other problems. SimCLP therefore paves an alternative way to the development of a generic tool for identifying unexplored phase transitions., Comment: 7 pages, 6 figures

The exploration of superconductivity in low-dimensional materials has attracted intensive attention for decades. Based on first-principles electronic structure calculations, we have systematically investigated the electronic and superconducting properties of the two-dimensional electride Ba$_2$N in the monolayer limit. Our results show that monolayer Ba$_2$N has a low work function of 3.0 eV and a predicted superconducting transition temperature ($T_c$) of 3.4 K. The superconductivity can be further improved with the tensile strain, which results from the increase of density of states at the Fermi level as well as the enhanced coupling between inner-layer electrons and phonons. Remarkably, at the 4$\%$ tensile strain, the acoustic branches have noticeable softening at the K point of Brillouin zone and the superconducting $T_c$ can reach 10.8 K. The effect of lattice strain on the electron transfer from the superficial region to the inner-layer region of monolayer Ba$_2$N may also apply to other electride materials and influence their physical properties., Comment: 8 pages, 9 figures

The recently synthesized two-dimensional electride Gd$_2$C was proposed to be a ferromagnetic metal that possesses multiple pairs of Weyl points and may display a large anomalous Hall conductivity [Liu \textit{et al.}, Phys. Rev. Lett. \textbf{125}, 187203 (2020)]. In view of its layered structure, here we carry out first-principles studies on the magnetic and electronic properties of Gd$_2$C in the ultrathin monolayer limit. We find that monolayer Gd$_2$C remains ferromagnetic like the bulk form and the hydrogenation can effectively tune its magnetism and electronic structure. With one-sided coverage of hydrogen atoms, monolayer Gd$_2$C becomes a half-metal with one spin channel around the Fermi level. For two-sided hydrogenation, monolayer Gd$_2$C transforms to an antiferromagnetic insulator with a band gap of 0.8 eV. Our studies show that monolayer electride Gd$_2$C can perform multiple magnetic and electronic transitions with different levels of hydrogenation and may be also adopted to construct a planar heterojunction with selective area adsorption of hydrogen atoms, which has promising applications in future electronic and spintronic devices., Comment: 6 pages, 6 figures, 1 table

Recently, Mixture-of-Experts (short as MoE) architecture has achieved remarkable success in increasing the model capacity of large-scale language models. However, MoE requires incorporating significantly more parameters than the base model being extended. In this paper, we propose building a parameter-efficient MoE architecture by sharing information among experts. We adopt the matrix product operator (MPO, a tensor decomposition from quantum many-body physics) to reconstruct the parameter matrix in the expert layer and increase model capacity for pre-trained language models by sharing parameters of the central tensor (containing the core information) among different experts while enabling the specificity through the auxiliary tensors (complementing the central tensor) of different experts. To address the unbalanced optimization issue, we further design the gradient mask strategy for the MPO-based MoE architecture. Extensive experiments based on T5 and GPT-2 show improved performance and efficiency of the pre-trained language model (27.2x reduction in total parameters for the superior model performance, compared with the Switch Transformers). Our code is publicly available at https://github.com/RUCAIBox/MPOE., Comment: 11 pages, 2 figures, 2 tables

Two spins located at the edge of a quantum spin Hall insulator may interact with each other via indirect spin-exchange interaction mediated by the helical edge states, namely the RKKY interaction, which can be measured by the magnetic correlation between the two spins. By means of the newly developed natural orbitals renormalization group (NORG) method, we investigated the magnetic correlation between two Kondo impurities interacting with the helical edge states, based on the Kane-Mele model defined in a finite zigzag graphene nanoribbon with spin-orbital coupling (SOC). We find that the SOC effect breaks the symmetry in spatial distribution of the magnetic correlation, leading to anisotropy in the RKKY interaction. Specifically, the total correlation is always ferromagnetic (FM) when the two impurities are located at the same sublattice, while it is always antiferromagnetic (AFM) when at the different sublattices. Meanwhile, the behavior of the in-plane correlation is consistent with that of the total correlation. However, the out-of-plane correlation can be tuned from FM to AFM by manipulating either the Kondo coupling or the interimpurity distance. Furthermore, the magnetic correlation is tunable by the SOC, especially that the out-of-plane correlation can be adjusted from FM to AFM by increasing the strength of SOC. Dynamic properties of the system, represented by the spin-staggered excitation spectrum and the spin-staggered susceptibility at the two impurity sites, are finally explored. It is shown that the spin-staggered susceptibility is larger when the two impurities are located at the different sublattices than at the same sublattice, which is consistent with the behavior of the out-of-plane correlation. On the other hand, our study further demonstrates that the NORG is an effective numerical method for studying the quantum impurity systems., Comment: 9 pages, 9 figures

Using the natural orbitals renormalization group (NORG) method, we have investigated the screening of the local spin of an Anderson impurity interacting with the helical edge states in a quantum spin Hall insulator. We find that there is a local spin formed at the impurity site and the local spin is completely screened by electrons in the quantum spin Hall insulator. Meanwhile, the local spin is screened dominantly by a single active natural orbital. We then show that the Kondo screening mechanism becomes transparent and simple in the framework of natural orbitals formalism. We project the active natural orbital respectively into real space and momentum space to characterize its structure. And we confirm the spin-momentum locking property of the edge states based on the occupancy of a Bloch state in the edge to which the impurity couples. Furthermore, we study the dynamical property of the active natural orbital represented by the local density of states, from which we observe the Kondo resonance peak., Comment: 5 pages, 6 figures

A multichannel Kondo model, where two or more equivalent but independent channels of electrons compete to screen a spin-1/2 impurity, shows overcompensation of the impurity spin, leading to the non-Fermi-liquid behavior in various thermodynamic and transport properties. However, when the channel symmetry is broken, an impurity quantum phase transition can occur at zero temperature. Identification of an order parameter describing the impurity quantum phase transition is very difficult since it is beyond the conventional Landau-Ginzburg-Wilson theory. By employing the natural orbitals renormalization group method, we study both two-channel and threechannel Kondo models, from the perspective of spin correlation between the impurity and electrons in electronic channels. Here we demonstrate that by introducing the spin-correlation ratio as an order parameter we can characterize impurity quantum phase transitions driven by channel asymmetry. In particular, the universal critical exponents $\beta$ of the spin-correlation ratio and $\nu$ of the correlation length are explicitly determined by finite-sizescaling analysis, namely, $\beta = 0.10(1), \nu = 2.0(1)$, and $\beta = 0.10(1), \nu = 2.5(1)$ for the two-channel and three-channel Kondo models, respectively., Comment: 7 pages, 7 figures

The recent discovery of superconductivity up to 32 K in the pressurized MoB2 reignites the interests in exploring high-Tc superconductors in transition-metal diborides. Inspired by that work, we turn our attention to the 5d transition-metal diborides. Here we systematically investigate the responses of both structural and physical properties of WB2 and ReB2 to external pressure, which possess different types of boron layers. Similar to MoB2, the pressure-induced superconductivity was also observed in WB2 above 60 GPa with a maximum Tc of 15 K at 100 GPa, while no superconductivity was detected in ReB2 in this pressure range. Interestingly, the structures at ambient pressure for both WB2 and ReB2 persist to high pressure without structural phase transitions. Theoretical calculations suggest that the ratio of flat boron layers in this class of transition-metal diborides may be crucial for the appearance of high Tc. The combined theoretical and experimental results highlight the effect of geometry of boron layers on superconductivity and shed light on the exploration of novel high-Tc superconductors in borides., Comment: 17 pages,5 figures

The MnBi$_{2}$Te$_{4}$ family has attracted significant attention due to its rich topological states such as the quantum anomalous Hall (QAH) insulator state, the axion insulator state, and the magnetic Weyl semimetal state. Nevertheless, the intrinsic antiferromagnetic (AFM) interlayer coupling in MnBi$_{2}$Te$_{4}$ partly hinders the realization of "high-temperature" QAH effect. Here, by using first-principles electronic structure calculations, we design a new class of materials Mn\emph{X}$_{2}$\emph{B}$_{2}$\emph{T}$_{6}$ (\emph{X}=Ge, Sn, or Pb; \emph{B}=Sb or Bi; \emph{T}=Se or Te) based on the \emph{X}$_{2}$\emph{B}$_{2}$\emph{T}$_{5}$ structures rather than the Bi$_{2}$Te$_{3}$ family. We find that each septuple-layer Mn\emph{B}$_{2}$\emph{T}$_{4}$ is sandwiched by two [\emph{X}\emph{T}] layers, which may turn the AFM interlayer coupling into a ferromagnetic (FM) coupling. The calculations specifically demonstrate that \emph{MnGe}$_{2}$\emph{Sb}$_{2}$\emph{Te}$_{6}$, \emph{MnGe}$_{2}$\emph{Bi}$_{2}$\emph{Te}$_{6}$, and \emph{MnPb}$_{2}$\emph{Bi}$_{2}$\emph{Te}$_{6}$ are FM axion insulators, while MnGe$_{2}$Sb$_{2}$Se$_{6}$, MnGe$_{2}$Bi$_{2}$Se$_{6}$, MnSn$_{2}$Sb$_{2}$Te$_{6}$, and MnSn$_{2}$Bi$_{2}$Te$_{6}$ are A-type AFM axion insulators. These seven materials all have an out-of-plane easy axis of magnetization. The Mn\emph{X}$_{2}$\emph{B}$_{2}$\emph{T}$_{6}$ family thus offers a promising platform beyond the MnBi$_{2}$Te$_{4}$ family for the realization of quantized magnetoelectric effect and "high-temperature" QAH effect in future experiments., Comment: 6 pages, 4 figures, 1 table

We investigate the evolutions of structural parameters, optical properties, and electronic structures of a van der Waals kagome semiconductor Pd$_{3}$P$_{2}$S$_{8}$ with Se doping. When the doping level of Se increases, the bandgaps of Pd$_{3}$P$_{2}$(S$_{1-x}$Se$_{x}$)$_{8}$ single crystals decrease gradually, accompanying with the expanded unit cells. The first-principles calculations show that there is a flat band (FB) near the Fermi level in bulk Pd$_{3}$P$_{2}$S$_{8}$. This FB mainly originates from the $d_{z^2}$-like orbitals of Pd atoms in the Pd kagome lattice, which have a finite interlayer electron hopping perpendicular to the PdS$_4$ square plane. The interlayer hopping can be reinforced with Se doping, inducing a stronger interlayer coupling via the chalcogen atoms at apical sites, which reduces the bandgap and enhances the cleavage energy. In contrast, the varnishing interlayer hopping in the two-dimensional limit results in the formation of ultra-FB in the monolayers of these compounds. The easy exfoliation and the existence of unique ultra-FB near $E_{\rm F}$ make Pd$_{3}$P$_{2}$(S$_{1-x}$Se$_{x}$)$_{8}$ a model system to explore the exotic physics of FB in 2D kagome lattice., Comment: 6 pages, 4 figures

The recent discovery and studies of 1144-phase compounds, e.g., CaKFe$_4$As$_4$, have attracted significant research interest. In this paper, based on the first-principles density functional calculations, we present a systematic study on the electronic structure of the recently synthetized 1144-type quaternary compound CaKRu$_4$P$_4$. We find that the Ru-based 1144-type compound possesses a different electronic structure from that of iron-based superconductors, even though they share very similar crystallographic structures. In CaKRu$_4$P$_4$, there is no hole-type carrier if spin-orbit interaction is not considered. And a long-range magnetic order is absent in its ground state. With the application of pressure, the electronic structure of CaKRu$_4$P$_4$ becomes similar to those of the ternary 122-type compounds LaRu$_2$P$_2$ and LaRu$_2$As$_2$. CaKRu$_4$P$_4$ is very likely to be a phonon-mediated medium coupled BCS superconductor. Furthermore, type-I and type-II Dirac fermions can be created and regulated in this system with pressure. The quaternary compound CaKRu$_4$P$_4$ therefore has a potential to be an attractive platform for the study of topological physics and superconductivity., Comment: 7 pages,5 figures