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Magnon Chern insulators (MCIs) exhibit unique topological magnon band structures featuring chiral edge states. Direct observations of the topologically protected magnon edge states have long been pursued. Here, we report the spatially resolved detection of magnon edge states in a two-dimensional ferromagnet with honeycomb lattice (single-layer chromium triiodide). Using scanning tunneling microscopy, we observed magnon-assisted inelastic tunneling conductance and revealed the gapped magnon spectra with enhanced signals at the van Hove singularities. Extra tunneling conductance contributed from the magnon edge states was detected at three different edge configurations. Our work provided direct evidence proving the existence of MCI states down to the single-layer limit, initiating spatially-resolved explorations on exotic properties arising from topological edge states of MCIs.

We investigate the excitation spectra of a spin-1/2 antiferromagnetic Heisenberg trimer spin chain by employing a combination of numerical and theoretical techniques. Utilizing the Krylov-space correction-vector method in density matrix renormalization group (DMRG), we calculate both the direct and indirect resonant inelastic x-ray scattering (RIXS) spectra for the trimer spin chain. To interpret the observed features in the RIXS spectra, we perform a theoretical perturbative analysis to compute the energy dispersions which are then utilized to determine the density of states (DOS) for both the single-particle and the two-particle excitation spectra. Our results show that the single-particle continua of the direct RIXS spectrum align with the energy levels observed in the DOS spectra of spinon, doublon, and quarton excitations. Furthermore, the two-particle continua are revealed in the indirect RIXS process, where all possible single particle excitations combine to form the various two-particle excitations of the trimer spin chain. Based on our calculations, we propose the RIXS mechanism of generating the fractionalized (spinon) and collective (doublon and quarton) excitations in the trimer spin chain at both the $L$-edge and the $K$-edge, including discussing the interplay of these excitations in the RIXS spectrum for various trimer coupling strength. The computed energy range of the excitations suggest the possibility of experimental detection at both the $L$-edge and the $K$-edge within the current capabilities of RIXS instrumentation resolution., Comment: 13 pages, 5 figures

The Einstein-de Haas (EdH) effect is an interesting phenomenon linking mechanics and magnetism, in which changes in magnetization induce mechanical rotation. Despite being discovered more than a century ago, the EdH effect still shows crucial significance in modern science, particularly in the realms of spintronics and ultrafast magnetism. Recently, it has been predicted that the EdH effect can be realised in topological magnon systems, which undoubtedly brings even richer properties. In this perspective, we aim to review the recent progress of the EdH effect and discuss its developments in three key aspects: the microscopic mechanism of the EdH effect, the EdH effect of topological magnons, and the chiral phonon--magnon conversion. These discussions are poised to inspire further explorations in physics and promising applications in different areas., Comment: 5 pages, 2 figures

In comparison to simpler data such as chemical formulas and lattice structures, electronic band structure data provide a more fundamental and intuitive insight into superconducting phenomena. In this work, we generate superconductor's lattice structure files optimized for density functional theory (DFT) calculations. Through DFT, we obtain electronic band superconductors, including band structures, density of states (DOS), and Fermi surface data. Additionally, we outline efficient methodologies for acquiring structure data, establish high-throughput DFT computational protocols, and introduce tools for extracting this data from large-scale DFT calculations. As an example, we have curated a dataset containing information on 2474 superconductors along with their experimentally determined superconducting transition temperatures, which is well-suited for machine learning applications. This work also provides guidelines for accessing and utilizing this dataset. Furthermore, we present a neural network model designed for training with this data. All the aforementioned data and code are publicly available at http://www.superband.work.

Energy band theory is a foundational framework in condensed matter physics. In this work, we employ a deep learning method, BNAS, to find a direct correlation between electronic band structure and superconducting transition temperature. Our findings suggest that electronic band structures can act as primary indicators of superconductivity. To avoid overfitting, we utilize a relatively simple deep learning neural network model, which, despite its simplicity, demonstrates predictive capabilities for superconducting properties. By leveraging the attention mechanism within deep learning, we are able to identify specific regions of the electronic band structure most correlated with superconductivity. This novel approach provides new insights into the mechanisms driving superconductivity from an alternative perspective. Moreover, we predict several potential superconductors that may serve as candidates for future experimental synthesis.

Motivated by the discovery of high-temperature superconductivity in bilayer nickelate La$_3$Ni$_2$O$_7$ under pressure, we investigate the ground-state phase diagram and correlation effects using determinant quantum Monte Carlo simulations in a simplified bilayer two-orbital Hubbard model at half filling. Our results reveal the emergence of a nonmagnetic weakly insulating phase at weak on-site Hubbard interactions, transitioning to an antiferromagnetic Mott insulating phase as the interaction strength exceeds a critical value $U/t_1^x\approx 4.15$. This phase transition is consistent with the 3D O(3) Heisenberg universality class. Additionally, we analyze dynamical properties such as the single-particle spectral function and dynamic spin structure factor. The pronounced inter-layer correlation of $d_{3z^2-r^2}$ orbitals results in a downward trend and an extended flatness in the $\gamma$ band, mirroring the angle-resolved photoemission spectroscopy findings under ambient pressure. Our numerical results provide important clues for understanding the strong correlation effects in La$_3$Ni$_2$O$_7$., Comment: 9 pages, 11 figures

We investigate the S=1/2 antiferromagnetic Heisenberg model with a 3$\times$3 checkerboard lattice structure in a longitudinal magnetic field. By using the stochastic series expansion quantum Monte Carlo (SSE-QMC) method, we obtain the properties of the non-plateau XY phase, 1/9, 3/9, 5/9, 7/9 magnetization plateau phases, and fully polarized phase. Then, we determine the precise phase transition critical points belonging to the 3D XY universality class through finite-size scaling. Moreover, we study the longitudinal and transverse dynamic spin structure factors of this model in different phases. For the non-plateau XY phase, the energy spectra present a gap between the low-energy gapless branch and the high-energy part under the competition of magnetic field and interaction. The gapless branch can be described by the spin wave theory in the canted antiferromagnetic phase of the effective "block spin" model. In the magnetization plateau phase, we identify that the excitation arises from localized disturbances within the sublattice, which are capable of spreading in momentum space. This study offers theoretical insights and interpretations for the characteristics of the ground state and the inelastic neutron scattering spectrum in two-dimensional quantum magnetic materials. Specifically, it focuses on materials with a checkerboard unit cell structure and odd-spin configurations under the influence of a longitudinal magnetic field., Comment: 11 pages, 12 figures

Transition metal dichalcogenides (TMDs), exhibit a range of crystal structures and topological quantum states. The 1$T$ phase, in particular, shows promise for superconductivity driven by electron-phonon coupling, strain, pressure, and chemical doping. In this theoretical investigation, we explore 1$T$-RhSeTe as a novel type of TMD superconductor with topological electronic states. The optimal doping structure and atomic arrangement of 1$T$-RhSeTe are constructed. Phonon calculations validate the integrity of the constructed doping structure. The analysis of the electron-phonon coupling (EPC) using the Electron-phonon Wannier (EPW) method has confirmed the existence of a robust electron-phonon interaction in 1$T$-RhSeTe, resulting in total EPC constant $\lambda$ = 2.02, the logarithmic average frequency $\omega_{\text{log}}$ = 3.15 meV and $T_c$ = 4.61 K, consistent with experimental measurements and indicative of its classification as a BCS superconductor. The band structure analysis revealed the presence of Dirac-like band crossing points. The topological non-trivial electronic structures of the 1$T$-RhSeTe are confirmed via the evolution of Wannier charge centers (WCCs). Collectively, these distinctive properties underscore 1$T$-RhSeTe as a possible candidate for a topological superconductor, warranting further investigation into its potential implications and applications., Comment: 7 pages, 4 figures

The recent discovery of high-temperature superconductivity in high-pressurized La$_3$Ni$_2$O$_{7-\delta}$ has garnered significant attention. Using density functional theory, we investigate the magnetic properties of La$_3$Ni$_2$O$_7$ at ambient pressure. Our calculations suggest that with $\delta=0$, the double spin stripe phase is favored as the magnetic ground state. Oxygen vacancies may effectively turn nearest Ni spins into charge sites. Consequently, with moderate $\delta$ values, our theoretical magnetic ground state exhibits characteristics of both double spin stripe and spin-charge stripe configurations, providing a natural explanation to reconcile the seemingly contradictory experimental findings that suggest both the configurations as candidates for the spin-density-wave phase. With higher $\delta$ values, we anticipate the ground state to become a spin-glass-like noncollinear magnetic phase with only short-range order. The oxygen vacancies are expected to significantly impact the magnetic excitations and the transition temperatures $T_{SDW}$. We further offer a plausible explanation for the experimental observations that the measured $T_{SDW}$ appears insensitive to the variation of samples and the lack of direct evidence for long-range magnetic ordering.

We propose a model with Weyl magnons and weak topological magnons ($\mathbb{Z}_2$) in a collinear altermagnet on the honeycomb lattice. Altermagnetic magnon bands can be realized by breaking the symmetry of the second nearest neighbor exchange couplings without the Dzyaloshinskii-Moriya (DM) interaction. Besides the Chern number and $\mathbb{Z}_2$ invariant, chirality is important to describe the band topology. The model shows the nonzero magnon Nernst effect for both the strong and weak topological phases when a longitudinal temperature gradient exists. Furthermore, we find the orbital angular momentum induced purely by the topology of magnons, which can be probed by the Einstein-de Haas effect., Comment: 7 pages, 5 figures

We investigate a fractional Chern insulator (FCI) candidate arising from Moir\'e bands with higher Chern number C=2 on a magic angle twisted bilayer checkboard lattice (MATBCB). There are two nearly flat low lying bands in the single particle energy spectrum under the first magic angle $\phi\approx 1.608^{\circ}$ and chiral limit. We find MATBCB hosts a nearly uniform Berry curvature distribution and exhibits tiny violation of quantum geometric trace condition in the first moir\'e Brillourin Zone (mBZ), indicating that there is a nearly ideal quantum geometry in MATBCB in single particle level. Turning on projected Coulomb interactions, we perform exact diagonalization and find a ten-fold ground state quasi-degeneracy in many body energy spectrum with filling fraction $\nu=1/5$. The ten-fold quasi-degenrate ground states further show spectra flow under flux pumping. By diagnosing the particle entanglement spectrum (PES) of the ground states, we obtain a clear PES gap and quasi-hole state counting consistent with Halperin spin singlet generalized Pauli principle, suggesting that a fractional Chern insulator is realized in this system., Comment: 13 pages, 9 figures

This review provides a comprehensive overview of current research on the structural, electronic, and magnetic characteristics of the recently discovered high-temperature superconductor La$_3$Ni$_2$O$_7$ under high pressures. We present the experimental results for synthesizing and characterizing this material, derived from measurements of transport, thermodynamics, and various spectroscopic techniques, and discuss their physical implications. We also explore theoretical models proposed to describe the electronic structures and superconducting pairing symmetry in La$_3$Ni$_2$O$_7$, highlighting the intricate interplay between electronic correlations and magnetic interactions. Despite these advances, challenges remain in growing high-quality samples free of extrinsic phases and oxygen deficiencies and in developing reliable measurement tools for determining diamagnetism and other physical quantities under high pressures. Further investigations in these areas are essential to deepening our understanding of the physical properties of La$_3$Ni$_2$O$_7$ and unlocking its superconducting pairing mechanism., Comment: 15 pages, 11 figures

Here we employed optical spectroscopy and ultrafast reflectivity measurements to investigate the density wave instability of trilayer nickelate La4Ni3O10 at ambient pressure. Our optical spectroscopy measurements indicate that La4Ni3O10 is metallic with a large plasma frequency at room temperature. As the temperature decreases, we observe the formation of an energy gap in reflectivity below TDW, signaling the charge/spin density wave transition. The Drude component was largely removed due to the gap opening in the Fermi surface. Our Drude-Lorentz analysis reveals that the energy gap in La4Ni3O10 is approximately 61 meV, which is three times larger than that obtained from ARPES measurements. The density wave gap feature is more prominent than that observed in bilayer nickelate La3Ni2O7, suggesting more carriers are gapped at the Fermi surface across the density wave transition. By comparing the measured plasma frequency with the first-principles calculation, we categorize La4Ni3O10 as a moderately electronic correlation material, similar to the parent compound of iron-based superconductors, however, being weaker than the bilayer nickelate La3Ni2O7. Our ultrafast pump-probe experiments also show that the relaxation time diverges near the transition temperature. By analyzing the amplitude and relaxation time with the Rothwarf-Taylor model, we estimate the energy gap to be 58 meV, which agrees with the result of optical spectroscopy. The more prominent gap feature and weaker electronic correlation might be the cause of a lower superconductivity transition temperature in La4Ni3O10 under high pressure. These findings significantly contribute to understanding the origin of density wave and superconductivity in trilayer nickelate La4Ni3O10.

Klein tunneling is an old topic in relativistic quantum physics, and has been observed recently in graphene where massless particles reside. Here, we propose a new heterostructure platform for Klein tunneling to occur, which consists of a Weyl-semimetal-based normal state/superconductor (NS) junction. By developing a Blonder-Tinkham-Klapwijk-like theory, we find that Klein tunneling occurs at normal incidence, which can lead to differential conductance doubling. If the (single) Weyl semimeltals are replaced by double Weyl semimetals, anti-Klein tunneling will take place of Klein tunneling. Our work provides a theoretical guide for the detection of (anti-)Klein tunneling in three-dimensional chiral NS junctions., Comment: 5 pages, 7 figures

The recent transport measurement of La$_3$Ni$_2$O$_7$ uncover a "right-triangle" shape of the superconducting dome in the pressure-temperature (P-T) phase diagram. Motivated by this, we perform theoretical first-principles studies of La$_3$Ni$_2$O$_7$ with the pressure ranging from 0 to 100 GPa. Notably, we reveal a pressure dependence of the Ni-$d_{z^2}$ electron density at the Fermi energy ($n_z^{EF}$) that highly coincides with such shape. On this basis, we further explore the electronic structure under uniaxial stress. By tracking the stress response of $n_z^{EF}$, we propose that superconductivity can be achieved by applying only about 2 GPa of compression along the c axis. The idea is further exemplified from the perspectives of lattice distortion, band structure, Fermi surface and superconducting phase coherence. We also discuss the possible charge modulation under the stress and provide an insight to the relation between n_z^EF and the superconducting Tc in La$_3$Ni$_2$O$_7$ system. Our study provides a helpful guide to the future experiment.

Resonant inelastic x-ray scattering (RIXS) experiment was performed at the Mn $L_3$ edge. A 10 $\%$ Mn-doped Sr$_{3}$Ru$_{2}$O$_{7}$ compound, where the Mn$^{3+}$ ions are in the 3$d^4$ state, were probed for $dd$ excitations. The dilute doping concentration allows one to treat the dopant Mn$^{3+}$ ions as effectively free in the host ruthenium compound. The local nature of $dd$ RIXS spectroscopy permits one to use a single-site model to simulate the experimental spectra. The simulated spectra reproduces the in-plane [100] experimental RIXS spectrum. We also predict the intensity for the in-plane [110] direction and the out-of-plane spin orientation configuration [001]. Based on our single-ion model we were able to fit the experimental data to obtain the crystal field parameters, the 10Dq value, and the intra-orbital spin-flip energy 2$\mathcal{J}$(or $3J_{H}$, where $J_{H}$ is the Hund's energy) of the Mn$^{3+}$ ion. Utilizing our computed RIXS quantum transition amplitudes between the various $d$ orbitals of the Mn$^{3+}$ ion, the expression for the Kramers-Heisenberg cross section, and a self-consistent fitting procedure we also identify the energy boundaries of the non-spin-flip and spin-flip $dd$ excitations present in the experimental data. From our fitting procedure we obtain $2\mathcal{J} (3J_{H})=2.06$ eV, a value which is in excellent agreement with that computed from the free ion Racah parameters. We also identified the charge transfer boundary. In addition to predicting the microscopic parameters, we find a quantum spin-flip transition in the non-cross ($\sigma_{in}-\sigma_{out}$, $\pi_{in}-\pi_{out}$) x-ray polarization channels of the $dd$ RIXS spectra. A similar transition, was previously predicted to occur in the $\pi-\pi$ channel of the magnon spectrum in the non-collinear non-coplanar Kagome compound composed of Cu$^{2+}$ 3d$^{9}$ ion., Comment: 12 pages, 7 figures, see PDF text for full abstract info

Low-dimensional magnetic structures coupled with superconductors are promising platforms for realizing Majorana zero modes, which have potential applications in topological quantum computing. Here, we report a two-dimensional (2D) magnetic-superconducting heterostructure consisting of single-layer chromium diiodide (CrI2) on a niobium diselenide (NbSe2) superconductor. Single-layer CrI2 nanosheets, which hold antiferromagnetic (AFM) ground states by our first-principles calculations, were epitaxially grown on the layered NbSe2 substrate. Using scanning tunneling microscopy/spectroscopy, we observed robust in-gap states spatially located at the edge of the nanosheets and defect-induced zero-energy peaks inside the CrI2 nanosheets. Magnetic-flux vortices induced by an external field exhibit broken threefold rotational symmetry of pristine NbSe2 superconductor, implying the efficient modulation of the interfacial superconducting states by the epitaxial CrI2 layer. A phenomenological model suggests the existence of chiral edge states in a 2D AFM-superconducting hybrid system with an even Chern number, providing a qualitatively plausible understanding for our experimental observation., Comment: 21 pages, 5 figures

Recently, the discovery of superconductivity in Ruddlesden-Popper (RP) $\mathrm{La_4Ni_3O_{10}}$ under pressure has further expanded the realm of nickelate-based superconductor family. In this paper, we performed a first-principle study of $\mathrm{La_4Ni_3O_{10}}$ for both $P2_1/a$ phase at ambient pressure and $I4/mmm$ phase at high pressure, with $U$=0, 3.5\ eV. Our results confirmed the characteristic upward shift of Ni-$d_{z^2}$ bonding band under pressure. Moreover, our analysis of electronic spectrum and orbital occupancy unveil the dynamic mechanism of electronic reconstructions under pressure, embedded in a critical dual effect. Based on our results, we further proposed a trilayer two-orbital model by performing Wannier downfolding on Ni-$e_g$ orbitals. Our model reveals four Fermi surface sheets with $\alpha,\beta,\beta^\prime,\gamma$ pockets, bearing resemblance to that of bilayer $\mathrm{La_3Ni_2O_7}$. According to the model, our calculated spin susceptibility under random phase approximation shows that $d_{x^2-y^2}$ orbital is also important for the magnetic fluctuation in RP series. Finally, a high energy sixteen-orbital model with direct $dp,pp$ hoppings is proposed, which implies that $\mathrm{La_4Ni_3O_{10}}$ also lies in charge-transfer picture within Zaanen-Sawatzky-Allen scheme. Our exposition of electronic reconstructions and multi-orbital models shed light on theoretical electronic correlation study and experimental exploration of lower pressure superconductor in RP series., Comment: 11 pages, 6 figures

Motivated by recent advancements in theoretical and experimental studies on the high-energy excitations, we theoretically explore the quantum phase transition and composite dynamics of the antiferromagnetic trimer chains in a magnetic field using the exact diagonalization, density matrix renormalization group, time-dependent variational principle and cluster perturbation theory. We measure the entanglement entropy to uncover the phase diagram, encompassing the XY-I, $1/3$ magnetization plateau, XY-II and ferromagnetic phases. Both critical XY-I and XY-II phases are both described by the conformal field theory with the central charge $c \simeq 1$. By analyzing the dynamical structure factor, we elucidate the distinct features of spin dynamics across different phases. In the regime of weak intertrimer interaction, we identify the intermediate-energy and high-energy modes in the XY-I and $1/3$ magnetization plateau phases as the internal trimer excitations, corresponding to the propagation of doublon and quarton, respectively. Notably, the application of a magnetic field splits the high-energy spectra into two branches labeled as the upper quarton and lower quarton. Furthermore, we also explore the spin dynamics of a trimerized model closely related to the quantum magnet \ce{Na_2Cu_3Ge_4O_12}, and discuss the possibility of the quarton Bose-Einstein condensation. Our results can be verified in the inelastic neutron scattering experiments and provide deep insights for exploring the high-energy exotic excitations., Comment: 14+7 pages, 16 figures

We investigate the magnetic excitations of the trimerized Heisenberg models with intra-trimer interaction $J_1$ and inter-trimer interaction $J_2$ on four different two-dimensional lattices using a combination of stochastic series expansion quantum Monte Carlo (SSE QMC) and stochastic analytic continuation methods (SAC), complemented by cluster perturbation theory (CPT). These models exhibit quasi-particle-like excitations when $g=J_2/J_1$ is small, characterized by low-energy magnons, intermediate-energy doublons, and high-energy quartons. The low-energy magnons are associated with the magnetic ground states. They can be described by the linear spin wave theory (LSWT) of the effective block spin model and the original spin model. Doublons and quartons emerge from the corresponding internal excitations of the trimers with distinct energy levels, which can be effectively analyzed using perturbation theory when the ratio of exchange interactions $g$ is small. In this small $g$ regime, we observe a clear separation between the magnon and higher-energy spectra. However, as $g$ increases, these three spectra gradually merge into the magnon modes or continua. Nevertheless, the LSWT fails to provide quantitative descriptions of the higher-energy excitation bands due to significant quantum fluctuations. Notably, in the Collinear II and trimerized hexagon lattice, a broad continuum emerges above the single-magnon spectrum, originating from the quasi-1D physics due to the dilute connections between chains. Our numerical analysis of these 2D trimers yields valuable theoretical predictions and explanations for the inelastic neutron scattering (INS) spectra of 2D magnetic materials featuring trimerized lattices.

Employing the projective formalism of determinant quantum Monte Carlo (DQMC) simulations, we meticulously explore the ground-state phase diagram and critical behavior of the half-filled Hubbard model on a square-hexagon-octagon (SHO) lattice. This lattice, a two-dimensional (2D) structure comprising squares, hexagons, and octagons, is representative of the biphenylene network (BPN). Our findings reveal an intriguing ground-state phase diagram, featuring an antiferromagnetic (AFM) Mott insulating phase enveloped by three valence-bond solid-like (VBS-like) insulating phases. Analyzing the single-particle gap, spin gap, and single-particle spectral function, we observe that the metallic state in the noninteracting case becomes unstable under the influence of Hubbard U. This interaction drives the system into a hexagon insulating phase before transitioning into an AFM Mott insulating phase. To quantify the critical exponents, we use finite-size scaling techniques. The critical exponents of quantum critical points between the AFM Mott insulating phase and two insulating phases, plaquette insulator and ethylene insulator, closely align with the 3D O(3) universality class. However, the critical exponents of quantum critical points between the hexagon insulating phase and the AFM Mott insulating phase deviate from the 3D O(3) universality class. This deviation is a finite-size effect and can be attributed to the coupling between the fluctuations of magnetic order parameter and very low-energy fermionic excitations. Our comprehensive study not only advances the understanding of correlation effects on the SHO lattice but also sheds light on the less-explored critical exponents in weakly insulating quantum critical point.

Atomic structure and electronic band structure are fundamental properties for understanding the mechanism of superconductivity. Motivated by the discovery of pressure-induced high-temperature superconductivity at 80 K in the bilayer Ruddlesden-Popper nickelate La3Ni2O7, the atomic structure and electronic band structure of the trilayer nickelate La4Ni3O10 under pressure up to 44.3 GPa are investigated. A structural transition from the monoclinic P21/a space group to the tetragonal I4/mmm around 12.6-13.4 GPa is identified, accompanying with a drop of resistance below 7 K. Density functional theory calculations suggest that the bonding state of Ni 3dz2 orbital rises and crosses the Fermi level at high pressures, which may give rise to possible superconductivity observed in resistance under pressure in La4Ni3O10. The trilayer nickelate La4Ni3O10 shows some similarities with the bilayer La3Ni2O7 and has unique properties, providing a new platform to investigate the underlying mechanism of superconductivity in nickelates., Comment: 19 pages, 4 figures

The disorder operator is often designed to reveal the conformal field theory information in quantum many-body systems. By using large-scale quantum Monte Carlo simulation, we study the scaling behavior of disorder operators on the boundary in the two-dimensional Heisenberg model on the square-octagon lattice with gapless topological edge state. In the Affleck-Kennedy-Lieb-Tasaki phase, the disorder operator is shown to hold the perimeter scaling with a logarithmic term associated with the Luttinger liquid parameter K. This effective Luttinger liquid parameter K reflects the low-energy physics and CFT for (1+1)D boundary. At bulk critical point, the effective K is suppressed but keeps finite value, indicating the coupling between the gapless edge state and bulk fluctuation. The logarithmic term numerically captures this coupling picture, which reveals the (1+1)D SU(2)1 CFT and (2+1)D O(3) CFT at boundary criticality. Our Letter paves a new way to study the exotic boundary state and boundary criticality., Comment: 8 Pages,7 figures

Transition-metal honeycomb compounds are capturing scientific attention due to their distinctive electronic configurations, underscored by the triangular-lattice spin-orbit coupling and competition between multiple interactions, paving the way for potential manifestations of phenomena such as Dirac semimetal, superconductivity, and quantum spin liquid states. These compounds can undergo discernible pressure-induced alterations in their crystallographic and electronic paradigms, as exemplified by our high-pressure (HP) synthesis and exploration of the honeycomb polymorph of ReO3 (P6322). This HP-P6322 polymorph bears a phase transition from P6322 to P63/mmc upon cooling around Tp = 250 K, as evidenced by the evolution of temperature-dependent magnetization (M-T curves), cell dimension, and conductivity initiated by an inherent bifurcation of the oxygen position in the ab plane. Insightful analysis of its band structure positions suggests this HP-P6322 polymorph being a plausible candidate for Dirac semimetal properties. This phase transition evokes anomalies in the temperature-dependent variation of paramagnetism (non-linearity) and a crossover from semiconductor to temperature-independent metal, showing a temperature independent conductivity behavior below ~200 K. Under increasing external pressure, both the Tp and resistance of this HP-polymorph is slightly magnetic-field dependent and undergo a "V"-style evolution (decreasing and then increasing) before becoming pressure independent up to 20.2 GPa. Theoretical calculations pinpoint this anionic disorder as a probable catalyst for the decrement in the conductive efficiency and muted temperature-dependent conductivity response.

Topological superconductors have drawn significant interest from the scientific community due to the accompanying Majorana fermions. Here, we report the discovery of electronic structure and superconductivity in high-entropy ceramics Ti0.2Zr0.2Nb0.2Mo0.2Ta0.2Cx (x = 1 and 0.8) combined with experiments and first-principles calculations. The Ti0.2Zr0.2Nb0.2Mo0.2Ta0.2Cx high-entropy ceramics show bulk type-II superconductivity with Tc about 4.00 K (x = 1) and 2.65 K (x = 0.8), respectively. The specific heat jump is equal to 1.45 (x = 1) and 1.52 (x = 0.8), close to the expected value of 1.43 for the BCS superconductor in the weak coupling limit. The high-pressure resistance measurements show that a robust superconductivity against high physical pressure in Ti0.2Zr0.2Nb0.2Mo0.2Ta0.2C, with a slight Tc variation of 0.3 K within 82.5 GPa. Furthermore, the first-principles calculations indicate that the Dirac-like point exists in the electronic band structures of Ti0.2Zr0.2Nb0.2Mo0.2Ta0.2C, which is potentially a topological superconductor. The Dirac-like point is mainly contributed by the d orbitals of transition metals M and the p orbitals of C. The high-entropy ceramics provide an excellent platform for the fabrication of novel quantum devices, and our study may spark significant future physics investigations in this intriguing material., Comment: 28 pages, 7 figures,The manuscript with the same title will be published by Advanced Science

The pairing symmetry in infinite-layer nickelate superconductors has been an intriguing problem under heated debates. In this work, we study a two-orbital Hubbard model with one strongly correlated $3d$ orbital and one more itinerant $5d$ orbital, by using an eight-site cellular dynamic mean field theory study. We establish a superconducting phase diagram with $d_{x^{2}-y^{2}}$, $s_{\pm}$ and $d+is$ wave pairing symmetries, based on which we clarify the roles of various relevant parameters including hybridization $V$, itinerant carrier density $\langle n_{c}\rangle$ and interaction $U_{c}$. We show that the inclusion of a less correlated $5d$ band in general suppresses the $d_{x^{2}-y^{2}}$ wave pairing. We demonstrate that the $d+is$ wave is maximized when the $5d$ orbital has a large Coulomb repulsion with intermediate hybridization parameter. We perform fluctuation diagnostics to show that the driving force behind the $d_{x^{2}-y^{2}}$ wave is the intraband antiferromagnetic fluctuations in the $3d$ orbital, while for the $s_{\pm}$ wave, the pairing is mainly from the antiferromagnetic correlations residing on the local $3d$-$5d$ bond in real space., Comment: 8 pages, 5 figures

A quadratic band crossing (QBC) is a crossing of two bands with quadratic dispersion, which has been intensively investigated due to its appearance in Bernal-stacked bilayer graphene. Here, we study an extension of QBCs, the triply degenerate quadratic band crossing (TQBC), which is a three-band crossing node containing two quadratic dispersing bands and a flat band. We focus on two types of TQBCs. The first type contains a symmetry-protected QBC and a free-electron band, the prototype of which is the AA-stacked bilayer squareoctagon lattice. In a magnetic field, such a TQBC exhibits an anomalous Landau level structure, leading to a distinctive quantum Hall effect which displays an infinite ladder of Hall plateaus when the chemical potential approaches zero. The other type of TQBC can be viewed as a pseudospin-1 extension of the bilayer-graphene QBC. Under perturbations, this type of TQBCs may split into linear pseudospin-1 Dirac-Weyl fermions. When tunneling through a potential barrier, the transmission probability of the first type decays exponentially with the barrier width for any incident angle, similar to the free-electron case, while the second type hosts an all-angle perfect reflection when the energy of the incident particles is equal to half the barrier height., Comment: 9 pages, 7 figures

The latest discovery of high temperature superconductivity near 80K in La3Ni2O7 under high pressure has attracted much attention. Many proposals are put forth to understand the origin of superconductivity.The determination of electronic structures is a prerequisite to establish theories to understand superconductivity in nickelates but is still lacking. Here we report our direct measurement of the electronic structures of La3Ni2O7 by high-resolution angle resolved photoemission spectroscopy. The Fermi surface and band structures of La3Ni2O7 are observed and compared with the band structure calculations. Strong electron correlations are revealed which are orbital- and momentum dependent. A flat band is formed from the Ni-3dz2 orbitals around the zone corner which is ~50meV below the Fermi level and exhibits the strongest electron correlation. In many theoretical proposals, this band is expected to play the dominant role in generating superconductivity in La3Ni2O7. Our observations provide key experimental information to understand the electronic structure and origin of high temperature superconductivity in La3Ni2O7., Comment: 20 pages, 5 figures

The recently discovered high-T$_C$ superconductor La$_3$Ni$_2$O$_7$ has sparked renewed interest in the unconventional superconductivity. Here we study superconductivity in pressurized La$_3$Ni$_2$O$_7$ based on a bilayer two-orbital $t-J$ model, using the renormalized mean-field theory. Our results reveal a robust $s^\pm-$wave pairing driven by the inter-layer $d_{z^2}$ magnetic coupling, which exhibits a transition temperature within the same order of magnitude as the experimentally observed $T_c \sim 80$ K. We establish a comprehensive superconducting phase diagram in the doping plane. Notably, the La$_3$Ni$_2$O$_7$ under pressure is found situated roughly in the optimal doping regime of the phase diagram. When the $d_{x^2-y^2}$ orbital becomes close to half-filling, $d-$wave and $d+is$ pairing can emerge from the system. We discuss the interplay between Fermi surface topology and different pairing symmetries. The stability of the $s^\pm-$wave pairing against Hund's coupling and other magnetic exchange couplings is discussed., Comment: 9 pages, 6 figures

The ferromagnetic metal-superconductor heterostructure with interface Rashba spin-orbit hopping is a promising candidate for topological superconductivity. We study the interplay between the interface Rashba hopping and the intrinsic Dresselhaus spin-orbit coupling in this heterostructure, and demonstrate rich topological phases with five distinct Chern numbers. In particular, we find a topological state with a Chern number as large as four in the parameter space of the heterostructure. We calculate the Berry curvatures that construct the Chern numbers, and show that these Berry curvatures induce anomalous thermal Hall transport of the superconducting quasiparticles. We reveal chiral edge states in the topological phases, as well as helical edge states in the trivial phase, and show that the wave functions of these edge states mostly concentrate on the ferrometal layer of the heterostructure.

Spin-rotation coupling (SRC) is a fundamental phenomenon that connects electronic spins with the rotational motion of a medium. We elucidate the Einstein-de Haas (EdH) effect and its inverse with SRC as the microscopic mechanism using the dynamic spin-lattice equations derived by elasticity theory and Lagrangian formalism. By applying the coupling equations to an iron disk in a magnetic field, we exhibit the transfer of angular momentum and energy between spins and lattice, with or without damping. The timescale of the angular momentum transfer from spins to the entire lattice is estimated by our theory to be on the order of 0.01 ns, for the disk with a radius of 100 nm. Moreover, we discover a linear relationship between the magnetic field strength and the rotation frequency, which is also enhanced by a higher ratio of Young's modulus to Poisson's coefficient. In the presence of damping, we notice that the spin-lattice relaxation time is nearly inversely proportional to the magnetic field. Our explorations will contribute to a better understanding of the EdH effect and provide valuable insights for magneto-mechanical manufacturing., Comment: 13 pages,6 figures, published to Frontiers of physics

Local constraint in the lattice gauge theory provides an exotic mechanism that facilitates the disorder-free localization. However, the understanding of nonequilibrium dynamics in the non-Hermitian lattice gauge model remains limited. Here, we investigate the quench dynamics in a system of spinless fermions with nonreciprocal hopping in the $\mathbb{Z}_2$ gauge field. By employing a duality mapping, we systematically explore the non-Hermitian skin effect, localization-delocalization transition, and real-complex transition. Through the identification of diverse scaling behaviors of quantum mutual information for fermions and spins, we propose that the non-Hermitian quantum disentangled liquids exist both in the localized and delocalized phases, the former originates from the $\mathbb{Z}_2$ gauge field and the latter arises from the non-Hermitian skin effect. Furthermore, we demonstrate that the nonreciprocal dissipation causes the flow of quantum information. Our results provide valuable insights into the nonequilibrium dynamics in the gauge field, and may be experimentally validated using quantum simulators., Comment: 11+4pages, 6+4 figures; accepted by Communications Physics

We systematically study the effects of higher-order interactions on the S = 3/2, 1 orthogonal dimer chains using exact diagonalization and density matrix renormalization group. Due to frustration and higher spin, there are rich quantum phases, including three Haldane phases, two gapless phases and several magnetically ordered phases. To characterize these phases and their phase transitions, we study various physical quantities such as energy gap, energy level crossing, fidelity susceptibility, spin correlation, entanglement spectrum and central charge. According to our calculations, the biquadratic term can enhance the Haldane phase regions. In particular, we numerically identify that a Haldane phase in S = 3/2 case is adiabatically connected to the exact AKLT point when adding bicubic term. Our study on the orthogonal dimer model, which is a 1D version of Shastry-Sutherland model, provides insights into understanding the possible S = 3/2, 1 Haldane phases in quasi-1D and 2D frustrated magnetic materials., Comment: 14 pages, 17 figures

Recently, a bulk nickelate superconductor $\mathrm{La_3Ni_2O_7}$ is discovered at pressures with a remarkable high transition temperature $T_c \sim 80K$. Here, we study a Hubbard model with tight-binding parameters derived from \textit{ab initio} calculations of $\mathrm{La_3Ni_2O_7}$, by employing large scale determinant quantum Monte Carlo and cellular dynamical mean-field theory. Our result suggests that the superexchange couplings in this system are comparable to that of cuprates. The system is a charge transfer insulator as hole concentration becomes four per site at large Hubbard $U$. Upon hole doping, two low-energy spin-singlet bands emerge in the system exhibiting distinct correlation properties: while the one composed of the out-of-plane Ni-$d_{3z^2-r^2}$ and O-$p_z$ orbitals demonstrates strong antiferromagnetic correlations and narrow effective bandwidth, the in-plane singlet band consisting of the Ni-$d_{x^2-y^2}$ and O-$p_x / p_y$ orbitals is in general more itinerant. Over a broad range of hole doping, the doped holes occupy primarily the $d_{x^2-y^2}$ and $p_x / p_y$ orbitals, whereas the $d_{3z^2-r^2}$ and $p_z$ orbitals retain underdoped. We propose an effective $ t-J$ model to capture the relevant physics and discuss the implications of our result for comprehending the $\mathrm{La_3Ni_2O_7}$ superconductivity., Comment: Hund's coupling is discussed

Presence of multiple competing periodicities may result in a system to go through states with modulated periodicities, an example of which is the self-similar staircase-like structure called the Devil's staircase. Herein we report on a novel staircase structure of domain periodicity in an amorphous and achiral Fe/Gd magnetic thin film wherein the reciprocal space wavevector \textbf{Q} due to the ordered stripe domains does not evolve continuously, rather exhibits a staircase structure. Resonant X-ray scattering experiments show jumps in the periodicity of the stripe domains as a function of an external magnetic field. When resolved in components, the step change along Q$_x$ was found to be an integral multiple of a minimum step height of 7 nm, which resembles closely to the exchange length of the system. Modeling the magnetic texture in the Fe/Gd thin film as an achiral spin arrangement, we have been able to reproduce the steps in the magnetization using a Landau-Lifshitz spin dynamics calculation. Our results indicate that anisotropy and not the dipolar interaction is the dominant cause for the staircase pattern, thereby revealing the effect of achiral magnetism., Comment: 10 pages, 5 figures

The pairing symmetry of superconducting states is a critical topic in the realm of topological superconductivity. However, the pairing symmetry of the $A\mathrm{V_3Sb_5}$ family, wherein $A=\mathrm{K,Rb,Cs}$, remains indeterminate. To address this issue, we formulate an effective model on the kagome lattice to describe topological superconducting states featuring chiral charge density wave. Through this model, we explore the topological phase diagrams and thermal Hall conductivity under various parameters, with and without spin-orbit coupling. Our analysis reveals that the disparities in thermal Hall conductivity curves between different pairing symmetries are safeguarded by the topology resulting from the interplay of spin-orbital coupling and superconducting states. Remarkably, this theoretical prediction can potentially enable the differentiation of various superconducting pairing symmetries in materials via experimental measurements of thermal Hall conductivity curves., Comment: 16 pages, 10 figures

We study topological magnons on an anisotropic square-hexagon-octagon (SHO) lattice which has been found by a two-dimensional Biphenylene network (BPN). We propose the concepts of type-II Dirac magnonic states where new schemes to achieve topological magnons are unfolded without requiring the Dzyaloshinsky-Moriya interactions (DMIs). In the ferromagnetic states, the topological distinctions at the type-II Dirac points along with one-dimensional (1D) closed lines of Dirac magnon nodes are characterized by the $\mathbb{Z}_2$ invariant. We find pair annihilation of the Dirac magnons and use the Wilson loop method to depict the topological protection of the band-degeneracy. The Green's function approach is used to calculte chiral edge modes and magnon density of states (DOS). We introduce the DMIs to gap the type-II Dirac magnon points and demonstrate the Dirac nodal loops (DNLs) are robust against the DMIs within a certain parameter range. The topological phase diagram of magnon bands is given via calculating the Berry curvature and Chern number. We find that the anomalous thermal Hall conductivity gives connection to the magnon edge current. Furthermore, we derive the differential gyromagnetic ratio to exhibit the Einstein-de Haas effect (EdH) of magnons with topological features., Comment: arXiv admin note: text overlap with arXiv:2207.02886

The newly discovered Ruddlesden-Popper bilayer La$_3$Ni$_2$O$_7$ reaches an remarkable superconducting transition temperature $T_c$ = 80 K under a pressure of above 14 GPa. Here we propose a minimal bilayer two-orbital model of the high-pressure phase of La$_3$Ni$_2$O$_7$. Our model is constructed with the Ni-3d$_{x^2-y^2}$, 3d$_{3z^2-r^2}$ orbitals by using Wannier downfolding of the density functional theory calculations, which captures the key ingredients of the material, such as band structure and Fermi surface topology. There are two electron pockets $\alpha$, $\beta$ and one hole pocket $\gamma$ on the Fermi surface, in which the $\alpha$, $\beta$ pockets show mixing of two orbitals, while the $\gamma$ pocket is associated with Ni-d$_{3z^2-r^2}$ orbital. The RPA spin susceptibility reveals a magnetic enhancement associating to the d$_{3z^2-r^2}$ state. A higher energy model with O-p orbitals is also provided for further study.

High-transition-temperature (high-T_c) superconductivity in cuprates has been discovered for more than three decades, but the underlying mechanism remains a mystery. Cuprates are the only unconventional superconducting family that host bulk superconductivity with T_cs above the liquid nitrogen boiling temperature at 77 Kelvin. Here we report an observation of superconductivity in single crystals of La3Ni2O7 with a maximum T_c of 80 Kelvin at pressures between 14.0-43.5 gigapascals using high-pressure resistance and mutual inductive magnetic susceptibility measurements. The superconducting phase under high pressure exhibits an orthorhombic structure of Fmmm space group with the 3d_(x^2-y^2 ) and 3d_(z^2 ) orbitals of Ni cations strongly interacting with oxygen 2p orbitals. Our density functional theory calculations suggest the superconductivity emerges coincidently with the metallization of the {\sigma}-bonding bands under the Fermi level, consisting of the 3d_(z^2 ) orbitals with the apical oxygens connecting Ni-O bilayers. Thus, our discoveries not only reveal important clues for the high-T_c superconductivity in this Ruddlesden-Popper double-layered perovskite nickelates but also provide a new family of compounds to investigate the high-T_c superconductivity mechanism., Comment: 15 pages with extended data

Recently, there has been a rapidly growing interest in two-dimensional (2D) transition metal chalcogenide monolayers (MLs) due to their unique magnetic and electronic properties. By using an evolutionary algorithm and first-principles calculations, we report the discovery of a previously unexplored, chemically, energetically, and thermodynamically stable 2D antiferromagnetic (AFM) CrSe ML with a N\'eel temperature higher than room temperature. Remarkably, we predict an electric field-controllable metal-insulator transition (MIT) in a van der Waals (vdW) heterostructure comprised of CrSe ML and ferroelectric Sc2CO2. This tunable transition in CrSe/Sc2CO2 heterostructure is attributed to the change in the band alignment between CrSe and Sc2CO2 caused by the ferroelectric polarization reversal in Sc2CO2. Our findings suggest that 2D AFM CrSe ML has important potential applications in AFM spintronics, particularly in the gate voltage conducting channel., Comment: 13 Pages, 4 Figures, published at Applied Physics Letters

The sawtooth lattice shares some structural similarities with the kagome lattice and may attract renewed research interest. Here, we report a comprehensive study on the physical properties of Fe$_2$SiSe$_4$, an unexplored member in the olivine chalcogenides with the sawtooth lattice of Fe. Our results show that Fe$_2$SiSe$_4$ is a magnetic semiconductor with band gap of 0.66~eV. It first undergoes an antiferromagnetic transition at T$_{m1}$=110~K, then an ferrimagnetic-like one at T$_{m2}$=50~K and finally a magnetic transition at T$_{m3}$=25~K which is likely driven by the thermal populations of spin-orbit manifold on the Fe site. Neutron diffraction analysis reveals a non-collinear antiferromagnetic structure with propagation vector $\mathbf{q_1}$=(0,0,0) at T$_{m2}$

Tuning the Gilbert damping of ferromagnetic (FM) metals via a nonvolatile way is of importance to exploit and design next-generation novel spintronic devices. Through systematical first-principles calculations, we study the magnetic properties of the van der Waals heterostructure of two-dimensional FM metal CrTe2 and ferroelectric (FE) In2Te3 monolayers. The ferromagnetism of CrTe2 is maintained in CrTe2/In2Te3 and its magnetic easy axis can be switched from in-plane to out-of-plane by reversing the FE polarization of In2Te3. Excitingly, we find that the Gilbert damping of CrTe2 is tunable when the FE polarization of In2Te3 is reversed from upward to downward. By analyzing the k-dependent contributions to the Gilbert damping, we unravel that such tunability results from the changed intersections between the bands of CrTe2 and Fermi level on the reversal of the FE polarizations of In2Te3 in CrTe2/In2Te3. Our work provides an appealing way to electrically tailor Gilbert dampings of two-dimensional FM metals by contacting them with ferroelectrics., Comment: 4 Figures, accepted by Applied Physics Letters

The Li-Haldane conjecture is one of the most famous conjectures in physics and opens a new research area in the quantum entanglement and topological phase. Although a lot of theoretical and numerical works have confirmed the conjecture in topological states with bulk-boundary correspondence, the cases with gapped boundary and the systems in high dimension are widely unknown. What is the valid scope of the Li-Haldane conjecture? Via the newly developed quantum Monte Carlo scheme, we are now able to extract the large-scale entanglement spectrum (ES) and study its relation with the edge energy spectrum generally. Taking the two-dimensional Affleck-Kennedy-Lieb-Tasaki model with a tunable boundary on the square-octagon lattice as an example, we find several counterexamples which cannot be explained by the Li-Haldane conjecture; e.g., the low-lying entanglement spectrum does not always show similar behaviors as the energy spectrum on the virtual boundary, and sometimes the ES resembles the energy spectrum of the edge even if it is gapped. Finally, we demonstrate that the newly proposed wormhole mechanism on the path integral of a reduced density matrix is the formation principle of the general ES. We find that the Li-Haldane conjecture is a particular case in some limit of the wormhole picture while all the examples of the conjecture we have studied can totally be explained within the wormhole mechanism framework. Our results provide important evidence for demonstrating that the wormhole mechanism is the fundamental principle to explain the ES., Comment: 11 pages, 11 figures

We investigate the experimental signatures of Raman spectroscopy of bi- and tri-magnon excitations in the distorted triangular lattice antiferromagnets alpha-LCr2O4 (L=Sr, Ca). We utilize spin wave theory to analyze the nearly 120 degree spin-3/2 spiral ordered antiferromagnetic ground state to compute the single-magnon density of states, single-magnon dispersion, and bimagnon and trimagnon Raman spectra (polarized and unpolarized). It is found that Raman scattering is capable of capturing the effect of the rotonlike M and M' points on the bimagnon Raman spectrum. Our calculation confirms the connection between single-magnon rotonlike excitation energy and bimagnon Raman excitation spectrum observed experimentally. The roton energy minimum in momentum space is half of the energy of a bimagnon excitation signal. The experimental magnetic Raman scattering result displays two peaks which have a Raman shift of 15 meV and 40 meV, respectively. Theoretical modeling and analysis of the experimental spectrum of alpha-SrCr2O4 within our distorted Heisenberg Hamiltonian lattice suggests that the low-energy peak at 15 meV is associated with the bimagnon excitation, whereas the high-energy peak around 40 meV is primarily a trimagnon excitation. Based on our fitting procedure we propose a new set of magnetic interaction parameters for alpha-SrCr2O4. These parameters reproduce not only the experimental Raman spectrum, but also the inelastic neutron scattering response (including capturing high energy magnon branches). We also compute the unpolarized bimagnon and trimagnon Raman spectra for alpha-CaCr2O4. Furhtermore, we found that the polarization sensitivity of Raman spectrum can be utilized to distinguish the bi- and tri-magnon excitation channels., Comment: 11 pages, 4 figures

NiPSe3 is regarded as a bandwidth-controlled Mott insulator, distinct from the widely studied Mott insulating magnetic graphene MPSe3 (M = Mn and Fe) family. By employing high-pressure synchrotron X-ray diffraction, we observe two structural transitions as a function of pressure. With the help of first-principles calculations, we discover the antiferromagnetic (AFM) moment directions of NiPSe3 switch from out-of-plane to in-plane and the honeycomb layers slide relative to each other at the first structural transition. The in-plane AFM order persists until the second structural transition, whereupon the two-dimensional (2D) structure assumes a more three-dimensional (3D) character. A bandwidth-controlled Mott insulator-metal transition (IMT) occurs between the two structural transitions at 8.0 GPa, concomitant with the emergence of superconductivity with 4.8 K. The superconductivity in NiPSe3 emerging in the 2D monoclinic phase coexists with the in-plane AFM order and continues into the 3D trigonal phase. Our electronic structure calculations reveal that the Mott IMT and superconductivity in NiPSe3 are both closely related to the enhanced Se2- 4p and Ni2+ 3d electronic hybridizations under pressure. From these results, we construct the temperature-pressure electronic phase diagram of NiPSe3, revealing rich physics and many similarities with copper oxide and iron-based superconductors., Comment: 15 pages with supplementary files

Recent experimental work shows that FePS$_3$ undergoes phase transitions from $C2/m$ ($\beta\sim107^{\circ}$) to $C2/m$ ($\beta\sim90^{\circ}$) at $6$ GPa and then to metallic $P\bar{3}1m$ at $14$ GPa, with the magnetic ordering wave vector turning from $k=(01\frac{1}{2})$ to $k=(010)$ at $2$ GPa and to short-range magnetic order accompanying the insulator-metal transition. By preserving the magnetic point groups in $ab \ initio$ calculations we report the following: (1) We successfully reproduce the first magnetic structure transition at $1.2$ GPa and briefly discuss the influence of the Hubbard U parameter on this transition. This isostructural transition causes a change of the Brillouin zone from base-centered monoclinic to primitive monoclinic, and an indrect band gap to direct band gap transition. (2) There is a rotation of the Fe-S octahedron about $0.5^\circ$ through the $[001]$ axis before the neighboring layers shift. (3) The shift between neighboring layers is predicted to occur at $10.0$ GPa and reverses the energy order between $d_{x^2-y^2}$ and $d_{xy}$. (4) A sudden decrease of Fe-S bond length to $2.20$ \AA \ accompanies the vanishing of magnetic moment in the insulator-metal transition. Our work shows the importance of symmetries of magnetic structures in pressure-induced phase transition of magnetic systems.