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Motivated by recent experimental evidences signalling the chiral charge order in the vanadium-based kagome superconductors, we theoretically investigate the impact of the chiral flux charge order over the experimental outcomes for the normal and the SC properties. It is revealed that the spectral weight on the Fermi surface (FS) is partially gaped by the chiral flux charge order with the reservation of the spectral weight on the $M$ points and the midpoint between the two adjacent $M$ points, resulting in the momentum-dependent energy gap being consistent with the recent experimental observations. More importantly, by considering the influence of the chiral flux charge order, we find that a conventional fully gapped SC pairing state evolves into a nodal gap feature for the spectral weight due to the spectral gap modulations on the FS. As a result, the U-shaped density of states (DOS) deforms to the V-shaped one along with the residual DOS near the Fermi energy. These results bear some resemblance to the experimental observations, and may serve as a promising proposal to mediate the divergent or seemingly contradictory experimental outcomes about the SC pairing symmetry.

We employ the fluctuation-exchange approximation to study the relation of superconducting pairing symmetries and density-wave fluctuations based on the extended triangular Hubbard model upon electron doping and interactions, with an possible application to the layered metal dichalcogenide SnSe

Excitons in solid state are bosons generated by electron-hole pairs as the Coulomb screening is sufficiently reduced. The exciton condensation can result in exotic physics such as super-fluidity and insulating state. In charge density wave (CDW) state, 1T-TiSe2 is one of the candidates that may host the exciton condensation. However, to envision its excitonic effect is still challenging, particularly at the two-dimensional limit, which is applicable to future devices. Here, we realize the epitaxial 1T-TiSe2 bilayer, the two-dimensional limit for its 2 × 2 × 2 CDW order, to explore the exciton-associated effect. By means of high-resolution scanning tunneling spectroscopy and quasiparticle interference, we discover an unexpected state residing below the conduction band and right within the CDW gap region. As corroborated by our theoretical analysis, this mysterious phenomenon is in good agreement with the electron-exciton coupling. Our study provides a material platform to explore exciton-based electronics and opto-electronics.

Starting from a tight-binding model on the kagome lattice near the van Hove filling, the superconducting (SC) properties are investigated self-consistently using the Bogoliubov-de Gennes equation with the consideration of the inequivalent third-neighbor (TN) bonds. Near the van Hove filling, the most favorable SC pairings are found to derive from the electrons belonging to the same sublattice sites, including the on-site $s$-wave and the spin-singlet/triplet TN pairings. The inequivalent TN bonds will result in multiple SC components with different orbital angular momentums (OAM) for the TN SC pairings. While the density of states (DOS) and the temperature ($T$) dependence of the spin-lattice relaxation rate ($T^{-1}_{1}$) exhibit distinct line shapes in the SC state for the three cases, a peak structure in the $T$ dependence of $T^{-1}_{1}$ can be found for both cases just below $T_{c}$ as a result of the van Hove singularity, even though the SC gap has nodes. The effects of magnetic vortices on the low energy excitations and on the $T$ dependence of $T^{-1}_{1}$ with the implications of the results are also discussed for both cases., 9 pages, 4 figures, 2 tables

$\alpha$-RuCl$_3$ has been studied extensively because of its proximity to the Kitaev quantum-spin-liquid (QSL) phase and the possibility of approaching it by tuning the competing interactions. Here we present the first polarized inelastic neutron scattering study on $\alpha$-RuCl$_3$ single crystals to explore the scattering continuum around the $\Gamma$ point at the Brillouin zone center, which was hypothesized to be resulting from the Kitaev QSL state but without concrete evidence. With polarization analyses, we find that while the spin-wave excitations around the M point vanish above the transition temperature $T_{\rm N}$, the pure magnetic continuous excitations around the $\Gamma$ point are robust against temperature. Furthermore, by calculating the dynamical spin-spin correlation function using the cluster perturbation theory, we derive magnetic dispersion spectra based on the $K$-$\Gamma$ model, which involves with a ferromagnetic Kitaev interaction of -7.2 meV and an off-diagonal interaction of 5.6 meV. We find this model can reproduce not only the spin-wave excitation spectra around the M point, but also the non-spin-wave continuous magnetic excitations around the $\Gamma$ point. These results provide evidence for the existence of fractional excitations around the $\Gamma$ point originating from the Kitaev QSL state, and further support the validity of the $K$-$\Gamma$ model as the effective minimal spin model to describe $\alpha$-RuCl$_3$., Comment: Published in Chinese Physics Letters as Express Letter, 8 pages, 4 figures

Disorder is important in the study of quantum spin liquids, but its role on the spin dynamics remains elusive. Here, we explore the disorder effect by investigating the magnetic-field dependence of the low-energy magnetic excitations in a triangular-lattice frustrated magnet YbZnGaO$_4$ with inelastic neutron scattering. With an intermediate field of 2.5 T applied along the $c$-axis, the broad continuum at zero field becomes more smeared both in energy and momentum. With a field up to 10 T, which fully polarizes the magnetic moments, we observe clear spin-wave excitations with a gap of $\sim$1.4 meV comparable to the bandwidth. However, the spectra are significantly broadened. The excitation spectra both at zero and high fields can be reproduced by performing classical Monte Carlo simulations which take into account the disorder effect arising from the random site mixing of nonmagnetic Zn$^{2+}$ and Ga$^{3+}$ ions. These results elucidate the critical role of disorder in broadening the magnetic excitation spectra and mimicking the spin-liquid features in frustrated quantum magnets., Comment: Published in PRB, 10 pages, 3 figures

Spontaneous orbital symmetry breaking in crystals gives rise to abundant novel and interesting physical properties, which sometimes are concealed by the absence of geometrical distortions. We show that a recently discovered 3d2 system, namely the layered VI3 ferromagnetic semiconductor, is a strongly correlated and orbital ordering system. Our analysis reveals that in a VI3-like system, there could be two types of orbital splitting, which are stabilized respectively by strong electronic correlation and inter-atomic exchange interactions. Consequently, on the basis of first-principles calculations, two competing low-energy phases of VI3 monolayer (denoted as twin orbital-order phases) are discovered, in which the metal–insulator transition is driven by strong electronic correlation, and the orbital symmetry breaking is robust against geometrical distortions. In addition, similar phenomena are also observed in other VI3-like systems. These findings shed light on the unusual electronic behavior of a strongly correlated 2D system and will be interesting for nanoscale multi-functional spintronic applications.

Topological magnons are bosonic analogues of topological fermions in electronic systems. They have been studied extensively by theory but rarely realized by experiment. Here, by performing inelastic neutron scattering measurements on single crystals of a two-dimensional ferromagnet CrBr$_3$, which was classified as Dirac magnon semimetal featured by the linear bands crossing at the Dirac points, we fully map out the magnetic excitation spectra, and reveal that there is an apparent gap of $\sim$3.5~meV between the acoustic and optical branches of the magnons at the K point. By collaborative efforts between experiment and theoretical calculations using a five-orbital Hubbard model obtained from first-principles calculations to derive the exchange parameters, we find that a Hamiltonian with Heisenberg exchange interactions, next-nearest-neighbor Dzyaloshinskii-Moriya (DM) interaction, and single-ion anisotropy is more appropriate to describe the system. Calculations using the model show that the lower and upper magnon bands separated by the gap exhibit Chern numbers of $\pm1$. These results indicate that CrBr$_3$ is a topological magnon insulator, where the nontrivial gap is a result of the DM interaction., Version as published in PRB Letter, main text 7 pages, supplementary materials 6 pages

The celebrated Kitaev honeycomb model provides an analytically tractable example with an exact quantum spin liquid ground state. While in real materials, other types of interactions besides the Kitaev coupling ($K$) are present, such as Heisenberg ($J$) and symmetric off-diagonal ($\mathrm{\ensuremath{\Gamma}}$) terms, these interactions can also be generalized to a triangular lattice. Here, we carry out a comprehensive study of the $J\ensuremath{-}K\ensuremath{-}\mathrm{\ensuremath{\Gamma}}$ model on a triangular lattice covering the whole parameter region, using a combination of exact diagonalization, classical Monte Carlo, and analytic methods, with an emphasis on the effects of the $\mathrm{\ensuremath{\Gamma}}$ term. In the HK limit ($\mathrm{\ensuremath{\Gamma}}=0$), we find five quantum phases which are quite similar to their classical counterparts. Among them, stripe-A and dual N\'eel phases are robust against the introduction of the $\mathrm{\ensuremath{\Gamma}}$ term, in particular, stripe A extends to the region connecting $K=\ensuremath{-}1$ and $K=1$ for $\mathrm{\ensuremath{\Gamma}}l0$. Though the ${120}^{\ensuremath{\circ}}$ N\'eel phase also extends to a finite $\mathrm{\ensuremath{\Gamma}}$, its region is largely reduced compared to the previous classical result. Interestingly, the ferromagnetic (dubbed FM-A) and stripe-B phases are unstable in response to an infinitesimal $\mathrm{\ensuremath{\Gamma}}$ interaction. Moreover, we find five additional phases for $\mathrm{\ensuremath{\Gamma}}\ensuremath{\ne}0$ which are elaborated by both the quantum and classical numerical methods. Part of the parameter space previously identified as the ${120}^{\ensuremath{\circ}}$ N\'eel phase in the classical study is found to give way to the modulated stripe phase. Depending on the sign of the $\mathrm{\ensuremath{\Gamma}}$ term, the FM-A phase transits into FM-B ($\mathrm{\ensuremath{\Gamma}}g0$) and FM-C ($\mathrm{\ensuremath{\Gamma}}l0$) phases with different spin orientations. Similarly, the stripe-B phase transits into stripe-C ($\mathrm{\ensuremath{\Gamma}}g0$) and stripe-A ($\mathrm{\ensuremath{\Gamma}}l0$) phases. Around the positive $\mathrm{\ensuremath{\Gamma}}$ point, due to the interplay of the Heisenberg, Kitaev, and $\mathrm{\ensuremath{\Gamma}}$ interactions, we find a possible quantum spin liquid in a noticeable region with a continuum in spin excitations.

The elementary excitations from the conventional magnetic ordered states, such as ferromagnets and antiferromagnets, are magnons. Here, we elaborate a case where the well-defined magnons are absent completely and the spin excitation spectra exhibit an entire continuum in the itinerant edge ferromagnetic state of graphene arising from the flatband edge electronic states. Based on the further studies of the entanglement entropy and finite-size analysis, we show that the continuum other than the Stoner part results from the spin-1/2 spinons deconfined from magnons. The spinon continuum in a magnetically ordered state is ascribed to a ferromagnetic Luttinger liquid in this edge ferromagnet. The investigation is carried out by using the numerical exact diagonalization method with a projection of the interacting Hamiltonian onto the flat band., 7 pages, 7 figures

We perform thermodynamic and inelastic neutron scattering (INS) measurements to study the lattice dynamics (phonons) of a cubic collinear antiferromagnet Cu$_3$TeO$_6$ which hosts topological spin excitations (magnons). While the specific heat and thermal conductivity results show that the thermal transport is dominated by phonons, the deviation of the thermal conductivity from a pure phononic model indicates that there is a strong coupling between magnons and phonons. In the INS measurements, we find a mode in the excitation spectra at 4.5 K, which exhibits a slight downward dispersion around the Brillouin zone center. This mode disappears above the N\'{e}el temperature, and thus cannot be a phonon. Furthermore, the dispersion is distinct from that of a magnon. Instead, it can be explained by the magnon-polaron mode, which is new collective excitations resulting from the hybridization between magnons and phonons. We consider the suppression of the thermal conductivity and emergence of the magnon-polaron mode to be evidence for magnon-phonon coupling in Cu$_3$TeO$_6$., Comment: 9 pages, 4 figures, formula Cu3TeO6 updated in the title and abstract

The quasiparticle spectra of interacting Weyl and nodal-line semimetals on a cubic lattice are studied using the cluster perturbation theory. By tracking the spectral functions under interaction, we find that the Weyl points will move to and meet at a specific point in one Weyl semimetal model, while in the other Weyl semimetal model they are immobile. In the nodal-line semimetals, we find that the nodal line shrinks to a point and then disappears under interaction in one-nodal-line system. When we add another nodal line to this system, we find that the two nodal lines both shrink to specific points, but the disappearing processes of the two nodal lines are not synchronized. We argue that the nontrivial evolution of Weyl points and nodal lines under interaction is due to the presence of symmetry breaking order, e.g., a ferromagnetic moment, in the framework of mean field theory, whereas the stability of Weyl points under interaction is protected by symmetry. Among all these models, the spectral gap is finally opened when the interaction is strong enough., 9 pages,5 figures

Dirac matters provide a platform for exploring the interplay of their carriers with other quantum phenomena. ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{1\ensuremath{-}y}{\mathrm{Sb}}_{2}$ has been proposed to be a magnetic Weyl semimetal and provides an excellent platform to study the coupling between Weyl fermions and magnons. Here, we report comprehensive inelastic neutron scattering (INS) measurements on single crystals of ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{1\ensuremath{-}y}{\mathrm{Sb}}_{2}$, which have been well characterized by magnetization and magnetotransport measurements, both of which demonstrate that the material is a topologically nontrivial semimetal. The INS spectra clearly show a spin gap of $\ensuremath{\sim}6$ meV. The dispersion in the magnetic Mn layer extends up to about 76 meV, while that between the layers has a narrow band width of 6 meV. We find that the linear spin-wave theory using a Heisenberg spin Hamiltonian can reproduce the experimental spectra with the following parameters: a nearest-neighbor ($S{J}_{1}\ensuremath{\sim}28.0$ meV) and next-nearest-neighbor in-plane exchange interaction ($S{J}_{2}\ensuremath{\sim}9.3$ meV), interlayer exchange coupling ($S{J}_{c}\ensuremath{\sim}\ensuremath{-}0.1$ meV), and spin anisotropy constant ($SD\ensuremath{\sim}\ensuremath{-}0.07$ meV). Despite the coexistence of Weyl fermions and magnons, we find no clear evidence that the magnetic dynamics are influenced by the Weyl fermions in ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{1\ensuremath{-}y}{\mathrm{Sb}}_{2}$, possibly because that the Weyl fermions and magnons reside in the Sb and Mn layers separately, and the interlayer coupling is weak due to the quasi-two-dimensional nature of the material, as also evident from the small $S{J}_{c}$ of $\ensuremath{-}0.1$ meV.

To compare the clinical characteristics of simple testicular yolk sac tumor (YST) in children with those in adults so as to improve the diagnosis and treatment of the malignance.This study included 75 cases of simple testicular YST pathologically confirmed between May 2008 and July 2018, which were divided into groups A (aged18 years, n = 64) and B (aged ≥18 years, n = 11). We analyzed the clinical data on all the cases and compared the clinical manifestations, laboratory results, pathological findings, clinical stages, treatment methods and prognostic outcomes between the two groups of patients.The patients of group A ranged in age from 6 months to 5 years (［1.38 ± 0.89］ yr), with the tumor diameter of 0.9－6.0 (2.48 ± 1.12) cm, while those of group B from 25 to 49 years (median 34 years), with the tumor diameter of 3.5－6.3 (5.16 ± 1.32) cm, most presenting with a painless scrotal mass, 4 (6.2%) in group A and 5 (45.5%) in group B with testis pain. There were statistically significant differences between the two groups in the tumor diameter and initial manifestations (P0.05). All the patients were treated by radical high-level spermatectomy and orchiectomy and, in addition, 1 in group A and 3 in group B by retroperitoneal lymph node dissection (RPLND), 24 in the former and 5 in the latter group followed by chemotherapy. Elevated levels of serum alpha-fetoprotein (AFP) were observed in all the cases. Sixty-five of the patients were followed up for 10－78 (52.00 ± 23.78) months, during which 2 cases of simple metastasis, 3 cases of simple relapse, 3 cases of relapse with metastasis and 5 cases of death were found in group A, and 5 cases of simple metastasis, 1 case of simple relapse, 1 case of relapse with metastasis and 4 cases of death in group B.There are significant differences in the clinical manifestation, biological behavior, treatment and prognosis of testicular YST between children and adults. In children, most of the testicular YST cases are at clinical stage I and preferably treated by radical high-level spermatectomy and orchiectomy with favorable prognosis. In adults, however, the tumor is highly malignant, with high incidences of recurrence and metastasis and poor prognosis, for the treatment of which the first choice is radical high-level spermatectomy and orchiectomy combined with RPLND and chemotherapy.

Motivated by the recent measurements of the spatial distribution of single particle excitation states in a hole-doped Mott insulator, we study the effects of impurity on the in-gap states, induced by the doped holes, in the Hubbard model on the square lattice by the cluster perturbation theory. We find that a repulsive impurity potential can move the in-gap state from the lower Hubbard band towards the upper Hubbard band, providing a good account for the experimental observation. The distribution of the spectral function in the momentum space can be used to discriminate the in-gap state induced by doped holes and that by the impurity. The spatial characters of the in-gap states in the presence of two impurities are also discussed and compared to the experiment.

Quantum interference and traditional domain wall effects are two common ways to manipulate the magnetism in magnetic materials. Here, we report both effects emerge in the designed graphene nanodisks simultaneously, and thus providing an accessible way to engineer the magnetism in graphene nanostructures. By adjusting the length of the armchair edges at the corners of hexagonal disk, connecting the adjacent zigzag edges, we show that the quantum interference among the zigzag edges remains robust and consequently determines the magnetic structure in the small-size systems, in analogy with the nanoribbons. More importantly, a domain–wall-like magnetic mechanism is numerically identified to dominate the larger-size disks. In particular, a magnetic state with fully spin-polarized edges achieved in a wide parameter region promises the future applications for spintronics.

Kitaev quantum spin liquids described by the Kitaev model represent an exotic state of matter with long-range entangled spins and topological order, which hold promise for quantum computation. $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, a material with van der Waals layered structure, is shown to be proximate to such a state recently. Here we report Raman spectroscopy of atomically thin $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. New phonon modes emerge at low temperature, signifying a phase transition to a crystal structure with lowered symmetry. The Fano line shape of two low-energy phonon modes and the magnetic scattering continuum in bulk $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, which evidence fractionalized Majorana fermions of the proximate quantum spin liquid, persist to the trilayer. Polarization-dependent measurements reveal increased anisotropy of the Kitaev exchange constants when approaching the two-dimensional limit. Our results demonstrate an intimate relation between the crystal structure and the symmetry of the proximate quantum spin liquid ground state.

Quantum spin liquids (QSLs) are an exotic state of matter that is subject to extensive research. However, the relationship between the ubiquitous disorder and the QSL behaviors is still unclear. Here, by performing comparative experimental studies on two kagom\'{e}-lattice QSL candidates, Tm$_3$Sb$_3$Zn$_2$O$_{14}$ and Tm$_3$Sb$_3$Mg$_2$O$_{14}$, which are isostructural to each other but with strong and weak structural disorder, respectively, we show unambiguously that the disorder can induce spin-liquid-like features. In particular, both compounds show dominant antiferromagnetic interactions with a Curie-Weiss temperature of -17.4 and -28.7 K for Tm$_3$Sb$_3$Zn$_2$O$_{14}$ and Tm$_3$Sb$_3$Mg$_2$O$_{14}$, respectively, but remain disordered down to about 0.05 K. Specific heat results suggest the presence of gapless magnetic excitations characterized by a residual linear term. Magnetic excitation spectra obtained by inelastic neutron scattering (INS) at low temperatures display broad continua. All these observations are consistent with those of a QSL. However, we find in Tm$_3$Sb$_3$Zn$_2$O$_{14}$ which has strong disorder resulting from the random mixing of the magnetic Tm$^{3+}$ and nonmagnetic Zn$^{2+}$, that the low-energy magnetic excitations observed in the specific heat and INS measurements are substantially enhanced, compared to those of Tm$_3$Sb$_3$Mg$_2$O$_{14}$ which has much less disorder. We believe that the effective spins of the Tm$^{3+}$ ions in the Zn$^{2+}$/Mg$^{2+}$ sites give rise to the low-energy magnetic excitations, and the amount of the random occupancy determines the excitation strength. These results provide direct evidence of the mimicry of a QSL caused by disorder., Comment: Version as published in PRB, 5 figures, 11 pages

Metallization of 1T-TaS_{2} is generally initiated at the domain boundary of a charge density wave (CDW), at the expense of its long-range order. However, we demonstrate in this study that the metallization of 1T-TaS_{2} can be also realized without breaking the long-range CDW order upon surface alkali doping. By using scanning tunneling microscopy, we find the long-range CDW order is always persisting, and the metallization is instead associated with additional in-gap excitations. Interestingly, the in-gap excitation is near the top of the lower Hubbard band, in contrast to a conventional electron-doped Mott insulator where it is beneath the upper Hubbard band. In combination with the numerical calculations, we suggest that the appearance of the in-gap excitations near the lower Hubbard band is mainly due to the effectively reduced on-site Coulomb energy by the adsorbed alkali ions.

In condensed matter physics, there is a novel phase termed "quantum spin liquid", in which strong quantum fluctuations prevent the long-range magnetic order from being established, and so the electron spins do not form an ordered pattern but remain "liquid" like even at absolute zero temperature. Such a phase is not involved with any spontaneous symmetry breaking and local order parameter, and to understand it is beyond the conventional phase transition theory. Due to the rich physics and exotic properties of quantum spin liquids, such as the long-range entanglement and fractional quantum excitations, which are believed to hold great potentials in quantum communication and computation, they have been intensively studied since the concept was proposed in 1973 by P. W. Anderson. Currently, experimental identifications of a quantum spin liquid still remain as a great challenge. Here, we highlight some interesting experimental progress that has been made recently. We also discuss some outstanding issues and raise questions that we consider to be important for future research., Comment: A short review paper published in npj Quantum Materials. Due to the limitation on the number of references, we are very unfortunate to miss many excellent ones

The confinement and deconfinement of spinons in the square-lattice antiferromagnetic ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model are elaborated by exploring the evolution of the whole excitation spectra with ${J}_{2}$, based on the spin cluster perturbation theory. We find that deconfined spin-$1/2$ spinons beyond the conventional spin-1 magnons have already emerged partially even in the limit ${J}_{2}=0$ and develop with ${J}_{2}$, exhibiting as a continuum close to $(\ensuremath{\pi},0)$ in the Brillouin zone. In the region near ${J}_{2}=0.5{J}_{1}$, the entire spectrum is characterized by a broad continuum in which all magnons are deconfined into spinons, whose ground state is attributed to a ${Z}_{2}$ quantum spin liquid with the aid of a variational-Monte-Carlo analysis. The spinon continua are also found in the stripe phase with ${J}_{2}g0.6{J}_{1}$. Our study provides spectroscopic evidences for the fractionalized excitations and quantum spin liquid and highlights the rising field to explore the exotic quantum phases from a perspective of excitation spectrum.

The magnetic properties of 4d and 5d transition-metal insulating compounds with the honeycomb structure are believed to be described by the Heisenberg-Kitaev model, which contains both the isotropic Heisenberg interaction J and anisotropic Kitaev interaction K. In this paper, to investigate the charge dynamics in these materials, we study the single-hole propagation of the t-J-K model in various magnetically ordered phases by the self-consistent Born approximation. We find that there are low-energy coherent quasiparticle (QP) excitations in all of these phases which appear firstly around the K point in the Brillouin zone (BZ), but the band-widths of these QPs are very small due to the hole-magnon coupling. Interestingly, in the zigzag phase relevant to recent experiments, though the QP weights are largely suppressed in the physical spectra in the first BZ, we find that they recover in the extended BZs. Moreover, our results reveal that the low-energy QP spectra are reduced with the increase of K., 9 pages, 5 figures

We study the spin-1 excitation spectra of the flatband ferromagnetic phases in interacting topological insulators. As a paradigm, we consider a quarter filled square lattice Hubbard model whose free part is the $\pi$ flux state with topologically nontrivial and nearly-flat electron bands, which can realize either the Chern or $Z_2$ Hubbard model. By using the numerical exact diagonalization method with a projection onto the nearly-flat band, we obtain the ferromagnetic spin-1 excitation spectra for both the Chern and $Z_2$ Hubbard models, consisting of spin waves and Stoner continuum. The spectra exhibit quite distinct dispersions for both cases, in particular the spin wave is gapless for the Chern Hubbard model, while gapped for the $Z_2$ Hubbard model. Remarkably, in both cases, the nonflatness of the free electron bands introduces dips in the lower boundary of the Stoner continuum. It significantly renormalizes the energies of the spin waves around these dips downward and leads to roton-like spin excitations. We elaborate that it is the softening of the roton-like modes that destabilizes the ferromagnetic phase, and determine the parameter region where the ferromagnetic phase is stable., Comment: Accepted by PRB

To study exotic excitations described by parafermions in the possible spin liquid states of SU($n$) spin systems, we introduce a parafermion parton approach. The SU($n$) spin operators can be represented by clock and shift matrices, which are shown to be the polynomials of parafermion operators in the parafermion representation. We find that SU($n$) spins can be decomposed into $n$ parafermion matrices of degree one. In this decomposition, the spin has a $\{\bigotimes{\rm SU}(n)\}^{n-1}$ gauge symmetry. As an application, we study the one-dimensional three-state clock model and generalized Kitaev model by a mean-field theory, both of them have been proved to be related to parafermion excitations. We find that with the symmetries of translations, $6$-fold rotation and combination of parity and time reversal, there are $9$ types and $102$ solutions for two-dimensional $Z_3$ parafermion spin liquids on the honeycomb lattice. On the contrast, there are $9$ types and $36$ solutions if both parity and time-reversal symmetries are present. Our results provide a novel route for the systematic search of new types of spin liquids with exotic anyon excitations., 13 pages, 1 figures

We study spin-wave excitations in $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$ by the spin-wave theory. Starting from the five-orbital Hubbard model and the perturbation theory, we derive an effective isospin-$1/2$ model in the large Hubbard ($U$) limit. Based on the energy-band structure calculated from the first-principles method, we find that the effective model can be further reduced to the $K\ensuremath{-}\mathrm{\ensuremath{\Gamma}}$ model containing a ferromagnetic nearest-neighbor (NN) Kitaev interaction ($K$) and a NN off-diagonal exchange interaction ($\mathrm{\ensuremath{\Gamma}}$). With the spin-wave theory, we find that the $K\ensuremath{-}\mathrm{\ensuremath{\Gamma}}$ model can give magnetic excitations, which is consistent with recent neutron-scattering experiments.

We report on comprehensive results identifying the ground state of a triangular-lattice structured YbZnGaO$_4$ to be spin glass, including no long-range magnetic order, prominent broad excitation continua, and absence of magnetic thermal conductivity. More crucially, from the ultralow-temperature a.c. susceptibility measurements, we unambiguously observe frequency-dependent peaks around 0.1 K, indicating the spin-glass ground state. We suggest this conclusion to hold also for its sister compound YbMgGaO$_4$, which is confirmed by the observation of spin freezing at low temperatures. We consider disorder and frustration to be the main driving force for the spin-glass phase., Version as accepted to PRL

Quantum confinement and interference often generate exotic properties in nanostructures. One recent highlight is the experimental indication of a magnetic phase transition in zigzag-edged graphene nanoribbons at the critical ribbon width of about 7 nm [G. Z. Magda et al., Nature \textbf{514}, 608 (2014)]. Here we show theoretically that with further increase in the ribbon width, the magnetic correlation of the two edges can exhibit an intriguing oscillatory behavior between antiferromagnetic and ferromagnetic, driven by acquiring the positive coherence between the two edges to lower the free energy. The oscillation effect is readily tunable in applied magnetic fields. These novel properties suggest new experimental manifestation of the edge magnetic orders in graphene nanoribbons, and enhance the hopes of graphene-like spintronic nanodevices functioning at room temperature., 22 pages, 9 figures

Kitaev interactions underlying a quantum spin liquid have long been sought, but experimental data from which their strengths can be determined directly, are still lacking. Here, by carrying out inelastic neutron scattering measurements on high-quality single crystals of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, we observe spin-wave spectra with a gap of $\ensuremath{\sim}2\text{ }\text{ }\mathrm{meV}$ around the $M$ point of the two-dimensional Brillouin zone. We derive an effective-spin model in the strong-coupling limit based on energy bands obtained from first-principles calculations, and find that the anisotropic Kitaev interaction $K$ term and the isotropic antiferromagnetic off-diagonal exchange interaction $\mathrm{\ensuremath{\Gamma}}$ term are significantly larger than the Heisenberg exchange coupling $J$ term. Our experimental data can be well fit using an effective-spin model with $K=\ensuremath{-}6.8\text{ }\text{ }\mathrm{meV}$ and $\mathrm{\ensuremath{\Gamma}}=9.5\text{ }\text{ }\mathrm{meV}$. These results demonstrate explicitly that Kitaev physics is realized in real materials.

The spin fluctuations and superconducting pairing symmetries in the dispersive band of Lieb lattice are studied by fluctuation exchange approximation. The antiferromagnetic spin density wave is found to exist on the A sublattice (the lattice sites with four nearest neighbors) at half filling. When slightly doped away from half filling, a balance between the combined effects of the ( π , π ) and ( 0.4 π , 0 ) spin fluctuations and the gaining of the condensation energy leads to the nearly degenerate d x 2 − y 2 - and g x y ( x 2 − y 2 ) -wave pairing states. After further doped, the d x y -wave state is favored via the intra-sublattice spin fluctuations with a wave vector ( π , 0 ). We emphasize that the sublattices' contribution and the renormalization of the spectral function play a crucial role on the spin fluctuations and the pairing symmetry. The effect of the imbalance of the on-site energy at different sublattices is also discussed.

The local magnetism induced by vacancies in the presence of the spin-orbital interaction is investigated based on the half-filled Kane-Mele-Hubbard model on the honeycomb lattice. Using the self-consistent mean-field theory, we find that the spin-orbital coupling will enhance the localization of the spin moments near a single vacancy. We further study the magnetic structures along the zigzag edges formed by a chain of vacancies. We find that the spin-orbital coupling tends to suppress the counter-polarized ferrimagnetic order on the upper and lower edges, because of the open of the spin-orbital gap. As a result, in the case of the balance number of sublattices, it will suppress completely this kind of ferrimagnetic order. But, for the imbalance case, a ferrimagnetic order along both edges exists because additional zero modes will not be affected by the spin-orbital coupling., 6 pages, 6 figures

We study various particle–hole excitations and possible superconducting pairings mediated by these fluctuations in doped α-RuCl3 by using multi-band Hubbard model with all t2g orbitals. By performing a random-phase-approximation (RPA) analysis, we find that among all particle–hole excitations, the j eff = 1/2 pseudospin fluctuations are dominant, suggesting the robustness of j eff = 1/2 picture even in the doped systems. We also find that the most favorable superconducting state has a d-wave pairing symmetry.

Kitaev interactions underlying a quantum spin liquid have long been sought, but experimental data from which their strengths can be determined directly, are still lacking. Here, by carrying out inelastic neutron scattering measurements on high-quality single crystals of α-RuCl_{3}, we observe spin-wave spectra with a gap of ∼2 meV around the M point of the two-dimensional Brillouin zone. We derive an effective-spin model in the strong-coupling limit based on energy bands obtained from first-principles calculations, and find that the anisotropic Kitaev interaction K term and the isotropic antiferromagnetic off-diagonal exchange interaction Γ term are significantly larger than the Heisenberg exchange coupling J term. Our experimental data can be well fit using an effective-spin model with K=-6.8 meV and Γ=9.5 meV. These results demonstrate explicitly that Kitaev physics is realized in real materials.

We study the half-filled Hubbard model on the triangular lattice with spin-dependent Kitaev-like hopping. Using the variational cluster approach, we identify five phases: a metallic phase, a non-coplanar chiral magnetic order, a $120^\circ$ magnetic order, a nonmagnetic insulator (NMI), and an interacting Chern insulator (CI) with a nonzero Chern number. The transition from CI to NMI is characterized by the change of the charge gap from an indirect band gap to a direct Mott gap. Based on the slave-rotor mean-field theory, the NMI phase is further suggested to be a gapless Mott insulator with a spinon Fermi surface or a fractionalized CI with nontrivial spinon topology, depending on the strength of Kitaev-like hopping. Our work highlights the rising field that interesting phases emerge from the interplay of band topology and Mott physics., published version, references updated