We employ polarization-resolved electronic Raman spectroscopy and density functional theory to study the primary and secondary order parameters, as well as their interplay, in the charge density wave (CDW) state of the kagome metal AV3Sb5. Previous x-ray diffraction data at 15K established that the CDW order in CsV3Sb5 comprises of a 2x2x4 structure: one layer of inverse-star-of-David and three consecutive layers of star-of-David pattern. We analyze the lattice distortions based the 2x2x4 structure at 15K, and find that U lattice distortion is the primary order parameter while M and L distortions are secondary order parameters for Vanadium displacements. This conclusion is confirmed by the calculation of bare susceptibility that shows a broad peak at around qz=0.25 along the hexagonal Brillouin zone face central line (U-line). We also identify several phonon modes emerging in the CDW state, which are lattice vibration modes related to V and Sb atoms as well as alkali atoms. The detailed temperature evolution of these modes' frequencies, HWHM, and integrated intensities support a phase diagram with two successive structural phase transitions in CsV3Sb5: the first one with a primary order parameter appearing at TS=94K and the second isostructural one appearing at around 70K.
Due to an uprise in the variety of candidate compounds, kagome metals have recently gained significant attention. Among other features, kagome metals host Dirac cones as a key band structure feature away from half filling, and potentially yield an exceptionally large fine structure, beyond values found in other 2D Dirac materials such as graphene. We investigate the possibility of chiral symmetry breaking in kagome metals. Based on a heuristic lattice model, we determine the critical coupling strength and the ordering pattern by means of a Schwinger-Dyson mean-field analysis. As the leading in…
The complex iridium oxide Na3Ir3O8 with a B-site ordered spinel structure was synthesized in single crystalline form, where the chiral hyper-kagome lattice of Ir atoms, as observed in the spin-liquid candidate Na4Ir3O8, was identified. The average valence of Ir is 4.33+ and, therefore, Na3Ir3O8 can be viewed as a doped analogue of the hyper-kagome spin liquid with Ir4+. The transport measurements showed that Na3Ir3O8 is in fact a semi-metal. The electronic structure calculation demonstrated that the strong spin-orbit coupling of Ir yields the semi-metallic state out of an otherwise band insula…
Motivated by the recent discovery of metallic kagome lattice materials, AV$_{3}$Sb$_{5}$ (A=K, Rb, Cs), we investigate the ground state of the half-filled kagome lattice Hubbard model by employing the density-matrix renormalization group (DMRG) method. We identify a metal-insulator transition around $U \thicksim U_{c1}$ and four distinct phases as a function of $U/t$ on narrower cylinders, including a metallic phase at $U < U_{c1}$, two insulating intermediate phases: a translational symmetry breaking phase at $U_{c1} < U < U_{c2}$ and a quantum spin liquid phase at $U_{c2} < U < U_{c3}$, and …
Kagome materials often host exotic quantum phases, including spin liquids, Chern gap, charge order, and superconductivity. Existing scanning microscopy studies of the kagome charge order have been limited to non-kagome surface layers. Here we tunnel into the kagome lattice of FeGe to uncover features of the charge order. Our spectroscopic imaging identifes a 2x2 charge order in the magnetic kagome lattice, resembling that discovered in kagome superconductors. Spin-mapping across steps of unit-cell-height demonstrates that this charge order emerges from spin-polarized electrons with an antiferr…
The kagome lattice is a fertile platform to explore topological excitations with both Fermi-Dirac and Bose-Einstein statistics. While relativistic Dirac Fermions and flat-bands have been discovered in the electronic structure of kagome metals, the spin excitations have received less attention. Here we report inelastic neutron scattering studies of the prototypical kagome magnetic metal FeSn. The spectra display well-defined spin waves extending up to 120 meV. Above this energy, the spin waves become progressively broadened, reflecting interactions with the Stoner continuum. Using linear spin w…
We discuss the metal-insulator transition of the spinless fermion model on the Kagomé lattice at 1/3-filling. The system is analyzed using exact diagonalization, the density-matrix renormalization group methods and the random phase approximation. In the strong-coupling region, the charge-ordered ground state is consistent with the predictions of the effective model with a plaquette order. We find that the qualitative properties of the metal-insulator transition are totally different depending on the sign of the hopping integrals, reflecting the difference of band structure at the Fermi level.
We have carried out muon spin relaxation and rotation measurements on the newly discovered kagome metal KV3Sb5, and find a local field dominated by weak magnetic disorder which we associate with the nuclear moments present, and a modest temperature dependence which tracks the bulk magnetic susceptibility. We find no evidence for the existence of V4+ local moments, suggesting that the physics underlying the recently reported giant unconventional anomalous Hall effect in this material warrants further studies.
RV6Sn6 (R=rare earth) compounds are appealing materials platforms for exploring the interplay between R-site magnetism and nontrivial band topology associated with the nonmagnetic vanadium-based kagome network. Here we present the synthesis and characterization of the kagome metal TbV6Sn6 via single-crystal x-ray diffraction, magnetization, transport, and heat capacity measurements. Magnetization measurements reveal strong, uniaxial magnetic anisotropy rooted in the alignment of Tb3Å moments in the interplane direction below 4.3(2) K. TbV6Sn6 exhibits multiband transport behavior with high mob…
Theory of unconventional magnetism in a Cu-based kagome metal
Universität Würzburg（维尔茨堡大学）；Istituto Officina dei Materiali, Consiglio Nazionale delle Ricerche（意大利国家研究委员会材料研究所）；ETH Zürich（苏黎世联邦理工学院）；University of Geneva（日内瓦大学）；University of Technology Sydney（悉尼科技大学）；Columbia University（哥伦比亚大学）；University of Bologna（博洛尼亚大学）
We study electronic instabilities of a kagome metal with a Fermi energy close to saddle points at the hexagonal Brillouin zone face centers. Using parquet renormalization group, we determine the leading and subleading instabilities, finding superconducting, charge, orbital moment, and spin density waves. We then derive and use Landau theory to discuss how different primary density wave orders give rise to charge density wave modulations, as seen in the AV$_3$Sb$_5$ family, with A=K,Rb,Cs. The results provide strong constraints on the mechanism of charge ordering and how it can be further refin…
We obtain the rich phase diagrams in the Hubbard model on the triangular Kagomé lattice as a function of interaction, temperature and asymmetry, by combining the cellular dynamical mean-field theory with the continuous time quantum Monte Carlo method. The phase diagrams show the asymmetry separates the critical points in Mott transition of two sublattices on the triangular Kagomé lattice and produces two novel phases called plaquette insulator with an obvious gap and a gapless Kondo metal. When the Coulomb interaction is stronger than the critical value Uc, a short range paramagnetic insulatin…
The study of electronic and magnetic properties of kagome lattice has been an active research area searching for topological phases of matters. In particular, the kagome system with transition metal stannides and etc exhibit interesting anomalous Hall effects driven by ferromagnetic or non-collinear magnetic ordering. In this paper, motivated by these pioneer works, we study strongly correlated spin-orbit coupled electrons in kagome lattice at 1/3 filling. Using both Hartree-Fock approach and effective model analysis, we report quantum phase transitions accompanied with distinct charge and mag…
Kagome magnets are expected to feature emergent properties due to the interplays among geometry, magnetism, electronic correlation, and band topology. The magnetism and topological electronic states can be tuned via the rare earth engineering in RV6Sn6 kagome metals, where R is a rare earth element. Herein, we present the synthesis and characterization of SmV6Sn6, a metal with two-dimensional kagome nets of vanadium and frustrated triangular Sm lattice. Partial of the Sm atoms are shifted from the normal R positions by c/2 along the c axis. Magnetic measurements reveal obvious anisotropy, wher…
We present a thorough tight-binding analysis of the band structure of a wide variety of lattices belonging to the class of honeycomb and Kagome systems including several mixed forms combining both lattices. The band structure of these systems are made of a combination of dispersive and flat bands. The dispersive bands possess Dirac cones (linear dispersion) at the six corners (K points) of the Brillouin zone although in peculiar cases Dirac cones at the center of the zone $(Γ$ point) appear. The flat bands can be of different nature. Most of them are tangent to the dispersive bands at the cent…
Tunable Electronic Correlations in 135-Kagome Metals
Universität Würzburg（维尔茨堡大学）；CINECA；ESPCI Paris, PSL Research University, CNRS, Sorbonne Université（巴黎高等物理化工学院、PSL研究大学、法国国家科学研究中心、索邦大学）；Alma Mater Studiorum, University of Bologna（博洛尼亚大学）
We report the results of ac and dc magnetic susceptibility and isothermal magnetization measurements (T= 2-300 K) on the single crystals of a metallic kagome lattice, Tb3Ru4Al12, reported recently to undergo reentrant magnetism with the onset of long range antiferromagnetic order below (TN=) 22K. The magnetization data obtained on the crystal with the c-axis orientation along magnetic-field reveal spin-glass-like characteristics near 17 K (below TN). However, for the orientation along basal plane, such glassy anomalies are not observable above 2 K. In this respect, this compound behaves like a…
Kagome metals possess peculiar optical spectra consisting of contributions from free charge carriers in a Drude-type response, localized carriers seen as a strongly temperature-dependent localization peak, and, in some cases, phonons displaying strong anomalies. The rare-earth kagome metal series, $R$Mn$_6$Sn$_6$, provides a marvelous playground to study the electronic properties of kagome metals in the presence of variable magnetic order. Here, we report temperature-dependent reflectivity studies on two members of the $R$Mn$_6$Sn$_6$ family, GdMn$_6$Sn$_6$ (in-plane ferrimagnet) and TbMn$_6$S…
The synthesis and characterization of vanadium-based kagome metals YV$_6$Sn$_6$ and GdV$_6$Sn$_6$ are presented. X-ray diffraction, magnetization, magnetotransport, and heat capacity measurements reveal an ideal kagome network of V-ions coordinated by Sn and separated by triangular lattice planes of rare-earth ions. The onset of low-temperature, likely noncollinear, magnetic order of Gd spins is detected in GdV$_6$Sn$_6$, while V-ions in both compounds remain nonmagnetic. Density functional theory calculations are presented modeling the band structures of both compounds, which can be classifie…
The kagome lattice based on 3d transition metals is a versatile platform for novel topological phases hosting symmetry-protected electronic excitations and exotic magnetic ground states. However, the paradigmatic states of the idealized two-dimensional (2D) kagome lattice - Dirac fermions and topological flat bands - have not been simultaneously observed, partly owing to the complex stacking structure of the kagome compounds studied to date. Here, we take the approach of examining FeSn, an antiferromagnetic single-layer kagome metal with spatially-decoupled kagome planes. Using polarization- a…
Superconductors with kagome lattices have been identified for over 40 years, with a superconducting transition temperature TC up to 7K. Recently, certain kagome superconductors have been found to exhibit an exotic charge order, which intertwines with superconductivity and persists to a temperature being one order of magnitude higher than TC. In this work, we use scanning tunneling microscopy (STM) to study the charge order in kagome superconductor RbV3Sb5. We observe both a 2x2 chiral charge order and nematic surface superlattices (predominantly 1x4). We find that the 2x2 charge order exhibits…
The geometrical frustration nature of the kagome lattice makes it a great host to flat electronic band, non-trivial topological properties, and novel magnetisms. Metallic kagome antiferromagnet YMn$_{6}$Sn$_{6}$ exhibits the topological Hall effect (THE) when an in-plane magnetic field is applied. THE is typically associated with the nanometer-sized non-coplanar spin structure of skyrmions in non-centrosymmetric magnets with large Dzyaloshinskii-Moriya interaction. Here we use single crystal neutron diffraction to determine the field/temperature dependence of the magnetic structure in YMn$_{6}…
Materials hosting kagome lattices have drawn interest for the diverse magnetic and electronic states generated by geometric frustration. In the $A$V$_3$Sb$_5$ compounds ($A$ = K, Rb, Cs), stacked vanadium kagome layers give rise to unusual charge density waves (CDW) and superconductivity. Here we report single-crystal growth and characterization of ScV$_6$Sn$_6$, a hexagonal HfFe$_6$Ge$_6$-type compound that shares this structural motif. We identify a first-order phase transition at 92 K. Single crystal X-ray and neutron diffraction reveal a charge density wave modulation of the atomic lattice…
In ordinary materials, electrons conduct both electricity and heat, where their charge-entropy relations observe the Mott formula and the Wiedemann-Franz law. In topological quantum materials, the transverse motion of relativistic electrons can be strongly affected by the quantum field arising around the topological fermions, where a simple model description of their charge-entropy relations remains elusive. Here we report the topological charge-entropy scaling in the kagome Chern magnet TbMn$_6$Sn$_6$, featuring pristine Mn kagome lattices with strong out-of-plane magnetization. Through both …
Coexistence of long-range magnetic order and dynamical magnetism in the V-based Kagome metals: A combined thermodynamic and $μ$SR study
Kyushu Institute of Technology（九州工业大学）；Forschungszentrum Jülich（于利希研究中心）；Technical University of Munich（慕尼黑工业大学）；National Cheng Kung University（国立成功大学）
In two-dimensional (2D) metallic kagome lattice materials, destructive interference of electronic hopping pathways around the kagome bracket can produce nearly localized electrons, and thus electronic bands that are flat in momentum space. When ferromagnetic order breaks the degeneracy of the electronic bands and splits them into the spin-up majority and spin-down minority electronic bands, quasiparticle excitations between the spin-up and spin-down flat bands should form a narrow localized spin-excitation Stoner continuum coexisting with well-defined spin waves in the long wavelengths. Here w…
We present the results of neutron diffraction studies on polycrystals of a metallic kagome lattice, Tb3Ru4Al12, reported recently to undergo reentrant magnetism, with the onset of long range antiferromagnetic order below (TN=) 22 K and spin-glass features below about 17 K. The present results reveal long-range antiferromagnetic order of an incommensurate type with the moments oriented along c-axis at all temperatures below TN. There are however notable changes in the T dependence of propagation vector along b-axis across 17 K. An observation of interest is that there is no decrease of intensit…
The synthesis and characterization of the vanadium-based kagome metal TbV${_6}$Sn${_6}$ is presented. X-ray measurements confirm this material forms with the same crystal structure type as the recently investigated kagome metals GdV$_6$Sn$_6$ and YV$_6$Sn$_6$, with space group symmetry P6/mmm. A signature of a phase transition at 4.1K is observed in heat capacity, resistivity, and magnetic susceptibility measurements, and both resistivity and magnetization measurements exhibit hysteresis in magnetic field. Furthermore, a strikingly large anisotropy in the magnetic susceptibility was observed, …
Following the discovery of a new family of kagomé prototypical materials with structure AV$_3$Sb$_5$ (A = K, Rb, Cs), there has been heightened interest in studying the correlation-driven electronic phenomena in these kagomé lattice systems. The study of these materials has gone beyond magneto-transport measurements to reveal exciting features such as Dirac bands, anomalous Hall effect, bulk superconductivity with $T_c$ $\sim$ 0.9 K-2.5 K, and the observation of charge density wave instabilities, suggesting an intertwining of topological physics and new quantum orders. Moreover, very recent wo…
Kagome metals with charge density wave (CDW) order exhibit a broad spectrum of intriguing quantum phenomena. The recent discovery of the novel kagome CDW compound ScV$_6$Sn$_6$ has spurred significant interest. However, understanding the interplay between CDW and the bulk electronic structure has been obscured by a profusion of surface states and terminations in this quantum material. Here, we employ photoemission spectroscopy and potassium dosing to elucidate the complete bulk band structure of ScV$_6$Sn$_6$, revealing multiple van Hove singularities near the Fermi level. We surprisingly disc…
Band-Saddle-Point Engineering in Mixed $A$-site $A$V$_3$Sb$_5$ Kagome Metals
Physikalisches Institut, Universität Stuttgart（斯图加特大学第一物理研究所）；Felix Bloch Institute for Solid-State Physics, Leipzig University（莱比锡大学费利克斯·布洛赫固体物理研究所）；Materials Department, University of California Santa Barbara（加州大学圣塔芭芭拉分校材料系）；Materials Science and Technology Division, Oak Ridge National Laboratory（橡树岭国家实验室材料科学与技术部）；Helmholtz-Zentrum Dresden-Rossendorf, Institute of Ion Beam Physics and Materials Research（德累斯顿罗森多夫亥姆霍兹中心离子束物理与材料研究所）
Coexisting density-wave and superconducting states along with the large anomalous Hall effect in the absence of local magnetism remain intriguing and enigmatic features of the AV$_3$Sb$_5$ kagome metals (A = K, Rb, Cs). Here, we demonstrate via optical spectroscopy and density-functional calculations that low-energy dynamics of KV$_3$Sb$_5$ is characterized by unconventional localized carriers, which are strongly renormalized across the density-wave transition and indicative of electronic correlations. Strong phonon anomalies are prominent not only below the density-wave transition, but also a…
Exploration of exotic transport behavior for quantum materials is of great interest and importance for revealing exotic orders to bring new physics. In this Letter, we report the observation of exotic prominent planar Hall effect (PHE) and planar anisotropic magnetoresistivity (PAMR) in strange kagome metal KV$_3$Sb$_5$. The PHE and PAMR, which are driven by an in-plane magnetic field and display sharp difference from other Hall effects driven by an out-of-plane magnetic field or magnetization, exhibit exotic higher-order oscillations in sharp contrast to those following empirical rule only al…
Spectroscopic origin of giant anomalous Hall effect in an interwoven magnetic kagome metal
Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；ShanghaiTech University（上海科技大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；Rutgers University（罗格斯大学）；Weizmann Institute of Science（魏茨曼科学研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Chinese Academy of Sciences（中国科学院）；Beijing National Laboratory for Condensed Matter Physics（北京凝聚态物理国家研究中心）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Stanford University（斯坦福大学）；Wuhan University（武汉大学）；University of Oxford（牛津大学）；Songshan Lake Materials Laboratory（松山湖材料实验室）
Materials with zero energy band gap display intriguing properties including high sensitivity of the electronic band structure to external stimulus such as pressure or magnetic field. An interesting candidate for zero energy band gap are Weyl nodes at the Fermi level EF. A prerequisite for the existence of Weyl nodes is to either have inversion or time reversal symmetry broken. Weyl nodes in systems with broken time reversal symmetry are ideal to realize the tunability of the electronic band structure by magnetic field. Theoretically, it has been shown that in ferromagnetic Weyl materials, the …
We investigate the real-space profile of effective Coulomb interactions in correlated kagome materials. By particularizing to KV$_3$Sb$_5$, Co$_3$Sn$_2$S$_2$, FeSn, and Ni$_3$In, we analyze representative cases that exhibit a large span of correlation-mediated phenomena, and contrast them to prototypical prevoskite transition metal oxides. From our constrained random phase approximation studies we find that the on-site interaction strength in kagome metals not only depends on the screening processes at high energy, but also on the low-energy hybriziation profile of the electronic density of st…
By means of the density functional theory in combination with the dynamical mean-field theory, we tried to examine the electronic structure of hexagonal FeGe, in which the Fe atoms form a quasi-2D layered Kagome lattice. We predict that it is a representative Kagome metal characterized by orbital selective Dirac fermions and extremely flat bands. Furthermore, Fe's 3$d$ electrons are strongly correlated. They exhibit quite apparent signatures of electronic correlation induced by Hund's rule coupling, such as sizable differentiation in band renormalization, non-Fermi-liquid behavior, spin-freezi…
The distribution of chemically similar transition-metal ions is a fundamental issue in the study of herbertsmithite-type kagome antiferromagnets. Using synchrotron radiation, we have performed resonant powder x-ray diffractions on newly synthesized CoCu3(OH)6Cl2, which provide an exact distribution of transition-metal ions in the frustrated antiferromagnet. Both magnetic susceptibility and specific heat measurements are quantitatively consistent with the occupation fractions determined by resonant x-ray diffraction. The distribution of transition-metal ions and residual magnetic entropy sugges…
The kagome lattice, consisting of interconnected triangles and hexagons uniquely, is an excellent model system for study frustrated magnetism, electronic correlation and topological electronic structure. After an intensive investigation on frustrated magnetism in insulating magnetic kagome lattices, the interplay between charge and spin degrees of freedom via spin-orbital coupling in metallic systems (kagome metals) has become an attractive topic recently. Here, we study centrosymmetric YMn6Sn6 with Mn kagome lattice. We discover that it exhibits giant topological Hall effect near room tempera…
The flat band has attracted a lot of attention because it gives rise to many exotic phases, as recently demonstrated in magic angle twisted bilayer graphene. Here, based on first-principles calculations, we identify a metal-insulator transition in boron triangular Kagome lattice with a spin-polarized flat band at 2/3-filling. This phase transition is accompanied by the formation of a Wigner crystal, which is driven by Fermi surface nesting effect and thereby strong electron-phonon interactions, keeping ferromagnetism. Our calculation results suggest that boron triangular Kagome lattices with p…
The kagome lattice, whose electronic valence band (VB) structure includes two Dirac bands and one flat band, offers a rich space to realise tuneable topological and strongly correlated electronic phases in two-dimensional (2D) and layered materials. While strong electron correlations have been observed in inorganic kagome crystals, they remain elusive in organic systems. The latter offer versatile synthesis protocols via molecular self-assembly and metal-ligand coordination. Here, we report the synthesis of a 2D metal-organic framework (MOF) where di-cyano-anthracene (DCA) molecules form a kag…
