3D Fermi surfaces from charge order in layered CsV$_3$Sb$_5$
Xiangwei Huang, Chunyu Guo, Carsten Putzke, Yan Sun, Maia G. Vergniory, Ion Errea, Martin Gutierrez-Amigo, Dong Chen, Claudia Felser, Philip J. W. Moll
The cascade of electronic phases in CsV$_3$Sb$_5$ raises the prospect to disentangle their mutual interactions in a clean, strongly interacting Kagome lattice. When the Kagome planes are stacked into a crystal, its electronic dimensionality encodes how much of the Kagome physics and its topological aspects survive. The layered structure of CsV$_3$Sb$_5$ reflects in Brillouin-zone-sized quasi-2D Fermi surfaces and a significant transport anisotropy. Yet here we demonstrate that CsV$_3$Sb$_5$ is a three-dimensional metal within the charge-density-wave (CDW) state. Small 3D pockets play a crucial role in its low-temperature magneto- and quantum transport. Their emergence at $T_{CDW}\sim 93$ K results in an anomalous sudden increase of the in-plane magnetoresistance by 4 orders of magnitude. The presence of these 3D pockets is further confirmed by quantum oscillations under in-plane magnetic fields - demonstrating their closed nature. These results emphasize the impact of interlayer coupling on the Kagome physics in 3D materials.
The ${\mathbb{Z}}_{2}$ topological metals $R$V$_3$Sb$_5$ ($R$ = K, Rb, Cs) with a layered kagome structure provide a unique opportunity to investigate the interplay between charge order, superconductivity and topology. Here, we report muon-spin relaxation/rotation ($μ$SR) measurements performed on CsV$_3$Sb$_5$ across a broad temperature range, in order to uncover the nature of the charge-density wave order and superconductivity in this material. From zero-field $μ$SR, we find that spontaneous magnetic fields appear below 50 K which is well below the charge-density wave transition ($T^* \sim 9…
Using first-principles calculations, we identify the origin of the observed charge density wave (CDW) formation in a layered kagome metal CsV$_3$Sb$_5$. It is revealed that the structural distortion of kagome lattice forming the trimeric and hexameric V atoms is accompanied by the stabilization of quasimolecular states, which gives rise to the opening of CDW gaps for the V-derived multibands lying around the Fermi level. This Jahn-Teller-like instability having the local lattice distortion and its derived quasimolecular states is a driving force of the CDW order. Specifically, the saddle point…
In strongly correlated electronic systems, several novel physical properties are induced by the orbital degree of freedom. In particular, orbital degeneracy near the Fermi level leads to spontaneous symmetry breaking, such as the nematic state in FeSe and the orbital ordering in several perovskite systems. Here, the novel layered perovskite material CsVF$_4$, with a $3d^2$ electronic configuration, was systematically studied using density functional theory and a multiorbital Hubbard model within the Hatree-Fock approximation. Our results show that CsVF$_4$ should be magnetic, with a G-type ant…
The connection between unconventional superconductivity and charge density waves (CDW) has intrigued the condensed matter community and found much interest in the recently discovered superconducting Kagome family of AV$_3$Sb$_5$ (A = K, Cs, Rb). Xray diffraction and Raman spectroscopy measurements established that the CDW order in CsV$_3$Sb$_5$ comprises of a 2x2x4 structure with stacking of layers of star-of-David (SD) and inverse-star-of-David (ISD) pattern along the $c$-axis direction. Such interlayer ordering will induce a vast normalization of the electronic ground state; however, it has …
The recently discovered family of AV$_3$Sb$_5$ (A: K, Rb Cs) kagome metals possess a unique combination of nontrivial band topology, superconducting ground states, and signatures of electron correlations manifest via competing charge density wave order. Little is understood regarding the nature of the charge density wave (CDW) instability inherent to these compounds and the potential correlation with the accompanying onset of a large anomalous Hall response. To understand the impact of the CDW order on the electronic structure in these systems, we present quantum oscillation measurements on si…
The recently discovered layered kagome metals AV$_3$Sb$_5$ (A=K, Rb, Cs) exhibit diverse correlated phenomena, which are intertwined with a topological electronic structure with multiple van Hove singularities (VHSs) in the vicinity of the Fermi level. As the VHSs with their large density of states enhance correlation effects, it is of crucial importance to determine their nature and properties. Here, we combine polarization-dependent angle-resolved photoemission spectroscopy with density functional theory to directly reveal the sublattice properties of 3d-orbital VHSs in CsV$_3$Sb$_5$. Four V…
CsV$_3$Sb$_5$ is a newly discovered Kagome superconductor that attracts great interest due to its topological nontrivial band structure and the coexistence of superconductivity and charge-density-wave (CDW) with many exotic properties. Here, we report the detailed characterization of the CDW gap in high-quality CsV$_3$Sb$_5$ single crystals using high-resolution angle-resolved photoemission spectroscopy. We find that the CDW gap is strongly momentum dependent. While gapped around the $M$ point, the electronic states remain gapless around the $Γ$ point and along the $Γ$-$K$ direction. Such mome…
We report on a detailed study of the optical properties of CsV$_{3}$Sb$_{5}$ at a large number of temperatures above and below the charge-density-wave (CDW) transition. Above the CDW transition, the low-frequency optical conductivity reveals two Drude components with distinct widths. An examination of the band structure allows us to ascribe the narrow Drude to multiple light and Dirac bands, and the broad Drude to the heavy bands near the $M$ points which form saddle points near the Fermi level. Upon entering the CDW state, the opening of the CDW gap is clearly observed. A large portion of the…
The layered vanadium antimonides AV3Sb5 (A = K, Rb, Cs) are a recently discovered family of topological kagome metals with a rich phenomenology of strongly correlated electronic phases including charge order and superconductivity. Understanding how the singularities inherent to the kagome electronic structure are linked to the observed many-body phases is a topic of great interest and relevance. Here, we combine angle-resolved photoemission spectroscopy and density functional theory to reveal multiple kagome-derived van Hove singularities (vHs) coexisting near the Fermi level of CsV3Sb5 and an…
The transition-metal-based kagome metals provide a versatile platform for correlated topological phases hosting various electronic instabilities. While superconductivity is rare in layered kagome compounds, its interplay with nontrivial topology could offer an engaging space to realize exotic excitations of quasiparticles. Here, we use scanning tunneling microscopy (STM) to study a newly discovered Z$_2$ topological kagome metal CsV$_3$Sb$_5$ with a superconducting ground state. We observe charge modulation associated with the opening of an energy gap near the Fermi level. When across single-u…
The diversity of emergent phenomena in quantum materials often arises from the interplay between different physical energy scales or broken symmetries. Cooperative interactions among them are rare; however, when they do occur, they often stabilize fundamentally new ground states or phase behaviors. For instance, a pair density wave can form when the superconducting order parameter borrows spatial periodical variation from charge order; a topological superconductor can arise when topologically nontrivial electronic states proximitize with or participate in the formation of the superconducting c…
Recently discovered alongside its sister compounds KV$_3$Sb$_5$ and RbV$_3$Sb$_5$, CsV$_3$Sb$_5$ crystallizes with an ideal kagome network of vanadium and antimonene layers separated by alkali metal ions. This work presents the electronic properties of CsV$_3$Sb$_5$, demonstrating bulk superconductivity in single crystals with a T$_{c} = 2.5$K. The normal state electronic structure is studied via angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT), which categorize CsV$_3$Sb$_5$ as a $\mathbb{Z}_2$ topological metal. Multiple protected Dirac crossings are pred…
Pressure evolution of the superconducting kagome metal CsV$_3$Sb$_5$ is studied with single-crystal x-ray diffraction and density-functional band-structure calculations. A highly anisotropic compression observed up to 5 GPa is ascribed to the fast shrinkage of the Cs-Sb distances and suppression of Cs rattling motion. This prevents Sb displacements required to stabilize the three-dimensional charge-density-wave (CDW) order and elucidates the disappearance of the CDW already at 2 GPa despite only minor changes in the electronic structure of the normal state. At higher pressures, vanadium bands …
The recently discovered layered kagome metals AV$_3$Sb$_5$ (A = K, Rb, and Cs) with vanadium kagome networks provide a novel platform to explore correlated quantum states intertwined with topological band structures. Here we report the prominent effect of hole doping on both superconductivity and charge density wave (CDW) order, achieved by selective oxidation of exfoliated thin flakes. A superconducting dome is revealed as a function of the effective doping content. The superconducting transition temperature ($T_{\mathrm{c}}$) and upper critical field in thin flakes are significantly enhanced…
We report the transport properties of kagome superconductor CsV$_{3}$Sb$_{5}$ single crystals at magnetic field up to 32 T. The Shubnikov de Haas (SdH) oscillations emerge at low temperature and four frequencies of $F_α=$ 27 T, $F_β=$ 73 T, $F_ε=$ 727 T, and $F_η=$ 786 T with relatively small cyclotron masses are observed. For $F_β$ and $F_ε$, the Berry phases are close to $π$, providing a clear evidence of nontrivial topological band structures of CsV$_{3}$Sb$_{5}$. Furthermore, the consistence between theoretical calculations and experimental results implies that these frequencies can be ass…
The recently discovered kagome superconductor CsV$_3$Sb$_5$ ($T_c \simeq 2.5$ K) has been found to host charge order as well as a non-trivial band topology, encompassing multiple Dirac points and probable surface states. Such a complex and phenomenologically rich system is, therefore, an ideal playground for observing unusual electronic phases. Here, we report on microscopic studies of its anisotropic superconducting properties by means of transverse-field muon spin rotation ($μ$SR) experiments. The temperature dependences of the in-plane and out-of-plane components of the magnetic penetration…
Fermi surface fluctuations and lattice instabilities in the 2D metallic kagome superconductor CsV$_3$Sb$_5$ are elucidated via polarization-resolved Raman spectroscopy. The presence of a weak electronic continuum in high-quality samples marks the cross-over into the charge-density-wave (CDW) ordered phase, while impurity-rich samples promote strong defect-induced electronic scattering processes that affect the coherence of the CDW phase. CDW-induced phonon anomalies appear below $T_{\mathrm{CDW}}$, with emergent $C2$ symmetry for one of the CDW amplitude modes, alluding to nematicity. In conju…
The entanglement of charge density wave (CDW), superconductivity, and topologically nontrivial electronic structure has recently been discovered in the kagome metal $A$V$_3$Sb$_5$ ($A$ = K, Rb, Cs) family. With high-resolution angle-resolved photoemission spectroscopy, we study the electronic properties of CDW and superconductivity in CsV$_3$Sb$_5$. The spectra around $\bar{K}$ is found to exhibit a peak-dip-hump structure associated with two separate branches of dispersion, demonstrating the isotropic CDW gap opening below $E_{\rm F}$. The peak-dip-hump lineshape is contributed by linearly di…
Momentum Structure of Superconductivity and Sublattice Effects from Quasiparticle Interference in CsV$_3$Sb$_5$
Yale University（耶鲁大学）；Aalto University School of Science（阿尔托大学理学院）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；Princeton University（普林斯顿大学）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）
Electron-electron and electron-phonon collision cross sections in CsV3Sb5
Laboratoire de Physique et d’Étude de Matériaux (CNRS) ESPCI Paris, PSL Research University（材料物理与研究实验室（法国国家科学研究中心）巴黎高等物理化工学院，巴黎文理研究大学）；Materials Department, University of California Santa Barbara（加州大学圣塔芭芭拉分校材料系）
The kagome lattice of transition metal atoms provides an exciting platform to study electronic correlations in the presence of geometric frustration and nontrivial band topology, which continues to bear surprises. In this work, using spectroscopic imaging scanning tunneling microscopy, we discover a cascade of different symmetry-broken electronic states as a function of temperature in a new kagome superconductor, CsV3Sb5. At a temperature far above the superconducting transition Tc ~ 2.5 K, we reveal a tri-directional charge order with a 2a0 period that breaks the translation symmetry of the l…
We show that spontaneous time-reversal-symmetry (TRS) breaking can naturally arise from the interplay between pair density wave (PDW) ordering at multiple momenta and nesting of Fermi surfaces (FS). Concretely, we consider pair-density-wave superconductivity on a hexagonal lattice with nested FS at $3/4$ electron filling, which is related to a recently discovered superconductor CsV$_3$Sb$_5$. Because of nesting of the FS, each momentum $\bk$ on the FS has at least two counterparts $-\bk\pm\mathbf{Q}_α$ ($α=1,2,3$) on the FS to form finite momentum ($\pm\mathbf{Q}_α$) Cooper pairs, resulting in…
In order to clarify superconducting properties of BiS$_2$-based layered superconductors LaO$_{1-x}$F$_x$BiS$_2$, we evaluate the superconducting transition temperature $T_{\rm c}$ and analyze the gap function in a weak-coupling limit on the basis of the two-dimensional two-orbital Hubbard model. It is found that $T_{\rm c}$ becomes maximum at $x=0.6$ in the present calculations. For $x<0.45$, we obtain the $d$-wave gap of which line nodes do not cross the pocket-like Fermi-surface curves with the centers at X and Y points. On the other hand, for $x>0.45$, the extended $s$-wave gap is found for…
Metallic materials with kagome lattice structure are interesting because their electronic structures can host flat bands, Dirac cones, and van Hove singularities, resulting in strong electron correlations, nontrivial band topology, charge density wave (CDW), and unconventional superconductivity. Recently, kagome lattice compounds AV$_3$Sb$_5$ (A = K, Rb, Cs) are found to have intertwined CDW order and superconductivity. The origin of the CDW has been suggested to be purely electronic, arising from Fermi-surface instabilities of van Hove singularity (saddle point) near the M points. Here we use…
The intertwining of charge order, superconductivity and band topology has promoted the AV$_3$Sb$_5$ (A=K, Rb, Cs) family of materials to the center of attention in condensed matter physics. Underlying those mysterious macroscopic properties such as giant anomalous Hall conductivity (AHC) and chiral charge density wave is their nontrivial band topology. While there have been numerous experimental and theoretical works investigating the nontrivial band structure and especially the van Hove singularities, the exact topological phase of this family remains to be clarified. In this work, we identif…
We present a comprehensive study performed with high-resolution angle-resolved photoemission spectroscopy on triple-layered Bi2Sr2Ca2Cu3O10+d single crystals. By measurements above TC the Fermi surface topology defined by the Fermi level crossings of the CuO2-derived band was determined. A hole-like Fermi surface as for single and double-CuO2 layered Bi-based cuprates is found, giving new input to the current debate of the general Fermi surface topology of the high Tc superconductors. Furthermore, we present measurements of the superconducting gap of Bi-2223 and show that there are clear indic…
First-principles density functional theory calculations are performed to understand the electronic structure and interaction parameters for recently discovered superconducting Kagome metal CsV$_3$Sb$_5$. A systematic analysis of the tight-binding parameters based on maximally localized Wannier function method demonstrates that the out-of-plane Sb$^{\rm out}$-$p$ orbital is a key element in complete description of the three Van Hove singularity structures known in this material at $M$ point near the Fermi level. Further, the correlation strengths are also largely determined by Sb$^{\rm out}$-$p…
We explain recently observed linear temperature dependence of the nodal Fermi velocity $v_F (T)$ in near-optimally doped cuprates. We argue that it originates from electron-electron interaction, and is a fundamental property of an arbitrary 2D Fermi liquid. We consider a spin-fermion model with the same parameters as in earlier studies, and show that the T term is about 30% at 300K, in agreement with the data. We show that the sub-leading term in $v_F (T)$ is a regular (and small) $T^2$ correction. We also show that at a $2k_F$ quantum-critical point, temperature corrections to the dispersion …
The electronic structure of electron doped iron-arsenide superconductors Ba(Fe1- xCox)2As2 has been measured with Angle Resolved Photoemission Spectroscopy. The data reveal a marked photon energy dependence of points in momentum space where the bands cross the Fermi energy, a distinctive and direct signature of three-dimensionality in the Fermi surface topology. By providing a unique example of high temperature superconductivity hosted in layered compounds with three-dimensional electronic structure, these findings suggest that the iron-arsenides are unique materials, quite different from the …
We report the Fermi surfaces of the superconductor Sr2RuO4 and the non-superconductor Sr1.8Ca0.2RuO4 probed by bulk-sensitive high-energy angle-resolved photoemission. It is found that there is one square-shaped hole-like, one square-shaped electron-like and one circle-shaped electron-like Fermi surface in both compounds. These results provide direct evidence for nesting instability giving rise to magnetic fluctuations. Our study clarifies that the electron correlation effects are changed with composition depending on the individual band.
The frequency dependence of the interlayer conductivity of a layered Fermi liquid in a magnetic field which is tilted away from the normal to the layers is considered. For both quasi-one- and quasi-two-dimensional systems resonances occur when the frequency is a harmonic of the frequency at which the magnetic field causes the electrons to oscillate on the Fermi surface within the layers. The intensity of the different harmonic resonances varies significantly with the direction of the field. The resonances occur for both coherent and weakly incoherent interlayer transport and so their observati…
We consider the quasiparticle c-axis conductivity in highly anisotropic layered compounds in the presence of the magnetic field parallel to the layers. We show that at low temperatures the quasiparticle interlayer conductivity depends strongly on the orientation of the in-plane magnetic field if the excitation gap has nodes on the Fermi surface. Thus measurements of the angle-dependent c-axis (out-of-plane) magnetoresistance, as a function of the orientation of the magnetic field in the layers, provide information on the momentum dependence of the superconducting gap (or pseudogap) on the Ferm…
The effect of incoherent interlayer transport on the interlayer resistance of a layered metal is considered. We find that for both quasi-one-dimensional and quasi-two-dimensional Fermi liquids the angular dependence of the magnetoresistance is essentially the same for coherent and incoherent transport. Consequently, the existence of a three-dimensional Fermi surface is not necessary to explain the oscillations in the magnetoresistance that are seen in many organic conductors as the field direction is varied.
In order to understand the material dependence of $T_c$ within the single-layered cuprates, we study a two-orbital model that considers both $d_{x^2-y^2}$ and $d_{z^2}$ orbitals. We reveal that a hybridization of $d_{z^2}$ on the Fermi surface substantially affects $T_c$ in the cuprates, where the energy difference $ΔE$ between the $d_{x^2-y2}$ and $d_{z^2}$ orbitals is identified to be the key parameter that governs both the hybridization and the shape of the Fermi surface. A smaller $ΔE$ tends to suppress $T_c$ through a larger hybridization, whose effect supersedes the effect of diamond-sha…
Dirac/Weyl semimetals hosting linearly-dispersing bands have received recent attention for potential thermoelectric applications, since their ultrahigh-mobility carriers could generate large thermoelectric and Nernst power factors. To optimize these efficiencies, the Fermi energy needs to be chemically controlled in a wide range, which is generally difficult in bulk materials because of disorder effects from the substituted ions. Here it is shown that the Fermi energy is tunable across the Dirac point for layered magnet EuMnBi$_2$ by partially substituting Gd$^{3+}$ for Eu$^{2+}$ in the insula…
We have performed soft x-ray spectroscopy in order to study the photoirradiation time dependence of the valence band structure and chemical states of layered transition metal nitride chloride TiNCl. Under the soft x-ray irradiation, the intensities of the states near the Fermi level (EF) and the Ti3+ component increased, while the Cl 2p intensity decreased. Ti 2p-3d resonance photoemission spectroscopy confirmed a distinctive Fermi edge with Ti 3d character. These results indicate the photo-induced metallization originates from deintercalation due to Cl desorption, and thus provide a new carri…
We show that electron wave functions in a quasi-two-dimensional conductor in a parallel magnetic field are always localized on conducting layers. Wave functions and electron spectrum in a quantum limit, where the "sizes" of quasi-classical electron orbits are of the order of nano-scale distances between the layers, are determined. AC infrared measurements to investigate Fermi surfaces and to test Fermi liquid theory in Q2D organic and high-Tc materials in high magnetic fields, H = 10-45 T, are suggested.
Flat bands and distinct density wave orders in correlated Kagome superconductor CsCr$_3$Sb$_5$
University of Science and Technology of China（中国科学技术大学）；Fuzhou University（福州大学）；Beijing Institute of Technology（北京理工大学）；Shanghai Advanced Research Institute, Chinese Academy of Sciences（中国科学院上海高等研究院）；National Synchrotron Radiation Laboratory and School of Nuclear Science and Technology, University of Science and Technology of China（中国科学技术大学核科学与技术学院/国家同步辐射实验室）；SLAC National Accelerator Laboratory（斯坦福直线加速器中心）
