Recently synthesized Kagome compounds AV$_3$Sb$_5$ attract great attention due to the unusual coexistence of the topology, charge density wave and superconductivity. In this {\it Letter}, based on the band structures for CsV$_3$Sb$_5$ in pristine phase, we fit an effective 6-band model for the low-energy processes; utilizing the random phase approximation (RPA) on the effective minimal model, we obtain the momentum-resolved static spin susceptibility attributing the spin-fluctuation pairing mechanism, we find that the superconducting pairing strengths increase with the lift of the Coulomb correlation, and the superconductive pairing symmetry is singlet, the gap functions are antisymmetric with respect to the x-axis and the y-axis in the intermediate to strong Coulomb correlated regime,indicating the unconventional superconductivity in Kagome compounds AV$_3$Sb$_5$.
This is a comment on Phys. Rev. Lett. {\bf 110}, 126405 (2013), showing it biases the ferromagnetic order more than mean field theories would do. With over-biases like this, the theoretical method applied in the given context is called into question.
The recent discovery of AV$_3$Sb$_5$ (A=K,Rb,Cs) has uncovered an intriguing arena for exotic Fermi surface instabilities in a kagome metal. Among them, superconductivity is found in the vicinity of multiple van Hove singularities, exhibiting indications of unconventional pairing. We show that the sublattice interference mechanism is central to understanding the formation of superconductivity in a kagome metal. Starting from an appropriately chosen minimal tight-binding model with multiple with multiple van Hove singularities close to the Fermi level for AV$_3$Sb$_5$, we provide a random phase…
The combination of non-trivial band topology and symmetry breaking phases gives rise to novel quantum states and phenomena such as topological superconductivity, quantum anomalous Hall effect and axion electrodynamics. Evidence of intertwined charge density wave (CDW) and superconducting order parameters has recently been observed in a novel kagome material AV3Sb5 (A=K,Rb,Cs) that features a Z2 topological invariant in the electronic structure. However, the origin of the CDW and its intricate interplay with topological state has yet to be determined. Here, using hard x-ray scattering, we demon…
Recently, kagome lattice metal AV$_3$Sb$_5$ (A = K, Rb, Cs) family has received wide attention due to its presence of superconductivity, charge density wave (CDW) and peculiar properties from topological nontrivial electronic structure. With time-resolved pump-probe spectroscopy, we show that the excited quasiparticle relaxation dynamics can be explained by formation of energy gap below the phase transition being similar to a usual second-order CDW condensate, by contrast, the structure change is predominantly first order phase transition. Furthermore, no CDW amplitude mode is identified in th…
The transition-metal kagome lattice materials host frustrated, correlated, and topological quantum states of matter. Recently, a new family of vanadium-based kagome metals AV3Sb5 (A=K, Rb, and Cs) with topological band structures has been discovered. These layered compounds are nonmagnetic and undergo charge density wave transitions before developing superconductivity at low temperatures. Here we report the observation of unconventional superconductivity and pair density wave (PDW) in CsV3Sb5 using scanning tunneling microscope/spectroscopy (STM/STS) and Josephson STS. We find that CsV3Sb5 exh…
Exotic quantum phase transitions in metals, such as the nematic and smectic states, were discovered one after another and found to be universal now. The emergence of unconventional density-wave order in frustrated kagome metal AV$_3$Sb$_5$ and its interplay with exotic superconductivity attract increasing attention. We reveal that the smectic bond-density-wave is naturally caused by the paramagnon interference mechanism, because strong scatterings among different van-Hove singularity points are induced. In addition, the fluctuations of the bond-order induce sizable "beyond-Migdal" pairing glue…
We derive the Ginzburg-Landau theory of unconventional singlet superconductors in the presence of a Zeeman field and impurities, in order to examine the resulting Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases. We show that the behavior of the FFLO phases in unconventional superconductors in the presence of impurities is qualitatively different from that found for s-wave superconductors.
Pressure-induced unconventional charge-density-wave states in kagome metal AV3Sb5 (A = K, Rb, Cs)
Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China（中国科学技术大学微观尺度物理国家研究中心）；Department of Physics, University of Science and Technology of China（中国科学技术大学物理系）；School of Physics, Hefei University of Technology（合肥工业大学物理学院）；Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学先进微结构协同创新中心）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）
Intertwining quantum order and nontrivial topology is at the frontier of condensed matter physics. A charge density wave (CDW) like order with orbital currents has been proposed as a powerful resource for achieving the quantum anomalous Hall effect in topological materials and for the hidden phase in cuprate high-temperature superconductors. However, the experimental realization of such an order is challenging. Here we use high-resolution scanning tunnelling microscopy (STM) to discover an unconventional charge order in a kagome material KV3Sb5, with both a topological band structure and a sup…
Direct Evidence of Unconventional Superconductivity in Doped Kagome system RV$_3$Sb$_5$
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；University of California Santa Barbara（加州大学圣塔芭芭拉分校）
Unconventional superconductivity in ScIr$_2$ chiral crystal with a kagome lattice
East China Normal University（华东师范大学）；Key Laboratory of Polar Materials and Devices (MOE), East China Normal University（华东师范大学极化材料器件教育部重点实验室）；Tianjin University（天津大学）；Technical University Dortmund（多特蒙德工业大学）；Laboratorium für Festkörperphysik, ETH Zürich（苏黎世联邦理工学院固体物理实验室）
Have you been lying awake wondering what symmetries determine whether a superconductor is spin singlet, triplet, or both? We show that if BCS theory is supplied with additional degrees of freedom, spin singlet can coexist with spin triplet superconductivity. In the first part, we didactically guide the reader to the most general superconducting state using symmetry arguments. If both singlet and triplet pairing channels are present, a magnetic field can convert between spin singlet and triplet states. In the second part, we discuss two possible singlet-triplet superconductors: CeRh$_2$As$_2$ a…
The discovery of multiple electronic orders in kagome superconductors AV3Sb5 (A = K, Rb, Cs) provides a promising platform for exploring unprecedented emergent physics. Under moderate pressure (< 2.2 GPa), the triple-Q charge density wave (CDW) order is monotonically suppressed by pressure, while the superconductivity displays a two-dome-like behavior, suggesting an unusual interplay between superconductivity and CDW order. Given that time-reversal symmetry breaking and electronic nematicity have been revealed inside the triple-Q CDW phase, understanding this CDW order and its interplay with s…
Resolving unconventional gap structure in kagome superconductors with hybrid microwave circuits
Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体和化学物理研究所）；Institute of Solid State and Material Physics, Technische Universität Dresden（德累斯顿工业大学固态与材料物理研究所）；Institute of Applied Physics, Technische Universität Dresden（德累斯顿工业大学应用物理研究所）；Leibniz Institute for Solid State and Materials Research Dresden（德累斯顿莱布尼茨固体与材料研究所）；Department of Physics, University of Naples Federico II（那不勒斯费德里科二世大学物理系）；Department of Electrical Engineering and Information Technology, University of Naples Federico II（那不勒斯费德里科二世大学电气与信息工程系）
We suggest that superconductivity (SC) in the organic charge transfer solids (CTS) is reached from a Bond-Charge Density Wave (BCDW). We discuss an effective model for the BCDW to SC transition, an attractive U extended Hubbard Hamiltonian with repulsive nearest neighbor interaction V. We discuss experimental consequences of the theory for different classes of CTS superconductors as well as related inorganic materials.
Recently, the superconductivity in a metal-organic framework (MOF) has been discovered for the first time in copper(II) benzenehexathiolate ([Cu$_3$(C$_6$S$_6$)]$_n$, Cu-BHT). The Cu atoms form a two-dimensional perfect Kagome lattice, which has the potential to host a metallic quantum spin liquid state. Here we present high-precision measurements of in-plane magnetic penetration depth $λ$ in Cu-BHT films down to 40\,mK. The temperature dependence of $λ$ shows a non-exponential, quasi-linear behavior at low temperatures, suggesting that unconventional superconductivity with low-energy quasipar…
Metal-organic frameworks (MOFs), which are self-assemblies of metal ions and organic ligands, provide a tunable platform to search a new state of matter. A two-dimensional (2D) perfect kagome lattice, whose geometrical frustration is a key to realizing quantum spin liquids, has been formed in the $π$-${d}$ conjugated 2D MOF [Cu$_{3}$(C$_{6}$S$_{6}$)]$_{n}$ (Cu-BHT). The recent discovery of its superconductivity with a critical temperature $T_{\rm c}$ of 0.25\,kelvin raises fundamental questions about the nature of electron pairing. Here, we show that Cu-BHT is a strongly correlated unconventio…
The kagome lattice, the most prominent structural motif in quantum physics, benefits from inherent nontrivial geometry to host diverse quantum phases, ranging from spin-liquid phases, topological matter to intertwined orders, and most rarely unconventional superconductivity. Recently, charge sensitive probes have suggested that the kagome superconductors AV_3Sb_5 (A = K, Rb, Cs) (A = K, Rb, Cs) exhibit unconventional chiral charge order, which is analogous to the long-sought-after quantum order in the Haldane model or Varma model. However, direct evidence for the time-reversal symmetry-breakin…
Direct Observation of Channelised Supercurrents in a Kagome Superconductor
Huygens-Kamerlingh Onnes Laboratory, Leiden University（莱顿大学休厄斯-卡末林·昂纳斯实验室）；University of California Santa Barbara（加州大学圣塔芭芭拉分校）；QuantaMap B.V.（QuantaMap有限公司）；Delft University of Technology（代尔夫特理工大学）；University of Zürich（苏黎世大学）；Ludwig-Maximilians-University Munich（慕尼黑路德维希-马克西米利安大学）
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）
Owing to its inherent non-trivial geometry, the unique structural motif of the recently discovered Kagome topological superconductor AV3Sb5 is an ideal host of diverse topologically non-trivial phenomena, including giant anomalous Hall conductivity, topological charge order, charge density wave, and unconventional superconductivity. Despite possessing a normal-state CDW order in the form of topological chiral charge order and diverse superconducting gaps structures, it remains unclear how fundamental atomic-level properties and many-body effects including Fermi surface nesting, electron-phonon…
The vanadium-based kagome superconductor CsV3Sb5 has attracted tremendous attention due to its unexcepted anomalous Hall effect (AHE), charge density waves (CDWs), nematicity, and a pseudogap pair density wave (PDW) coexisting with unconventional strong-coupling superconductivity (SC). The origins of CDWs, unconventional SC, and their correlation with different electronic states in this kagome system are of great significance, but so far, are still under debate. Chemical doping in the kagome layer provides one of the most direct ways to reveal the intrinsic physics, but remains unexplored. Her…
We study electron correlation driven superconductivity on a decorated honeycomb lattice (DHL), which has a low-energy flat band. On doping, we find singlet superconductivity with extended-s, extended-d and f-wave symmetry mediated by magnetic exchange. f-wave singlet pairing is enabled by the lattice decoration. The critical temperature is predicted to be significantly higher than on similar lattices lacking flat bands. We discuss how high-temperature superconductivity could be realized in the DHL materials such as Rb3TT. 2 H2O and Mo3S7(dmit)3.
A kagome lattice naturally features Dirac fermions, flat bands and van Hove singularities in its electronic structure. The Dirac fermions encode topology, flat bands favour correlated phenomena such as magnetism, and van Hove singularities can lead to instabilities towards long-range many-body orders, altogether allowing for the realization and discovery of a series of topological kagome magnets and superconductors with exotic properties. Recent progress in exploring kagome materials has revealed rich emergent phenomena resulting from the quantum interactions between geometry, topology, spin a…
We report muon spin rotation ($μ$SR) experiments together with first-principles calculations on microscopic properties of superconductivity in the kagome superconductor LaRu$_3$Si$_2$ with $T_{\rm c}$ ${\simeq}$ 7K. We find that the calculated normal state band structure features a kagome flat band and Dirac as well as van Hove points formed by the Ru-$dz^2$ orbitals near the Fermi level. Below $T_{\rm c}$, $μ$SR reveals isotropic type-II superconductivity, which is robust against hydrostatic pressure up to 2 GPa. Intriguingly, the ratio 2$Δ/k_{\rm B}T_{\rm c}$ ${\simeq}$ 4.3 (where $Δ$ is the…
The nature of superconductivity in newly discovered Kagome materials, $\text{AV}_3\text{Sb}_5$ (A=K, Rb, Cs), has been a subject of intense debate. Recent experiments suggest the presence of orbital current order on top of the charge density wave (CDW) and superconductivity. Since the orbital current order breaks time-reversal symmetry, it may fundamentally affect possible superconducting states. In this work, we investigate the mutual influence between the orbital current order and superconductivity in Kagome metal with characteristic van Hove singularity (vHS). By explicitly deriving the Lan…
As one of the most fundamental physical phenomena, the anomalous Hall effect (AHE) typically occurs in ferromagnetic materials but is not expected in the conventional superconductors. Here, we have observed a giant AHE in kagome superconductor CsV3Sb5 with transition temperature (Tc) of 2.7 K. The anomalous Hall conductivity reaches up to 2.1*10^4 Ω-1 cm-1 which is larger than those observed in most of the ferromagnetic metals. Strikingly, the emergence of AHE exactly follows the higher-temperature charge-density-wave (CDW) transition with TCDW ~ 94 K, indicating a strong correlation between t…
$A$V$_3$Sb$_5$ ($A$ = K, Rb, Cs) is a novel kagome superconductor coexisting with the charge density wave (CDW) order. Identifying the structure of the CDW order is crucial for understanding the exotic normal state and superconductivity in this system. Here, we report $^{51}$V nuclear magnetic resonance (NMR) and $^{121/123}$Sb nuclear quadrupole resonance (NQR) studies on kagome-metal CsV$_3$Sb$_5$. Below the CDW transition temperature $T_\textrm{CDW} \sim$ 98 K, an abrupt change of spectra was observed, indicating that the transition is of the first order. By further analysing the spectra, w…
Recently, intensive studies have revealed fascinating physics, such as charge density wave and superconducting states, in the newly synthesized kagome-lattice materials $A$V$_3$Sb$_5$ ($A$=K, Rb, Cs). Despite the rapid progress, fundamental aspects like the magnetic properties and electronic correlations in these materials have not been clearly understood yet. Here, based on the density functional theory plus the single-site dynamical mean-field theory calculations, we investigate the correlated electronic structure and the magnetic properties of the KV$_3$Sb$_5$ family materials in the normal…
A Strongly Anisotropic Superconducting Gap in the Kagome Superconductor CsV$_3$Sb$_5$: A Study of Directional Point-Contact Andreev Reflection Spectroscopy
The recently reported \textit{A}V$_3$Sb$_5$ (\textit{A} = K, Rb, Cs) family of kagome metals are candidates for unconventional superconductivity and chiral charge density wave (CDW) order; both potentially arise from nested saddle points in their band structures close to the Fermi energy. Here we use chemical substitution to introduce holes into CsV$_3$Sb$_{5}$ and unveil an unconventionalcoupling of the CDW and superconducting states. Specifically, we generate a phase diagram for CsV$_3$Sb$_{5-x}$Sn$_{x}$ that illustrates the impact of hole-doping the system and lifting the nearest vHs toward…
Discovery of parity-violating chiral polar-nematic charge density wave and superconductivity in kagome metals
Beijing National Center for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Hefei National Laboratory（合肥国家实验室）；Department of Physics, Boston College（波士顿学院物理系）；Department of Applied Physics, The Hong Kong Polytechnic University（香港理工大学应用物理系）；Department of Chemistry, National University of Singapore（新加坡国立大学化学系）
Unconventional superconductors often feature competing orders, small superfluid density, and nodal electronic pairing. While unusual superconductivity has been proposed in the kagome metals AV3Sb5, key spectroscopic evidence has remained elusive. Here we utilize pressure-tuned (up to 1.85 GPa) and ultra-low temperature (down to 18 mK) muon spin spectroscopy to uncover the unconventional nature of superconductivity in RbV3Sb5. At ambient pressure, we detect an enhancement of the width of the internal magnetic field distribution sensed by the muon ensemble, indicative of time-reversal symmetry b…
We analyze the transport properties of contacts between unconventional superconductor and normal diffusive metal in the framework of the extended circuit theory. We obtain a general boundary condition for the Keldysh-Nambu Green's functions at the interface that is valid for arbitrary transparencies of the interface. This allows us to investigate the voltage-dependent conductance (conductance spectrum) of a diffusive normal metal (DN)/ unconventional singlet superconductor junction in both ballistic and diffusive cases. For d-wave superconductor, we calculate conductance spectra numerically fo…
The quasi two-dimensional (quasi-2D) kagome materials AV$_3$Sb$_5$ (A=K, Rb, Cs) were found to be a prime example of kagome superconductors, a new quantum platform to investigate the interplay between electron correlation effects, topology and geometric frustration. In this review, we report recent progress on the experimental and theoretical studies of AV$_3$Sb$_5$ and provide a broad picture of this fast-developing field in order to stimulate an expanded search for unconventional kagome superconductors. We review the electronic properties of AV$_3$Sb$_5$, the experimental measurements of the…
Layered kagome metals AV3Sb5 (A=K, Rb, Cs) exhibit diverse correlated electron phenomena. It includes charge density wave formation and superconductivity the pairing symmetry of which, however, is controversial due to contradictory experimental evidence. Through calculations based on real-space lattice models at the mean-field level, we investigate the vortex and surface spectra of all competitive pairing propensities suggested for AV3Sb5 from a weak coupling analysis of unconventional superconductivity. Chiral p-wave pairing emerges as the only option to host Majorana bound states in the vort…
We present a general theory of the proximity effect in junctions between diffusive normal metals (DN) and unconventional superconductors in the framework of the quasiclassical Green's function formalism. Various possible symmetry classes in a superconductor are considered which are consistent with the Pauli principle: even-frequency spin-singlet even-parity (ESE) state, even-frequency spin-triplet odd-parity (ETO) state, odd-frequency spin-triplet even-parity (OTE) state and odd-frequency spin-singlet odd-parity (OSO) state. For each of the above four cases symmetry and spectral properties of …
