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The recent discovery of a superconductivity signature in La3Ni2O7-{\delta} under a pressure of 14 GPa, with a superconducting transition temperature of around 80 K, has attracted considerable attention. An important aspect of investigating electronic structures is discerning the extent to which the electronic ground state of La3Ni2O7-{\delta} resembles the parent state of the cuprate superconductor, a charge transfer insulator with long-range antiferromagnetism. Through X-ray absorption spectroscopy, we have uncovered the crucial influence of oxygen ligands on the electronic ground states of the Ni ions, displaying a charge transfer nature akin to cuprate but with distinct orbital configurations. Both in-plane and out-of-plane Zhang-Rice singlets associated with Ni d_(x^2-y^2 ) and d_(z^2) orbitals are identified, together with a strong interlayer coupling through inner apical oxygen. Additionally, in La3Ni2O7-{\delta} films, we have detected a superlattice reflection (1/4, 1/4, L) at the Ni L absorption edge using resonant X-ray scattering measurements. Further examination of the resonance profile indicates that the reflection originates from the Ni d orbitals. By evaluating the reflection's azimuthal angle dependence, we have confirmed the presence of collinear antiferromagnetic spin ordering and charge-like anisotropy ordered with the same periodicity. Notably, our findings reveal a microscopic relationship between these two components in the temperature dependence of the scattering intensity of the reflection. This investigation enriches our understanding of high-temperature superconductivity in La3Ni2O7-{\delta} under high pressure.

Superconductivity and magnetism are antagonistic quantum matter, while their intertwining has long been considered in frustrated-lattice systems1-3. In this work, we utilize scanning tunneling microscopy and muon spin resonance to discover time-reversal symmetry-breaking superconductivity in kagome metal Cs(V,Ta)3Sb5, where the Cooper pairing exhibits magnetism and is modulated by it. In the magnetic channel, we observe spontaneous internal magnetism in a full-gap superconducting state. Under perturbations of inverse magnetic fields, we detect a time-reversal asymmetrical interference of Bogoliubov quasi-particles at a circular vector. At this vector, the pairing gap spontaneously modulates, which is distinct from pair density waves occurring at a point vector and consistent with the theoretical proposal of unusual interference effect under time-reversal symmetry-breaking. The correlation between internal magnetism, Bogoliubov quasi-particles, and pairing modulation provides a chain of experimental clues for time-reversal symmetry-breaking kagome superconductivity., Comment: To appear in Nature Materials (2024)

Superconductivity involving finite momentum pairing can lead to spatial gap and pair density modulations, as well as Bogoliubov Fermi states within the superconducting gap. However, the experimental realization of their intertwined relations has been challenging. Here, we detect chiral kagome superconductivity modulations with residual Fermi arcs in KV3Sb5 and CsV3Sb5 by normal and Josephson scanning tunneling microscopy down to 30mK with resolved electronic energy difference at microelectronvolt level. We observe a U-shaped superconducting gap with flat residual in-gap states. This gap exhibits chiral 2 by 2 spatial modulations with magnetic field tunable chirality, which align with the chiral 2 by 2 pair density modulations observed through Josephson tunneling. These findings demonstrate a chiral pair density wave (PDW) that breaks time-reversal symmetry. Quasiparticle interference imaging of the in-gap zero-energy states reveals segmented arcs, with high-temperature data linking them to parts of the reconstructed V d-orbital states within the charge order. The detected residual Fermi arcs can be explained by the partial suppression of these d-orbital states through an interorbital 2 by 2 PDW and thus serve as candidate Bogoliubov Fermi states. Additionally, we differentiate the observed PDW order from impurity-induced gap modulations. Our observations not only uncover a chiral PDW order with orbital-selectivity, but also illuminate the fundamental space-momentum correspondence inherent in finite momentum paired superconductivity., Comment: To appear in Nature (2024)

Recent experiments have identified fascinating electronic orders in kagome materials, including intriguing superconductivity, charge density wave (CDW) and nematicity. In particular, some experimental evidence for AV$_3$Sb$_5$ (A = K,Rb,Cs) and related kagome metals hints at the formation of orbital currents in the charge density wave ordered regime, providing a mechanism for spontaneous time-reversal symmetry breaking in the absence of local moments. In this work, we comprehensively explore the competitive charge instabilities of the spinless kagome lattice with inter-site Coulomb interactions at the pure-sublattice van Hove filling. From the analysis of the charge susceptibility, we find that, at the nesting vectors, while the onsite charge order is dramatically suppressed, the bond charge orders are substantially enhanced owing to the sublattice texture on the hexagonal Fermi surface. Furthermore, we demonstrate that nearest-neighbor and next nearest-neighbor bonds are characterized by significant intrinsic real and imaginary bond fluctuations, respectively. The 2$\times$2 loop current order is thus favored by the next nearest-neighbor Coulomb repulsion. Interestingly, increasing interactions further leads to a nematic state with intra-cell sublattice density modulation that breaks the $C_6$ rotational symmetry. We further explore superconducting orders descending from onsite and bond charge fluctuations, and discuss our model's implications on the experimental status quo.

In the recently discovered kagome superconductor AV3Sb5 (A = K, Rb, and Cs), the superconductivity is intertwined with an unconventional charge density wave order. Its pairing symmetry remains elusive owing to the lack of direct measurement of the superconducting gap in the momentum space. In this letter, utilizing laser-based ultra-high-resolution and low-temperature angle-resolved photoemission spectroscopy, we observe anisotropic Cooper pairing in kagome superconductor CsV3Sb5. We detect a highly anisotropic superconducting gap structure with an anisotropy over 80% and the gap maximum along the V-V bond direction on a Fermi surface originated from the 3d-orbital electrons of the V kagome lattice. It is in stark contrast to the isotropic superconducting gap structure on the other Fermi surface that is occupied by Sb 5p-orbital electrons. Our observation of the anisotropic Cooper pairing in pristine CsV3Sb5 is fundamental for understanding intertwined orders in the ground state of kagome superconductors.

The recent observation of high-T$_c$ superconductivity in the bilayer nickelate La$_3$Ni$_2$O$_7$ under pressure has garnered significant interests. While researches have predominantly focused on the role of electron-electron interactions in the superconducting mechanism, the impact of electron-phonon coupling (EPC) has remained elusive. In this work, we perform first-principles calculations to study the phonon spectrum and electron-phonon coupling within La$_3$Ni$_2$O$_7$ under pressure and explore of the interplay between EPC and electronic interactions on the superconductivity by employing functional renormalization group approach. Our calculations reveal that EPC alone is insufficient to trigger superconductivity in La$_3$Ni$_2$O$_7$ under pressure. We identify unique out-of-plane and in-plane breathing phonon modes which selectively couple with the Ni $d_{z^2}$ and $d_{x^2-y^2}$ orbitals, showcasing an orbital-selective EPC. Within the bilayer two-orbital model, it is revealed that solely electronic interactions foster $s_{\pm}$-wave pairing characterized by notable frustration in the band space, leading to a low transition temperature. Remarkably, we find that this out-of-plane EPC can act in concert with electronic interactions to promote the onsite and interlayer pairing in the $d_{z^2}$ orbital, partially releasing the pairing frustration and thus elevating T$_c$. In contrast, the inclusion of in-plane EPC only marginally affects the superconductivity, distinct from the cuprates. Potential experimental implications in La$_3$Ni$_2$O$_7$ are also discussed., Comment: 6 pages, 4 figures

When two different electronic materials are brought together, the resultant interface often shows unexpected quantum phenomena, including interfacial superconductivity and Fu-Kane topological superconductivity (TSC). Here, we use molecular beam epitaxy (MBE) to synthesize heterostructures formed by stacking together two magnetic materials, a ferromagnetic topological insulator (TI) and an antiferromagnetic iron chalcogenide (FeTe). We discover emergent interface-induced superconductivity in these heterostructures and demonstrate the trifecta occurrence of superconductivity, ferromagnetism, and topological band structure in the magnetic TI layer, the three essential ingredients of chiral TSC. The unusual coexistence of ferromagnetism and superconductivity can be attributed to the high upper critical magnetic field that exceeds the Pauli paramagnetic limit for conventional superconductors at low temperatures. The magnetic TI/FeTe heterostructures with robust superconductivity and atomically sharp interfaces provide an ideal wafer-scale platform for the exploration of chiral TSC and Majorana physics, constituting an important step toward scalable topological quantum computation., Comment: 14 pages, 4 figures. Accepted by Science. Comments are welcome

Quantum materials whose atoms are arranged on a lattice of corner-sharing triangles, $\textit{i.e.}$, the kagome lattice, have recently emerged as a captivating platform for investigating exotic correlated and topological electronic phenomena. Here, we combine ultra-low temperature angle-resolved photoemission spectroscopy (ARPES) with scanning tunneling microscopy and density functional theory calculations to reveal the fascinating electronic structure of the bilayer-distorted kagome material $\textit{Ln}$Ti${_3}$Bi${_4}$, where $\textit{Ln}$ stands for Nd and Yb. Distinct from other kagome materials, $\textit{Ln}$Ti${_3}$Bi${_4}$ exhibits two-fold, rather than six-fold, symmetries, stemming from the distorted kagome lattice, which leads to a unique electronic structure. Combining experiment and theory we map out the electronic structure and discover double flat bands as well as multiple van Hove singularities (VHSs), with one VHS exhibiting higher-order characteristics near the Fermi level. Notably, in the magnetic version NdTi${_3}$Bi${_4}$, the ultra-low base temperature ARPES measurements unveil an unconventional band splitting in the band dispersions which is induced by the ferromagnetic ordering. These findings reveal the potential of bilayer-distorted kagome metals $\textit{Ln}$Ti${_3}$Bi${_4}$ as a promising platform for exploring novel emergent phases of matter at the intersection of strong correlation and magnetism.

Over the last decade, the possibility of realizing topological superconductivity (TSC) has generated much excitement, mainly due to the potential use of its excitations (Majorana zero modes) in a fault-tolerant topological quantum computer 1,2. TSC can be created in electronic systems where the topological and superconducting orders coexist3, motivating the continued exploration of candidate material platforms to this end. Here, we use molecular beam epitaxy (MBE) to synthesize heterostructures that host emergent interfacial superconductivity when a non-superconducting antiferromagnet (FeTe) is interfaced with a topological insulator (TI) (Bi, Sb)2Te3 wherein the chemical potential can be tuned through varying the Bi/Sb ratio. By performing in-vacuo angle-resolved photoemission spectroscopy (ARPES) and ex-situ electrical transport measurements, we find that the superconducting transition temperature and the upper critical magnetic field are suppressed when the chemical potential approaches the Dirac point. This observation implies a direct correlation between the interfacial superconductivity and Dirac electrons of the TI layer. We provide evidence to show that the observed interfacial superconductivity and its chemical potential dependence is the result of the competition between the Ruderman-Kittel-Kasuya-Yosida-type ferromagnetic coupling mediated by Dirac surface states and antiferromagnetic exchange couplings that generate the bicollinear antiferromagnetic order in the FeTe layer. The Dirac-fermion-assisted interfacial superconductivity in (Bi,Sb)2Te3/FeTe heterostructures provides a new approach to probe TSC and Majorana physics in hybrid devices and potentially constitutes an alternative platform for topological quantum computation., Comment: 32 pages and 4 figures. Accepted by Nature Communications

At magic twisted angles, Dirac cones in twisted bilayer graphene (TBG) can evolve into flat bands, serving as a critical playground for the study of strongly correlated physics. When chiral symmetry is introduced, rigorous mathematical proof confirms that the flat bands are locked at zero energy in the entire Moir\'e Brillouin zone (BZ). Yet, TBG is not the sole platform that exhibits this absolute band flatness. Central to this flatness phenomenon are topological nodes and their specific locations in the BZ. In this study, considering twisted bilayer systems that preserve chiral symmetry, we classify various ordered topological nodes in base layers and all possible node locations across different BZs. Specifically, we constrain the node locations to rotational centers, such as {\Gamma} and M points, to ensure the interlayer coupling retains equal strength in all directions. Using this classification as a foundation, we systematically identify the conditions under which Moir\'e flat bands emerge. Additionally, through the extension of holomorphic functions, we provide proof that flat bands are locked at zero energy, shedding light on the origin of the band flatness. Remarkably, beyond Dirac cones, numerous twisted bilayer nodal platforms can host flat bands with a degeneracy number of more than two, such as four-fold, six-fold, and eight-fold. This multiplicity of degeneracy in flat bands might unveil more complex and enriched correlation physics., Comment: 13 pages, 10 figures, 2 tables

The recently discovered layered kagome superconductors $\textit{A}$V$_{3}$Sb$_{5}$ ($\textit{A}$ = K, Rb, Cs) have garnered significant attention, as they exhibit an intriguing combination of superconductivity, charge density wave (CDW) order, and nontrivial band topology. As such, these kagome systems serve as an exceptional quantum platform for investigating the intricate interplay between electron correlation effects, geometric frustration, and topological electronic structure. A comprehensive understanding of the underlying electronic structure is crucial for unveiling the nature and origin of the CDW order, as well as determining the electron pairing symmetry in the kagome superconductors. In this review, we present a concise survey of the electronic properties of $\textit{A}$V$_{3}$Sb$_{5}$, with a particular focus on the insights derived from angle-resolved photoemission spectroscopy (ARPES). Through the lens of ARPES, we shed light on the electronic characteristics of the kagome superconductors $\textit{A}$V$_{3}$Sb$_{5}$, which will pave the way for exciting new research frontiers in kagome-related physics.

Since the discovery of cuprate, the origin of high-T$_c$ superconductivity has been an outstanding puzzle. Recently, high-T$_c$ superconductivity was observed in a bilayer nickelate La$_3$Ni$_2$O$_7$ under pressure, whose structure hosts the apical oxygen between two layers, distinct from multi-layer cuprates. Motivated by this discovery, we investigate its electronic structure using first-principle calculations and superconducting instabilities from both weak-coupling and strong-coupling perspective. Based on the first-principle band structures, we construct a bilayer two-orbital model on a square lattice, consisting of $d_{x^2-y^2}$ and $d_{z^2}$ orbitals, which accurately captures the low-energy electronic properties. Within this model, we study pairing instability using both functional renormalization group approach and multi-orbital t-J model. An $s_{\pm}$-wave pairing with sign-reversal gaps on different Fermi surfaces is revealed, reminiscent of iron based superconductors. The Ni-$d_{z^2}$ orbital and its associated interlayer and intralayer exchange couplings are found to be crucial for the high-T$_c$ superconductivity. Our study provides valuable insights into unique nature of electronic structure and superconductivity in La$_3$Ni$_2$O$_7$ and contributes to the understanding of unconventional superconductors., Comment: 5 pages, 4 figures + SM

We investigate topological superconductivity in the Rashba-Hubbard model, describing heavy-atom superlattice and van der Waals materials with broken inversion. We focus in particular on fillings close to the van Hove singularities, where a large density of states enhances the superconducting transition temperature. To determine the topology of the superconducting gaps and to analyze the stability of their surface states in the presence of disorder and residual interactions, we employ an fRG+MFT approach, which combines the unbiased functional renormalization group (fRG) with a real-space mean-field theory (MFT). Our approach uncovers a cascade of topological superconducting states, including $A_1$ and $B_1$ pairings, whose wave functions are of dominant $p$- and $d$-wave character, respectively, as well as a time-reversal breaking $A_1 + i B_1$ pairing. While the $A_1$ and $B_1$ states have first order topology with helical and flat-band Majorana edge states, respectively, the $A_1 + i B_1$ pairing exhibits second-order topology with Majorana corner modes. We investigate the disorder stability of the bulk superconducting states, analyze interaction-induced instabilites of the edge states, and discuss implications for experimental systems.

Charge density wave (CDW) orders in vanadium-based kagome metals have recently received tremendous attention due to their unique properties and intricate interplay with exotic correlated phenomena, topological and symmetry-breaking states. However, the origin of the CDW order remains a topic of debate. The discovery of ScV$_{6}$Sn$_{6}$, a vanadium-based bilayer kagome metal exhibiting an in-plane $\sqrt{3}$ x $\sqrt{3} $ $\textit{R}$30${\deg}$ CDW order with time-reversal symmetry breaking, provides a novel platform to explore the underlying mechanism behind the unconventional CDW. Here, we combine high-resolution angle-resolved photoemission spectroscopy, Raman scattering measurements and density functional theory to investigate the electronic structures and phonon modes of ScV$_{6}$Sn$_{6}$ and their evolution with temperature. We identify topologically nontrivial Dirac surface states and multiple van Hove singularities (VHSs) in the vicinity of the Fermi level, with one VHS near the K point exhibiting nesting wave vectors in proximity to the $\sqrt{3}$ x $\sqrt{3}$ $\textit{R}$30${\deg}$ CDW wave vector. Additionally, Raman measurements indicate a strong intrinsic electron-phonon coupling in ScV$_{6}$Sn$_{6}$, as evidenced by the presence of a two-phonon mode and a large frequency amplitude mode. Our findings highlight the fundamental role of lattice degrees of freedom in promoting the CDW in ScV$_{6}$Sn$_{6}$ and provide important insights into the fascinating correlation phenomena observed in kagome metals.

Type-II Dirac semimetals exhibit a unique Fermi surface topology, which allows them to host novel topological superconductivity (TSC). We reveal a novel inter-orbital superconducting state, corresponding to the B1u and B2u pairings under the D4h point group. Intriguingly, we find that both first- and second-order TSC coexist in this novel state. It is induced by a dominant inter-orbital attraction and possesses surface helical Majorana cones and hinge Majorana flat bands, spanning the entire z-directed hinge Brillouin zone. Further investigation uncovers that these higher-order hinge modes are robust against the C4z symmetry-breaking perturbation., Comment: published version

Exciton-polaritons resulting from the strong exciton-photon interaction stimulate the development of novel coherent light sources with low threshold, long range spatial, and temporal coherence to circumvent the ever increasing energy demands of optical communications. Polaritons from bound states in the continuum (BICs) are promising for Bose-Einstein condensation owing to their infinite quality factors that enlarge photon lifetimes and benefit polariton accumulations. However, BIC polariton condensation remains limited to cryogenic temperatures ascribed to the small exciton binding energies of conventional material platforms. Herein, we demonstrated a room-temperature BIC polaritonic platform based on halide perovskite air-hole photonic crystals, profiting from the non-radiative BIC states and stable excitons of cesium lead bromide. BIC polariton condensation was achieved near the dispersion minimum that generates directional vortex beam emission with long-range coherence. Our work provides a significant basis for the applications of polariton condensates for integrated photonic and topological circuits., Comment: 16 pages,4 figures

We derive two fundamental laws of chiral band crossings: (i) a local constraint relating the Chern number to phase jumps of rotation eigenvalues; and (ii) a global constraint determining the number of chiral crossings on rotation axes. Together with the fermion doubling theorem, these laws describe all conditions that a network of chiral band crossing must satisfy. We apply the fundamental laws to prove the existence of enforced double Weyl points, nodal planes, and generic Weyl points, among others. In addition, we show that chiral space-group symmetries cannot stabilize nodal lines with finite Chern numbers. Combining the local constraint with explicit low-energy models, we determine the generic topological phase diagrams of all multi-fold crossings. Remarkably, we find a four-fold crossing with Chern number 5, which exceeds the previously conceived maximum Chern number of 4. We identify BaAsPt as a suitable material with this four-fold crossing exhibiting Chern number 5 near the Fermi energy., Comment: 34 pages, 16 figures

The newly discovered kagome superconductors represent a promising platform for investigating the interplay between band topology, electronic order, and lattice geometry. Despite extensive research efforts on this system, the nature of the superconducting ground state remains elusive. In particular, consensus on the electron pairing symmetry has not been achieved so far, in part owing to the lack of a momentum-resolved measurement of the superconducting gap structure. Here we report the direct observation of a nodeless, nearly isotropic, and orbital-independent superconducting gap in the momentum space of two exemplary CsV$_3$Sb$_5$-derived kagome superconductors -- Cs(V$_{0.93}$Nb$_{0.07}$)$_3$Sb$_5$ and Cs(V$_{0.86}$Ta$_{0.14}$)$_3$Sb$_5$, using ultrahigh resolution and low-temperature angle-resolved photoemission spectroscopy (ARPES). Remarkably, such a gap structure is robust to the appearance or absence of charge order in the normal state, tuned by isovalent Nb/Ta substitutions of V. Moreover, we observe a signature of the time-reversal symmetry (TRS) breaking inside the superconducting state, which extends the previous observation of TRS-breaking CDW in the kagome lattice. Our comprehensive characterizations of the superconducting state provide indispensable information on the electron pairing of kagome superconductors, and advance our understanding of unconventional superconductivity and intertwined electronic orders.

The recently discovered vanadium-based Kagome metals $A$V$_{3}$Sb$_{5}$ ($A = \text{K, Rb, Cs}$) are of great interest with the interplay of charge density wave (CDW) order, band topology and superconductivity. In this paper, by identifying elementary band representations (EBRs), we construct a two-EBR graphene-Kagome model to capture the two low-energy van-Hove-singularity dispersions and, more importantly, the nontrivial band topology in these Kagome metals. This model consists of $A_g@3g$ (V-$d_{x^2-y^2/z^2}$, Kagome sites) and $A_2''@2d$ EBRs (Sb1-$p_z$, honeycomb sites). We have investigated the Fermi surface instability by calculating the electronic susceptibility $\chi(\mathbf{q})$. Prominent Fermi-surface nesting peaks are obtained at three L points, where the $z$ component of the nesting vector shows intimate relationship with the anticrossing point along M--L. The nesting peaks at L are consistent with the $2\times 2\times 2$ CDW reconstruction in these compounds. In addition, the sublattice-resolved bare susceptibility is calculated and similar sharp peaks are observed at the L points, indicating a strong antiferromagnetic fluctuation. Assuming a bulk $s$-wave superconducting pairing, helical surface states and nontrivial superconducting gap are obtained on the (001) surface. In analogous to FeTe$_{1-x}$Se$_{x}$ superconductor, our results establish another material realization of a stoichiometric superconductor with nontrivial band topology, providing a promising platform for studying exotic Majorana physics in condensed matter

Van Hove singularities (VHSs) in proximity to the Fermi level promote electronic interactions and generate diverse competing instabilities. It is also known that a nontrivial Berry phase derived from spin-orbit coupling (SOC) can introduce an intriguing decoration into the interactions and thus alter correlated phenomena. However, it is unclear how and what type of new physics can emerge in a system featured by the interplay between VHSs and the Berry phase. Here, based on a general Rashba model on the square lattice, we comprehensively explore such an interplay and its significant influence on the competing electronic instabilities by performing a parquet renormalization group analysis. Despite the existence of a variety of comparable fluctuations in the particle-particle and particle-hole channels associated with higher-order VHSs, we find that the chiral $p \pm ip$ pairings emerge as two stable fixed trajectories within the generic interaction parameter space, namely the system becomes a robust topological superconductor. The chiral pairings stem from the hopping interaction induced by the nontrivial Berry phase. The possible experimental realization and implications are discussed. Our work sheds new light on the correlated states in quantum materials with strong SOC and offers fresh insights into the exploration of topological superconductivity., Comment: 6 pages, 4 figures

Motivated by the experimental identification of a higher-order van Hove singularity (VHS) in AV$_3$Sb$_5$ kagome metals, we study electronic instabilities of 2D lattice models with higher-order VHS and flavor degeneracy. In contrast to conventional VHSs, the larger power-law density of states and the weaker nesting propensity of higher-order VHSs conspire together to generate distinct competing instabilities. After discussing the occurrence of higher-order VHSs on square and kagome lattice models, we perform unbiased renormalization group calculations to study competing instabilities and find a rich phase diagram containing ferromagnetism, anti-ferromagnetism, superconductivity and Pomeranchuk orders. Remarkably, there is a generic transition from superconductivity to a $d$-wave Pomeranchuk order with increasing flavor number. Implications for the intriguing quantum states of AV$_3$Sb$_5$ kagome metals are also discussed., Comment: 14 pages, 10 figures

Electronic nematicity that spontaneously breaks rotational symmetry has been shown as a generic phenomenon in correlated quantum systems including high-temperature superconductors and the AV3Sb5 (A = K, Rb, Cs) family with a kagome network. Identifying the driving force has been a central challenge for understanding nematicity. In iron-based superconductors, the problem is complicated because the spin, orbital and lattice degrees of freedom are intimately coupled. In vanadium-based kagome superconductors AV3Sb5, the electronic nematicity exhibits an intriguing entanglement with the charge density wave order (CDW), making understanding its origin difficult. Recently, a new family of titanium-based kagome superconductors ATi3Bi5 has been synthesized. In sharp contrast to its vanadium-based counterpart, the electronic nematicity occurs in the absence of CDW. ATi3Bi5 provides a new window to explore the mechanism of electronic nematicity and its interplay with the orbital degree of freedom. Here, we combine polarization-dependent angle-resolved photoemission spectroscopy with density functional theory to directly reveal the band topology and orbital characters of the multi-orbital RbTi3Bi5. The promising coexistence of flat bands, type-II Dirac nodal line and nontrivial Z2 topological states is identified in RbTi3Bi5. Remarkably, our study clearly unveils the orbital character change along the G-M and G-K directions, implying a strong intrinsic inter-orbital coupling in the Ti-based kagome metals, reminiscent of iron-based superconductors. Furthermore, doping-dependent measurements directly uncover the orbital-selective features in the kagome bands, which can be well explained by the d-p hybridization. The suggested d-p hybridization, in collaboration with the inter-orbital coupling, could account for the electronic nematicity in ATi3Bi5.

The origin of the high temperature superconductivity in the iron-based superconductors remains elusive after being extensively studied for more than a decade. Determination of the pairing symmetry is essential in understanding the superconductivity mechanism. In the iron-based superconductors that have hole pockets around the Brillouin zone center and electron pockets around the zone corners, the pairing symmetry is generally considered to be s$_\pm$, endowing a sign change in the superconducting gap between the hole and electron pockets. For the iron-based superconductors with only hole pockets, however, a couple of pairing scenarios have been proposed but the exact symmetry is still highly controversial. Here we report our determination of the pairing symmetry in KFe$_2$As$_2$ which is a prototypical iron-based superconductor with hole pockets both around the zone center and around the zone corners. By taking laser-based angle resolved photoemission measurements with super-high resolution and at ultra-low temperature, we have precisely determined the superconducting gap distribution and identified the locations of the gap nodes on all the Fermi surface around the zone center and the zone corners. The complete superconducting gap structure, in combination with the observation of the spin resonance in neutron scattering, provides strong evidence on the s$_\pm$ pairing symmetry in KFe$_2$As$_2$ with a gap sign reversal between the hole pockets around the zone center and the hole pockets around the zone corners. These results unify the pairing symmetry in the hole-doped iron-based superconductors and point to the spin fluctuation as the pairing glue in generating superconductivity.

Twisted bilayer graphene (TBG) can host the moir\'{e} energy flat bands with two-fold degeneracy serving as a fruitful playground for strong correlations and topological phases. However, the number of degeneracy is not limited to two. Introducing a spatially alternative magnetic field, we report that the induced magnetic phase becomes an additional controllable parameter and leads to an undiscovered generation of four-fold degenerate flat bands. This emergence stems from the band inversion at $\Gamma$ point near the Fermi level with a variation of both twisted angle and magnetic phase. We present the conditions for the emergence of multi-fold degenerate flat bands, which are associated with the eigenvalue degeneracy of a Birman-Schwinger operator. Using holomorphic functions, which explain the origin of the double flat bands in the conventional TBG, we can generate analytical wave functions in the magnetic TBG to show absolute flatness with four-fold degeneracy. Moreover, we identify an orbital-related intervalley coherent state as the many-body ground state at charge neutrality. In contrast, the conventional TBG has only two moir\'{e} energy flat bands, and the highly degenerate flat bands with additional orbital channels in this magnetic platform might bring richer correlation physics., Comment: 15 pages and 8 figures

We study electron-electron and electron-phonon mediated pairing in the Holstein extended Hubbard model on the Kagome lattice near the van Hove fillings, and investigate their combined effects on electron pairing states. We find that their combination can promote exotic pairings in a crossover region, where the filling is close to a van Hove singularity. In particular, at the $p$-type van Hove filling the $E_{1u}$ ($p$-wave) and $B_{2u}$ ($f_{y^3-3yx^2}$-wave) pairings become leading, and at the $m$-type van Hove filling the $E_{1u}$ and $A_{2g}$ ($i$-wave) pairings get promoted. Moreover, we show that the electron-phonon interaction acquires a significant momentum dependence, due to the sublattice texture of the Fermi surfaces, which can promote non $s$-wave pairing. We present a detailed analysis of these pairing propensities and discuss implications for the vanadium-based kagome superconductors AV$_3$Sb$_5$., Comment: 15 pages, 16 figures

We study the quasiparticle interference (QPI) pattern emanating from a pair of adjacent impurities on the surface of a gapped superconductor (SC). We find that hyperbolic fringes (HF) in the QPI signal can appear due to the loop contribution of the two-impurity scattering, where the location of the two impurities are the hyperbolic focus points. For a single pocket Fermiology, an HF pattern signals chiral SC order for non-magnetic impurities and requires magnetic impurities for non-chiral SC. For a multi-pocket scenario, a sign-changing order parameter such as $s_{\pm}$-wave likewise yields an HF signature. We discuss twin impurity QPI as a new tool to complement the analysis of superconducting order from local spectroscopy.

Transition-metal-based kagome materials at van Hove filling are a rich frontier for the investigation of novel topological electronic states and correlated phenomena. To date, in the idealized two-dimensional kagome lattice, topologically nontrivial Dirac surface states (TDSSs) have not been unambiguously observed, and the manipulation of TDSSs and van Hove singularities (VHSs) remains largely unexplored. Here, we reveal TDSSs originating from a Z${_2}$ bulk topology and identify multiple VHSs near the Fermi level ($\textit{E}$${_F}$) in magnetic kagome material GdV${_6}$Sn${_6}$. Using in-situ surface potassium deposition, we successfully realize manipulation of the TDSSs and VHSs. The Dirac point of the TDSSs can be tuned from above to below ($\textit{E}$${_F}$), which reverses the chirality of the spin texture at the Fermi surface. These results establish GdV${_6}$Sn${_6}$ as a fascinating platform for studying the nontrivial topology, magnetism and correlation effects native to kagome lattices. They also suggest potential application of spintronic devices based on kagome materials.

Here we report on a new kind of compound, X{\delta}Ir4X12-{\delta} (X = P, As), the first hole-doped skutterudites superconductor. We provide atomic resolution images of the caging As atoms using scanning transmission electron microscopy (STEM). By inserting As atoms into the caged structure under a high pressure, superconductivity emerges with a maximum transition temperature (Tc) of 4.4 K (4.8 K) in IrAs3 (IrP3). In contrast to all of the electron-doped skutterudites, the electronic states around the Fermi level in X{\delta}Ir4X12-{\delta} are dominated by the caged X atom, which can be described by a simple body-centered tight-binding model, implying a distinct paring mechanism. Our density functional theory (DFT) calculations reveal an intimate relationship between the pressure-dependent local-phonon mode and the enhancement of Tc. The discovery of X{\delta}Ir4X12-{\delta} provides an arena to investigate the uncharted territory of hole-doped skutterudites, and the method proposed here represents a new strategy of carrier doping in caged structures, without introducing extra elements., Comment: 14 pages, 4 figures, 1 table

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 vortex core. We find chiral edge states for both p-wave and d-wave pairing, along with flat Andreev surface bound states for f -wave pairing. Our results expand the fingerprint of superconducting pairing, and thus will contribute to resolving the nature of superconductivity in AV3Sb5., Comment: 7 pages, 8 figures

The recently discovered layered kagome metals AV$_3$Sb$_5$(A=K, Rb, Cs) have attracted much attention because of their unique combination of superconductivity, charge density wave (CDW) order, and nontrivial band topology. The CDW order with an in-plane 2x2 reconstruction is found to exhibit exotic properties, such as time-reversal symmetry breaking and rotational symmetry breaking. However, the nature of the CDW, including its dimensionality, structural pattern, and effect on electronic structure, remains elusive despite intense research efforts. Here, using angle-resolved photoemission spectroscopy, we unveil for the first time characteristic double-band splittings and band reconstructions, as well as the band gap resulting from band folding, in the CDW phase. Supported by density functional theory calculations, we unambiguously show that the CDW in AV$_3$Sb$_5$ originates from the intrinsic coexistence of Star-of-David and Tri-Hexagonal distortions. The alternating stacking of these two distortions naturally leads to three-dimensional 2x2x2 or 2x2x4 CDW order. Our results provide crucial insights into the nature and distortion pattern of the CDW order, thereby laying down the basis for a substantiated understanding of the exotic properties in the family of AV$_3$Sb$_5$ kagome metals.

The recently discovered AV3Sb5 (A=K, Rb, Cs) family, possessing V kagome nets, has received considerable attention due to the topological electronic structure and intriguing correlated phenomena, including an exotic charge density wave (CDW) and superconductivity. Detailed electronic structure studies are essential to unravel the characteristics and origin of the CDW as well as its interplay with superconductivity. Here, we present angle-resolved photoemission spectroscopy (ARPES) measurements for CsV3Sb5 at multiple temperatures and photon energies to reveal the nature of the CDW from an electronic structure perspective. We present evidence for a three-dimensional (3D) CDW order. In the process we also pinpoint a surface state attributed to a Cs terminated surface. This state was previously attributed to band folding band due to a CDW along the c direction or a quantum well state from quantum confinement. The CDW expected 2-fold lattice reconstruction along c axis is observed to be a quadrupling of the unit cell, thus for the first time directly demonstrating the 3D nature of the CDW from the electronic structure perspective. Moreover, this 3D CDW configuration originates from two distinct types of distortions in adjacent kagome layers. These present results not only provide key insights into the nature of the unconventional CDW in CsV3Sb5 but also provides an important reference for further studies on the relationship between the CDW and superconductivity., Comment: 19 pages, 4 figures

The recently synthesized air-insensitive hydrogen doped KCr$_3$As$_3$ superconductor has aroused great research interests. This material has, for the first time in the research area of the quasi-one-dimensional Cr-based superconductivity (SC), realized a tunability through charge doping, which will potentially significantly push the development of this area. Here based on the band structure from first-principle calculations, we construct a six-band tight-binding (TB) model equipped with multi-orbital Hubbard interactions, and adopt the random-phase-approximation approach to study the hydrogen-doping dependence of the pairing symmetry and superconducting $T_c$. Under the rigid-band approximation, our pairing phase diagram is occupied by the triplet $p_z$-wave pairing through out the hydrogen-doping regime $x\in (0.4,1)$ in which SC has been experimentally detected. Remarkably, the $x$-dependence of $T_c$ shows a peak at the 3D-quasi-1D Lifshitz transition point, although the total density of state exhibit a dip there. A thorough investigation of the band structure reveals type-II van-Hove singularities (VHSs) in the $\gamma$ band, which favor the formation of the triplet SC. It turns out that the $\gamma$- Fermi surface (FS) comprises two flat quasi-1D FS sheets almost parallel to the $k_z=0$ plane and six almost perpendicular tube-like FS sheets, and the type-II VHS just lies in the boundary between these two FS parts. Furthermore, the $\left|k_z\right|$ of the VH planes reaches the maximum near the Lifshitz-transition point, which pushes the $T_c$ of the $p_z$-wave SC to the maximum. Our results appeal more experimental access into this intriguing superconductor., Comment: 11 pages, 6 figures, accepted version by Phys. Rev. B

From first-principles calculations, we investigate the structural and electronic properties of the kagome metals AV3Sb5 (A = Cs, K, Rb) under isotropic and anisotropic pressure. Charge ordering patterns are found to be unanimously suppressed, while there is a significant rearrangement of p-type and m-type van Hove point energies with respect to the Fermi level. Already for moderate tensile strain along the V plane and compressive strain normal to the V layer, we find that a van Hove point can be shifted to the Fermi energy. Such a mechanism provides an invaluable tuning knob to alter the correlation profile in the kagome metal, and suggests itself for further experimental investigation. It might allow to reconcile possible multi-dome superconductivity in kagome metals not only from phonons, but also from the viewpoint of unconventional pairing., Comment: 7 pages, 5 figures

In this work, we establish a new theoretical paradigm for vortex Majorana physics in the recently discovered topological iron-based superconductors (tFeSCs). While tFeSCs are widely accepted as an exemplar of topological insulators (TIs) with intrinsic $s$-wave superconductivity, our theory implies that such common belief could be oversimplified. Our main finding is that the normal-state bulk Dirac nodes, usually ignored in TI-based vortex Majorana theories for tFeSCs, will play a key role of determining the vortex state topology. In particular, the interplay between TI and Dirac nodal bands will lead to multiple competing topological phases for a superconducting vortex line in tFeSCs, including an unprecedented hybrid topological vortex state that carries both Majorana bound states and a gapless dispersion. Remarkably, this exotic hybrid vortex phase generally exists in the vortex phase diagram for our minimal model for tFeSCs and is directly relevant to tFeSC candidates such as LiFeAs.When the four-fold rotation symmetry is broken by vortex-line tilting or curving, the hybrid vortex gets topologically trivialized and becomes Majorana-free, which could explain the puzzle of ubiquitous trivial vortices observed in LiFeAs. Origin of Majorana signal in other tFeSC candidates such as FeTe$_x$Se$_{1-x}$ and CaKFe$_4$As$_4$ are also interpreted within our theory framework. Our theory sheds new light on theoretically understanding and experimentally engineering Majorana physics in high-temperature iron-based systems., Comment: 7+19 pages, 4+9 figures

We report the structure and physical properties of two newly-discovered compounds AV8Sb12 and AV6Sb6 (A = Cs, Rb), which have C2 (space group: Cmmm) and C3 (space group: R-3m) symmetry, respectively. The basic V-kagome unit is present in both compounds, but stacking differently. A V2Sb2 layer is sandwiched between two V3Sb5 layers in AV8Sb12, altering the V-kagome lattice and lowering the symmetry of kagome layer from hexagonal to orthorhombic. In AV6Sb6, the building block is a more complex slab made up of two half-V3Sb5 layers that are intercalated by Cs cations along the c-axis. Transport property measurements demonstrate that both compounds are nonmagnetic metals, with carrier concentrations at around 1021cm-3. No superconductivity has been observed in CsV8Sb12 above 0.3 K under in-situ pressure up to 46 GPa. In contrast to CsV3Sb5, theoretical calculations and angle-resolved photoemission spectroscopy (ARPES) reveal a quasi-two-dimensional electronic structure in CsV8Sb12 with C2 symmetry and no van Hove singularities near the Fermi level. Our findings will stimulate more research into V-based kagome quantum materials., Comment: 11 pages 6 figures

We identify all symmetry-enforced band crossings in nonmagnetic orthorhombic crystals with and without spin-orbit coupling and discuss their topological properties. We find that orthorhombic crystals can host a large number of different band degeneracies, including movable Weyl and Dirac points with hourglass dispersions, fourfold double Weyl points, Weyl and Dirac nodal lines, almost movable nodal lines, nodal chains, and topological nodal planes. Interestingly, spin-orbit coupled materials in the space groups 18, 36, 44, 45, and 46 can have band pairs with only two Weyl points in the entire Brillouin zone. This results in a simpler connectivity of the Fermi arcs and more pronounced topological responses than in materials with four or more Weyl points. In addition, we show that the symmetries of the space groups 56, 61, and 62 enforce nontrivial weak $\mathbb{Z}_2$ topology in materials with strong spin-orbit coupling, leading to helical surface states. With these classification results in hand, we perform extensive database searches for orthorhombic materials crystallizing in the relevant space groups. We find that Sr$_2$Bi$_3$ and Ir$_2$Si have bands crossing the Fermi energy with a symmetry-enforced nontrivial $\mathbb{Z}_2$ invariant, CuIrB possesses nodal chains near the Fermi energy, Pd$_7$Se$_4$ and Ag$_2$Se exhibit fourfold double Weyl points, the latter one even in the absence of spin-orbit coupling, whereas the fourfold degeneracies in AuTlSb are made up from intersecting nodal lines. For each of these examples we compute the ab-initio band structures, discuss their topologies, and for some cases also calculate the surface states., Comment: 26 pages, 14 figures, supplemental material

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 VHSs are identified around the M point and three of them are close to the Fermi level, with two having sublattice-pure and one sublattice-mixed nature. Remarkably, the VHS just below the Fermi level displays an extremely flat dispersion along MK, establishing the experimental discovery of higher-order VHS. The characteristic intensity modulation of Dirac cones around K further demonstrates the sublattice interference embedded in the electronic structure. The crucial insights into the electronic structure, revealed by our work, provide a solid starting point for the understanding of the intriguing correlation phenomena in the kagome metals AV$_3$Sb$_5$.

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 compared with the bulk, which is accompanied by the suppression of CDW. Our detailed analyses establish the pivotal role of van Hove singularities (VHSs) in promoting correlated quantum orders in these kagome metals. Our experiment not only demonstrates the intriguing nature of superconducting and CDW orders, but also provides a novel route to tune the carrier concentration through both selective oxidation and electric gating. This establishes AV$_3$Sb$_5$ as a tunable 2D platform for the further exploration of topology and correlation among 3$d$ electrons in kagome lattices., Comment: 13 pages, 12 figures