Superconductivity from flat dispersion designed in doped mott insulators

Giant self spin-valve effect in the kagome helimagnet

Kagome magnets can combine non-trivial band topology and electron correlations, offering a versatile playground for various quantum phenomena. In this work we propose that kagome magnets with frustrated interlayer interactions can intrinsically support a self spin-valve effect, and experimentally confirm this in the kagome helimagnet TmMn6Sn6. Under a magnetic field perpendicular to the helical axis, using magnetic force microscopy we observed stripe domains that stack strictly along the helical axis, which we attribute to the stability loss of the kagome helimagnetic state. Such a domain pattern spontaneously mimics the artificial multilayered structure in traditional spin valves, which, combined with the high spin polarization, leads to a giant magnetoresistance (GMR) ratio over 160%. This discovery opens an avenue to realize inherent spin valves in a variety of quantum magnets, and can hold promise in future spintronics.

1D Flat Bands in Phosphorene Nanoribbons with Pentagonal Nature

Materials with flat bands can serve as a promising platform to investigate strongly interacting phenomena. However, experimental realization of ideal flat bands is mostly limited to artificial lattices or moiré systems. Here, a general way is reported to construct 1D flat bands in phosphorene nanoribbons (PNRs) with a pentagonal nature: penta-hexa-PNRs and penta-dodeca-PNRs, wherein the corresponding 1D flat bands are directly verified by using angle-resolved photoemission spectroscopy. It is confirmed that the observed 1D flat bands originate from the electronic 1D zigzag and Lieb lattices, respectively, as revealed by the combination of bond-resolved scanning tunneling microscopy, scanning tunneling spectroscopy, tight-binding models, and first-principles calculations. The study demonstrates a general way to construct 1D flat bands in 1D solid materials system, which provides a robust platform to explore strongly interacting phases of matter.

Electronic Flat Band in Distorted Colouring Triangle Lattice

Dispersionless flat bands (FBs) in momentum space, given rise to electron destructive interference in frustrated lattices, offer opportunities to enhance electronic correlations and host exotic many-body phenomena, such as Wigner crystal, fractional quantum hall state, and superconductivity. Despite successes in theory, great challenges remain in experimentally realizing FBs in frustrated lattices due to thermodynamically structural instability. Here, the observation of electronic FB in a potassium distorted colouring triangle (DCT) lattice is reported, which is supported on a blue phosphorene-gold network. It is verified that the interaction between potassium and the underlayer dominates and stabilizes the frustrated structures. Two-dimensional electron gas is modulated by the DCT lattice, and in turn results in a FB dispersion due to destructive quantum interferences. The FB exhibits suppressed bandwidth with high density of states, which is directly observed by scanning tunneling microscopy and confirmed by the first-principles calculation. This work demonstrates that DCT lattice is a promising platform to study FB physics and explore exotic phenomena of correlation and topological matters.

Designer artificial chiral kagome lattice with tunable flat bands and topological boundary states

The kagome lattice is a well-known model system for the investigation of strong correlation and topological electronic phenomena due to the intrinsic flat band, magnetic frustration, etc. Introducing chirality into the kagome lattice would bring about new physics due to the unique symmetry, which is still yet to be fully explored. Here we report the investigation on a two-dimensional chiral kagome lattice utilizing tight binding band calculation and topological index analysis. It is found that the periodic chiral kagome lattice would bring about a robust zero-energy flat band. Furthermore, in the Su-Schrieffer-Heeger type dimer-/trimerized breathing chiral kagome lattice with particular edge terminations, topological corner states or metallic edge states would appear, implying new candidates for the second-order topological insulator. We also proposed the construction strategy for such lattices employing the scanning tunneling microscope atom manipulation technique.

New two-dimensional flat band materials: B3C11O6 and B3C15O6

Recently, there has been growing interest in the field of flat-band physics due to its attractive properties and wide range of practical applications. In this study, we introduce two novel two-dimensional monolayers, namely B3C11O6 and B3C15O6, which exhibit a flat band near the Fermi level. These monolayers have been found to be energetically favorable, dynamically stable, and thermodynamically stable based on formation energies, phonon spectra, and molecular dynamics simulations. The nearly flat band (NFB) in B3C11O6 arises from the extended kagome sublattice of carbon atoms. Due to the strong interaction between carbon atoms beyond their nearest neighbors, the bandwidth of the initial flat band is extended to approximately 0.5 eV. Nevertheless, there is still a prominent peak in the density of states near the Fermi level. On the other hand, the NFB in B3C15O6 originates from the localized states of the carbon five-ring structure, which forms a distorted kagome lattice. The presence and characteristics of the NFB strongly depend on the interactions between next-nearest neighbors. Interestingly, the partially occupied NFB in B3C11O6 leads to spin splitting, resulting in a transformation of the system into a ferromagnetic metal. Our research not only presents two types of lattices capable of hosting flat bands or NFBs, but also provides two monolayers that can be employed to investigate various intriguing quantum phases.

Realization of a Two-Dimensional Checkerboard Lattice in Monolayer Cu2N

Two-dimensional checkerboard lattice, the simplest line-graph lattice, has been intensively studied as a toy model, while material design and synthesis remain elusive. Here, we report theoretical prediction and experimental realization of the checkerboard lattice in monolayer Cu₂N. Experimentally, monolayer Cu₂N can be realized in the well-known N/Cu(100) and N/Cu(111) systems that were previously mistakenly believed to be insulators. Combined angle-resolved photoemission spectroscopy measurements, first-principles calculations, and tight-binding analysis show that both systems host checkerboard-derived hole pockets near the Fermi level. In addition, monolayer Cu₂N has outstanding stability in air and organic solvents, which is crucial for further device applications.

Effect of electron- and hole-doping on properties of kagomé-lattice ferromagnet Fe3Sn2

We report a theoretical investigation of effects of Mn and Co substitution in the transition metal sites of the kagomé-lattice ferromagnet, Fe₃Sn₂. Herein, hole- and electron-doping effects of Fe₃Sn₂have been studied by density-functional theory calculations on the parent phase and on the substituted structural models of Fe_3-xM_xSn₂(M = Mn, Co;x= 0.5, 1.0). All optimized structures favor the ferromagnetic ground state. Analysis of the electronic density of states (DOS) and band structure plots reveals that the hole (electron) doping leads to a progressive decrease (increase) in the magnetic moment per Fe atom and per unit cell overall. The high DOS is retained nearby the Fermi level in the case of both Mn and Co substitutions. The electron doping with Co results in the loss of nodal band degeneracies, while in the case of hole doping with Mn emergent nodal band degeneracies and flatbands initially are suppressed in Fe_2.5Mn_0.5Sn₂but re-emerge in Fe₂MnSn₂. These results provide key insights into potential modifications of intriguing coupling between electronic and spin degrees of freedom observed in Fe₃Sn₂.

Observation of Topological Flat Bands in the Kagome Semiconductor Nb3Cl8

The destructive interference of wavefunctions in a kagome lattice can give rise to topological flat bands (TFBs) with a highly degenerate state of electrons. Recently, TFBs have been observed in several kagome metals, including Fe₃Sn₂, FeSn, CoSn, and YMn₆Sn₆. Nonetheless, kagome materials that are both exfoliable and semiconducting are lacking, which seriously hinders their device applications. Herein, we show that Nb₃Cl₈, which hosts a breathing kagome lattice, is gapped out because of the absence of inversion symmetry, while the TFBs survive because of the protection of the mirror reflection symmetry. By angle-resolved photoemission spectroscopy measurements and first-principles calculations, we directly observe the TFBs and a moderate band gap in Nb₃Cl₈. By mechanical exfoliation, we successfully obtain monolayer Nb₃Cl₈, which is stable under ambient conditions. In addition, our calculations show that monolayer Nb₃Cl₈ has a magnetic ground state, thus providing opportunities to study the interplay among geometry, topology, and magnetism.

Observation of a Flat and Extended Surface State in a Topological Semimetal

A flat band structure in momentum space is considered key for the realization of novel phenomena. A topological flat band, also known as a drumhead state, is an ideal platform to drive new exotic topological quantum phases. Using angle-resolved photoemission spectroscopy experiments, we reveal the emergence of a highly localized surface state in a topological semimetal BaAl4 and provide its full energy and momentum space topology. We find that the observed surface state is localized in momentum, inside a square-shaped bulk Dirac nodal loop, and in energy, leading to a flat band and a peak in the density of state. These results imply this class of materials as an experimental realization of drumhead surface states and provide an important reference for future studies of the fundamental physics of correlated quantum effects in topological materials.

Flat-Band-Induced Anomalous Anisotropic Charge Transport and Orbital Magnetism in Kagome Metal CoSn

For solids, the dispersionless flat band has long been recognized as an ideal platform for achieving intriguing quantum phases. However, experimental progress in revealing flat-band physics has so far been achieved mainly in artificially engineered systems represented as magic-angle twisted bilayer graphene. Here, we demonstrate the emergence of flat-band-dominated anomalous transport and magnetic behaviors in CoSn, a paramagnetic kagome-lattice compound. By combination of angle-resolved photoemission spectroscopy measurements and first-principles calculations, we reveal the existence of a kagome-lattice-derived flat band right around the Fermi level. Strikingly, the resistivity within the kagome lattice plane is more than one order of magnitude larger than the interplane one, in sharp contrast with conventional (quasi-) two-dimensional layered materials. Moreover, the magnetic susceptibility under the out-of-plane magnetic field is found to be much smaller as compared with the in-plane case, which is revealed to be arising from the introduction of a unique orbital diamagnetism. Systematic analyses reveal that these anomalous and giant anisotropies can be reasonably attributed to the unique properties of flat-band electrons, including large effective mass and self-localization of wave functions. Our results broaden the already fascinating flat-band physics, and demonstrate the feasibility of exploring them in natural solid-state materials in addition to artificial ones.

Emerging flat bands in large-angle twisted bi-layer graphene under pressure

Recent experiments on magic-angle twisted bi-layer graphene have attracted intensive attention due to exotic properties such as unconventional superconductivity and correlated insulation. These phenomena were often found at a magic angle less than 1.1°. However, the preparation of precisely controlled bi-layer graphene with a small magic angle is challenging. In this work, electronic properties of large-angle twisted bi-layer graphene (TBG) under pressure are investigated with density functional theory. We demonstrate that large-angle TBG can display flat bands nearby the Fermi level under pressure, which may also induce interesting properties such as superconductivity which have only been found in small-angle TBG at ambient pressure. The Fermi velocity is found to decrease monotonously with pressure for large twisted angles, e.g., 21.8°. Our work indicates that applying pressure provides opportunities for flat-band engineering in larger angle TBG and supports further exploration in related investigations.

Dirac cone, flat band and saddle point in kagome magnet YMn6Sn6

Kagome-lattices of 3d-transition metals hosting Weyl/Dirac fermions and topological flat bands exhibit non-trivial topological characters and novel quantum phases, such as the anomalous Hall effect and fractional quantum Hall effect. With consideration of spin-orbit coupling and electron correlation, several instabilities could be induced. The typical characters of the electronic structure of a kagome lattice, i.e., the saddle point, Dirac-cone, and flat band, around the Fermi energy (EF) remain elusive in magnetic kagome materials. We present the experimental observation of the complete features in ferromagnetic kagome layers of YMn6Sn6 helically coupled along the c-axis, by using angle-resolved photoemission spectroscopy and band structure calculations. We demonstrate a Dirac dispersion near EF, which is predicted by spin-polarized theoretical calculations, carries an intrinsic Berry curvature and contributes to the anomalous Hall effect in transport measurements. In addition, a flat band and a saddle point with a high density of states near EF are observed. These multi-sets of kagome features are of orbital-selective origin and could cause multi-orbital magnetism. The Dirac fermion, flat band and saddle point in the vicinity of EF open an opportunity in manipulating the topological properties in magnetic materials.

Realistic flat-band model based on degenerate p-orbitals in two-dimensional ionic materials

Though several theoretical models have been proposed to design electronic flat-bands, the definite experimental realization in two-dimensional atomic crystal is still lacking. Here we propose a novel and realistic flat-band model based on threefold degenerate p-orbitals in two-dimensional ionic materials. Our theoretical analysis and first-principles calculations show that the proposed flat-band can be realized in 1T layered materials of alkali-metal chalogenides and metal-carbon group compounds. Some of the former are theoretically predicted to be stable as layered materials (e.g., K₂S), and some of the latter have been experimentally fabricated in previous works (e.g., Gd₂CCl₂). More interestingly, the flat-band is partially filled in the heterostructure of a K₂S monolayer and graphene layers. The spin polarized nearly flat-band can be realized in the ferromagnetic state of a Gd₂CCl₂ monolayer, which has been fabricated in experiments. Our theoretical model together with the material predictions provide a realistic platform for the study of flat-bands and related exotic quantum phases.

Interaction-Enhanced Group Velocity of Bosons in the Flat Band of an Optical Kagome Lattice

Geometric frustration of particle motion in a kagome lattice causes the single-particle band structure to have a flat s-orbital band. We probe this band structure by placing a Bose-Einstein condensate into excited Bloch states of an optical kagome lattice, and then measuring the group velocity through the atomic momentum distribution. We find that interactions renormalize the band structure, greatly increasing the dispersion of the third band, which is nearly non-dispersing the single-particle treatment. Calculations based on the lattice Gross-Pitaevskii equation indicate that band structure renormalization is caused by the distortion of the overall lattice potential away from the kagome geometry by interactions.

Electronic correlations and flattened band in magnetic Weyl semimetal candidate Co3Sn2S2

The interplay between electronic correlations and topological protection may offer a rich avenue for discovering emergent quantum phenomena in condensed matter. However, electronic correlations have so far been little investigated in Weyl semimetals (WSMs) by experiments. Here, we report a combined optical spectroscopy and theoretical calculation study on the strength and effect of electronic correlations in a magnet Co₃Sn₂S₂. The electronic kinetic energy estimated from our optical data is about half of that obtained from single-particle ab initio calculations in the ferromagnetic ground state, which indicates intermediate-strength electronic correlations in this system. Furthermore, comparing the energy and side-slope ratios between the interband-transition peaks at high energies in the experimental and single-particle-calculation-derived optical conductivity spectra with the bandwidth-renormalization factors obtained by many-body calculations enables us to estimate the Coulomb-interaction strength (U ∼ 4 eV) in Co₃Sn₂S₂. Besides, a sharp experimental optical conductivity peak at low energy, which is absent in the single-particle-calculation-derived spectrum but is consistent with the optical conductivity peaks obtained by many-body calculations with U ∼ 4 eV, indicates that an electronic band connecting the two Weyl cones is flattened by electronic correlations and emerges near the Fermi energy in Co₃Sn₂S₂. Our work paves the way for exploring flat-band-generated quantum phenomena in WSMs.

Designing Kagome Lattice from Potassium Atoms on Phosphorus-Gold Surface Alloy

Materials with flat bands are considered as ideal platforms to explore strongly correlated physics such as the fractional quantum hall effect, high-temperature superconductivity, and more. In theory, a Kagome lattice with only nearest-neighbor hopping can give rise to a flat band. However, the successful fabrication of Kagome lattices is still very limited. Here, we provide a new design principle to construct the Kagome lattice by trapping atoms into Kagome arrays of potential valleys, which can be realized on a potassium-decorated phosphorus-gold surface alloy. Theoretical calculations show that the flat band is less correlated with the neighboring trivial electronic bands, which can be further isolated and dominate around the Fermi energy with increased Kagome lattice parameters of potassium atoms. Our results provide a new strategy for constructing Kagome lattices, which serve as an ideal platform to study topological and more general flat band phenomena.

Seltrapping in flat band lattices with nonlinear disorder

We study the transport properties of an initially localized excitation in several flat band lattices, in the presence of nonlinear (Kerr) disorder. In the weak nonlinearity regime, the dynamics is controlled by the degeneracy of the bands leading to a linear form of selftrapping. In the strong nonlinearity regime, the dynamics of the excitations depends strongly on the local environment around the initial excitation site that leads to a highly fluctuating selfrapping profile. For a binary nonlinear disorder, it is shown that the spreading of the flat band fundamental mode, is completely inhibited for a finite fraction of all cases. This fraction corresponds to the fraction of times the same value of (random) nonlinearity is assigned to all sites of the fundamental mode.

Methods for the construction of interacting many-body Hamiltonians with compact localized states in geometrically frustrated clusters

Adding interactions to many-body Hamiltonians of geometrically frustrated lattices often leads to diminished subspaces of localized states. In this paper, we show how to construct interacting many-body Hamiltonians, starting from the non-interacting tight-binding Hamiltonians, that preserve or even expand these subspaces. The methods presented involve modifications in the one-body network representation of the many-body Hamiltonians which generate new interacting terms in these Hamiltonians. The subspace of many-particle localized states can be preserved in the interacting Hamiltonian, by projecting the interacting terms onto the subspace of many-body extended states or by constructing the interacting Hamiltonian applying origami rules to the network. Expanded subspaces of localized states are found if interacting terms that mix subspaces with different number of particles are introduced. Furthermore, we present numerical methods for the determination of many-body localized states that allows one to address larger clusters and larger number of particles than those accessible by full diagonalization of the interacting Hamiltonian. These methods rely on the generalization of the concept of compact localized state in the network. Finally, we suggest a method to determine localized states that use a considerable fraction of the network.

Flatbands and Emergent Ferromagnetic Ordering in Fe_{3}Sn_{2} Kagome Lattices

A flatband representing a highly degenerate and dispersionless manifold state of electrons may offer unique opportunities for the emergence of exotic quantum phases. To date, definitive experimental demonstrations of flatbands remain to be accomplished in realistic materials. Here, we present the first experimental observation of a striking flatband near the Fermi level in the layered Fe_{3}Sn_{2} crystal consisting of two Fe kagome lattices separated by a Sn spacing layer. The band flatness is attributed to the local destructive interferences of Bloch wave functions within the kagome lattices, as confirmed through theoretical calculations and modelings. We also establish high-temperature ferromagnetic ordering in the system and interpret the observed collective phenomenon as a consequence of the synergetic effect of electron correlation and the peculiar lattice geometry. Specifically, local spin moments formed by intramolecular exchange interaction are ferromagnetically coupled through a unique network of the hexagonal units in the kagome lattice. Our findings have important implications to exploit emergent flat-band physics in special lattice geometries.

Defect States Emerging from a Non-Hermitian Flatband of Photonic Zero Modes

We show the existence of a flatband consisting of photonic zero modes in a gain and loss modulated lattice system as a result of the underlying non-Hermitian particle-hole symmetry. This general finding explains the previous observation in parity-time symmetric systems where non-Hermitian particle-hole symmetry is hidden. We further discuss the defect states in these systems, whose emergence can be viewed as an unconventional alignment of a pseudospin under the influence of a complex-valued pseudomagnetic field. These defect states also behave as a chain with two types of links, one rigid in a unit cell and one soft between unit cells, as the defect states become increasingly localized with the gain and loss strength.

Compact modes in quasi one dimensional coupled magnetic oscillators

In this work we study analytically and numerically the spectrum and localization properties of three quasi-one-dimensional (ribbons) split-ring resonator arrays which possess magnetic flatbands, namely, the stub, Lieb and kagome lattices, and how their spectra are affected by the presence of perturbations that break the delicate geometrical interference needed for a magnetic flatband to exist. We find that the stub and Lieb ribbons are stable against the three types of perturbations considered here, while the kagome ribbon is, in general, unstable. When losses are incorporated, all flatbands remain dispersionless but become complex, with the kagome ribbon exhibiting the highest loss rate. The stability of flatband modes of certain split-ring resonator arrays suggests that they could be used as components of future stable magnetic storage devices.

Flow-induced charge modulation in superfluid atomic fermions loaded into an optical kagome lattice

We study the superfluid state of atomic fermions in a tunable optical kagome lattice motivated by recent experiments. We show that the imposed superflow induces spatial modulations in the density and order parameter of the pair condensate and leads to a charge modulated superfluid state analogous to a supersolid state. The spatial modulations in the superfluid emerge due to the geometric effect of the kagome lattice that introduces anisotropy in hopping amplitudes of fermion pairs in the presence of superflow. We also study superflow instabilities and find that the critical current limited by the dynamical instability is quite enhanced due to the large density of states associated with the flatband. The charge modulated superfluid state can sustain high temperatures close to the transition temperature that is also enhanced due to the flatband and is therefore realizable in experiments.

Ultracold atoms in a tunable optical kagome lattice

We realize a two-dimensional kagome lattice for ultracold atoms by overlaying two commensurate triangular optical lattices generated by light at the wavelengths of 532 and 1064 nm. Stabilizing and tuning the relative position of the two lattices, we explore different lattice geometries including a kagome, a one-dimensional stripe, and a decorated triangular lattice. We characterize these geometries using Kapitza-Dirac diffraction and by analyzing the Bloch-state composition of a superfluid released suddenly from the lattice. The Bloch-state analysis also allows us to determine the ground-state distribution within the superlattice unit cell. The lattices implemented in this work offer a near-ideal realization of a paradigmatic model of many-body quantum physics, which can serve as a platform for future studies of geometric frustration.