Electron doping of a double-perovskite flat-band system.

Electronic structure calculations indicate that the Sr2FeSbO6 double perovskite has a flat-band set just above the Fermi level that includes contributions from ordinary subbands with weak kinetic electron hopping plus a flat subband that can be attributed to the lattice geometry and orbital interference. To place the Fermi energy in that flat band, electron-doped samples with formulas Sr2-xLaxFeSbO6 (0 ≤ x ≤ 0.3) were synthesized, and their magnetism and ambient temperature crystal structures were determined by high-resolution synchrotron X-ray powder diffraction. All materials appear to display an antiferromagnetic-like maximum in the magnetic susceptibility, but the dominant spin coupling evolves from antiferromagnetic to ferromagnetic on electron doping. Which of the three subbands or combinations is responsible for the behavior has not been determined.

Engineering Two-Dimensional Nodal Semimetals in Functionalized Biphenylene by Fluorine Adatoms.

We propose a band engineering scheme on the biphenylene network, a newly synthesized carbon allotrope. We illustrate that the electronic structure of the biphenylene network can be significantly altered by controlling conditions affecting the symmetry and destructive interference of wave functions through periodic fluorination. First, we investigate the mechanism for the appearance of a type-II Dirac fermion in a pristine biphenylene network. We show that the essential ingredients are mirror symmetries and stabilization of the compact localized eigenstates via destructive interference. While the former is used for the band-crossing point along high symmetry lines, the latter induces highly inclined Dirac dispersions. Subsequently, we demonstrate the transformation of the biphenylene network's type-II Dirac semimetal phase into various Dirac phases such as type-I Dirac, gapped type-II Dirac, and nodal line semimetals through the deliberate disruption of mirror symmetry or modulation of destructive interference by varying the concentration of fluorine atoms.

Nonlocal, Flat-Band Meta-Optics for Monolithic, High-Efficiency, Compact Photodetectors.

Miniaturized photodetectors are becoming increasingly sought-after components for next-generation technologies, such as autonomous vehicles, integrated wearable devices, or gadgets embedded on the Internet of Things. A major challenge, however, lies in shrinking the device footprint while maintaining high efficiency. This conundrum can be solved by realizing a nontrivial relation between the energy and momentum of photons, such as dispersion-free devices, known as flat bands. Here, we leverage flat-band meta-optics to simultaneously achieve critical absorption over a wide range of incidence angles. For a monolithic silicon meta-optical photodiode, we achieved an ∼10-fold enhancement in the photon-to-electron conversion efficiency. Such enhancement over a large angular range of ∼36° allows incoming light to be collected via a large-aperture lens and focused on a compact photodiode, potentially enabling high-speed and low-light operation. Our research unveils new possibilities for creating compact and efficient optoelectronic devices with far-reaching impact on various applications, including augmented reality and light detection and ranging.

Emergence of Improper Electronic Ferroelectricity and Flat Band in Twisted Bilayer Tl2S.

Two-dimensional (2D) ferroelectrics possessing out-of-plane (OP) polarization are highly desirable for applications and fundamental physics. Here, by first-principles calculations, we reveal that large-angle interlayer twisting can efficiently stabilize an unexpected ordering of sizable electric dipoles, producing OP polarization out of the centrosymmetric ground-state structure of Tl2S, in great contrast to the recently proposed interlayer-sliding ferroelectricity. The ferroelectricity originates from a nonlinear coupling between a polar order dominantly contributed by electrons and an unstable phonon mode associated with a commensurate k point (1/3, 1/3, 0) in the two constituent monolayers, therefore indicating an improper and electronic ferroelectric nature. More interestingly, a flat band and a van Hove singularity occur in its electronic structures just below the Fermi level in the large-angle twisted bilayer Tl2S. The unusual coexistence of improper electronic ferroelectricity, a flat band, and a van Hove singularity in one 2D material offers exceptional opportunities for exploring novel physics and applications.

Realization of Material with an Atomic Ruby Lattice.

The ruby lattice is one of the tight-binding models which hosts a flat band in its electronic structure and has potential applications in future spintronics and quantum devices. However, the experimental realization of a ruby lattice in realistic materials remains elusive. Here, we have experimentally realized an atomic ruby lattice by fabricating monolayer CuCl1+x on a Au(111) substrate. Scanning tunneling microscopy/spectra (STM/STS) measurements combined with density-functional theory (DFT) calculations reveal that the Cu atoms are arranged in a ruby lattice in this monolayer. Moreover, a significant density of states (DOS) peak corresponding to the characteristic of a ruby system is observed, consistent with both the tight-binding model and first-principles calculations on the band structure. Our work provides a promising platform to explore the physics of the ruby model.

Atomic-Limit Mott Insulator in [4]Triangulene Frameworks.

Triangulene, one unique class of zigzag-edged triangular graphene molecules, has attracted tremendous research interest. In this work, as an ultimate phase of the Mott insulator, we present the realization of the atomic-limit Mott insulator in experimentally synthesized [4]triangulene frameworks ([4]-TGFs) from first-principles calculations. The frontier molecular orbitals of the nonmagnetic [4]triangulene consist of three coupled corner modes. After the isolated [4]triangulene is assembled into [4]-TGF, one special enantiomorphic flat band is created through the coupling of these corner modes, which is identified to be a second-order topological insulator with half-filled topological corner states at the Fermi level. Moreover, [4]-TGF prefers an antiferromagnetic ground state under Hubbard interactions, which further splits these metallic zero-energy states into an atomic-limit Mott insulator with spin-polarized corners. Since the fractional filling of topological corner states is a smoking-gun signature of higher-order topology, our results demonstrate a universal approach to explore the atomic-limit Mott insulators in higher-order topological materials.

Atomically Thin Kagome-Structured Co9Te16 Achieved through Self-Intercalation and Its Flat Band Visualization.

Kagome materials have recently garnered substantial attention due to the intrinsic flat band feature and the stimulated magnetic and spin-related many-body physics. In contrast to their bulk counterparts, two-dimensional (2D) kagome materials feature more distinct kagome bands, beneficial for exploring novel quantum phenomena. Herein, we report the direct synthesis of an ultrathin kagome-structured Co-telluride (Co9Te16) via a molecular beam epitaxy (MBE) route and clarify its formation mechanism from the Co-intercalation in the 1T-CoTe2 layers. More significantly, we unveil the flat band states in the ultrathin Co9Te16 and identify the real-space localization of the flat band states by in situ scanning tunneling microscopy/spectroscopy (STM/STS) combined with first-principles calculations. A ferrimagnetic order is also predicted in kagome-Co9Te16. This work should provide a novel route for the direct synthesis of ultrathin kagome materials via a metal self-intercalation route, which should shed light on the exploration of the intriguing flat band physics in the related systems.

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.

Reveal Ultrafast Electron Relaxation across Sub-bands of Tellurium by Time- and Energy-Resolved Photoemission Microscopy.

Exploring ultrafast carrier dynamics is crucial for the materials' fundamental properties and device design. In this work, we employ time- and energy-resolved photoemission electron microscopy with tunable pump wavelengths from visible to near-infrared to reveal the ultrafast carrier dynamics of the elemental semiconductor tellurium. We find that two discrete sub-bands around the Γ point of the conduction band are involved in excited-state electron ultrafast relaxation and reveal that hot electrons first go through ultrafast intra sub-band cooling on a time scale of about 0.3 ps and then transfer from the higher sub-band to the lower one on a time scale of approximately 1 ps. Additionally, theoretical calculations reveal that the lower one has flat-band characteristics, possessing a large density of states and a long electron lifetime. Our work demonstrates that TR- and ER-PEEM with broad tunable pump wavelengths are powerful techniques in revealing the details of ultrafast carrier dynamics in time and energy domains.

Magnetic Real Chern Insulator in 2D Metal-Organic Frameworks.

Real Chern insulators have attracted great interest, but so far, their material realization is limited to nonmagnetic crystals and systems without spin-orbit coupling. Here, we reveal the magnetic real Chern insulator (MRCI) state in a recently synthesized metal-organic framework material Co3(HITP)2. Its ground state with in-plane ferromagnetic ordering hosts a nontrivial real Chern number, enabled by the C2zT symmetry and robustness against spin-orbit coupling. Distinct from previous nonmagnetic examples, the topological corner zero modes of MRCIs are spin-polarized. Furthermore, under small tensile strains, the material undergoes a topological phase transition from the MRCI to a magnetic double-Weyl semimetal phase, via a pseudospin-1 critical state. Similar physics can also be found in closely related materials Mn3(HITP)2 and Fe3(HITP)2, which also exist. Possible experimental detections and implications of an emerging magnetic flat band in the system are discussed.

ARPES Signatures of Few-Layer Twistronic Graphenes.

Diverse emergent correlated electron phenomena have been observed in twisted-graphene layers. Many electronic structure predictions have been reported exploring this new field, but with few momentum-resolved electronic structure measurements to test them. We use angle-resolved photoemission spectroscopy to study the twist-dependent (1° < θ < 8°) band structure of twisted-bilayer, monolayer-on-bilayer, and double-bilayer graphene (tDBG). Direct comparison is made between experiment and theory, using a hybrid k·p model for interlayer coupling. Quantitative agreement is found across twist angles, stacking geometries, and back-gate voltages, validating the models and revealing field-induced gaps in twisted graphenes. However, for tDBG at θ = 1.5 ± 0.2°, close to the magic angle θ = 1.3°, a flat band is found near the Fermi level with measured bandwidth Ew = 31 ± 5 meV. An analysis of the gap between the flat band and the next valence band shows deviations between experiment (Δh = 46 ± 5 meV) and theory (Δh = 5 meV), indicative of lattice relaxation in this regime.

Chiral Decomposition of Twisted Graphene Multilayers with Arbitrary Stacking.

We formulate the chiral decomposition rules that govern the electronic structure of a broad family of twisted N + M multilayer graphene configurations that combine arbitrary stacking order and a mutual twist. We show that at the magic angle in the chiral limit the low-energy bands of such systems are composed of chiral pseudospin doublets that are energetically entangled with two flat bands per valley induced by the moiré superlattice potential. The analytic construction is supported by explicit numerical calculations based on realistic parametrization. We further show that vertical displacement fields can open energy gaps between the pseudospin doublets and the two flat bands, such that the flat bands may carry nonzero valley Chern numbers. These results provide guidelines for the rational design of topological and correlated states in generic twisted graphene multilayers.

Magnetic Field-Stabilized Wigner Crystal States in a Graphene Moiré Superlattice.

ABC-stacked trilayer graphene on boron nitride (ABC-TLG/hBN) moiré superlattices provides a tunable platform for exploring Wigner crystal states in which the electron correlation can be controlled by electric and magnetic fields. Here we report the observation of magnetic field-stabilized Wigner crystal states in a ABC-TLG/hBN. We show that correlated insulating states emerge at multiple fractional and integer fillings corresponding to ν = 1/3, 2/3, 1, 4/3, 5/3, and 2 electrons per moiré lattice site under a magnetic field. These correlated insulating states can be attributed to generalized Mott states for the integer fillings and generalized Wigner crystal states for the fractional fillings. The generalized Wigner crystal states are stabilized by a vertical magnetic field and are strongest at one magnetic flux quantum per three moiré superlattices. The ν = 2 insulating state persists up to 30 T, which can be described by a Mott-Hofstadter transition at a high magnetic field.

Epitaxial Kagome Thin Films as a Platform for Topological Flat Bands.

Systems with flat bands are ideal for studying strongly correlated electronic states and related phenomena. Among them, kagome-structured metals such as CoSn have been recognized as promising candidates due to the proximity between the flat bands and the Fermi level. A key next step will be to realize epitaxial kagome thin films with flat bands to enable tuning of the flat bands across the Fermi level via electrostatic gating or strain. Here, we report the band structures of epitaxial CoSn thin films grown directly on the insulating substrates. Flat bands are observed by using synchrotron-based angle-resolved photoemission spectroscopy (ARPES). The band structure is consistent with density functional theory (DFT) calculations, and the transport properties are quantitatively explained by the band structure and semiclassical transport theory. Our work paves the way to realize flat band-induced phenomena through fine-tuning of flat bands in kagome materials.

A new type of stable borophene with flat-band-induced magnetism.

Based on first-principles calculations, we propose a new type of thermally and dynamically stable magnetic borophene (B11) with a tetragonal lattice. The magnetism is found coming from spin polarization of one bonding flat band located at the Fermi level. Despite of the 'anti-molecular' behavior in the monolayer, the interactions between thepzorbitals of the B atoms in the double-octahedron structural unit lead to the formation of the flat bands with localization behaviors. One tight binding model is built to comprehend the magnetic mechanism, which can guide us to tune other nonmagnetic borophene becoming magnetic. Biaxial tensile strain (>2.1%) is found triggering a phase transition from a semimetal to a semiconductor in the B11monolayer. The mechanism is analyzed based on the orbital-resolved crystal field effect. Our work provides a new route for designing and achieving two-dimensional magnetic materials with light elements.

Tunable Mott Dirac and Kagome Bands Engineered on 1T-TaS2.

Strongly interacting electrons in hexagonal and kagome lattices exhibit rich phase diagrams of exotic quantum states, including superconductivity and correlated topological orders. However, material realizations of these electronic states have been scarce in nature or by design. Here, we theoretically propose an approach to realize artificial lattices by metal adsorption on a 2D Mott insulator 1T-TaS2. Alkali, alkaline-earth, and group 13 metal atoms are deposited in (√3 × âˆš3)R30° and 2 × 2 TaS2 superstructures of honeycomb- and kagome-lattice symmetries exhibiting Dirac and kagome bands, respectively. The strong electron correlation of 1T-TaS2 drives the honeycomb and kagome systems into correlated topological phases described by Kane-Mele-Hubbard and kagome-Hubbard models. We further show that the 2/3 or 3/4 band filling of Mott Dirac and flat bands can be achieved with a proper concentration of Mg adsorbates. Our proposal may be readily implemented in experiments, offering an attractive condensed-matter platform to exploit the interplay of correlated topological order and superconductivity.

Gate-Tunable Magnetism and Giant Magnetoresistance in Suspended Rhombohedral-Stacked Few-Layer Graphene.

Conventionally, magnetism arises from the strong exchange interaction among the magnetic moments of d- or f-shell electrons. It can also emerge in perfect lattices from nonmagnetic elements, such as that exemplified by the Stoner criterion. Here we report tunable magnetism in suspended rhombohedral-stacked few-layer graphene (r-FLG) devices with flat bands. At small doping levels (n ∼ 1011 cm-2), we observe prominent conductance hysteresis and giant magnetoconductance that exceeds 1000% as a function of magnetic fields. Both phenomena are tunable by density and temperature and disappear at n > 1012 cm-2 or T > 5 K. These results are confirmed by first-principles calculations, which indicate the formation of a half-metallic state in doped r-FLG, in which the magnetization is tunable by electric field. Our combined experimental and theoretical work demonstrate that magnetism and spin polarization, arising from the strong electronic interactions in flat bands, emerge in a system composed entirely of carbon atoms.

Experimental Realization of Two-Dimensional Weak Topological Insulators.

We report the experimental realization of a two-dimensional (2D) weak topological insulator (WTI) in spinless Su-Schrieffer-Heeger circuits with parity-time and chiral symmetries. Strong and weak Z2 topological indexes are adopted to explain the experimental findings that a Dirac semimetal (DSM) phase and four WTI phases emerge in turn when we modulate the centrosymmetric circuit deformations. In the DSM phase, it is found that the Dirac cone is highly anisotropic and that it is not pinned to any high-symmetry points but can widely move within the Brillouin zone, which eventually leads to the phase transition between WTIs. In addition, we observe a pair of flat-band domain wall states by designing spatially inhomogeneous node connections. Our work provides the first experimental evidence for 2D WTIs, which significantly advances our understanding of the strong and weak nature of topological insulators, the robustness of flat bands, and the itinerant and anisotropic features of Dirac cones.

Excited quantum anomalous and spin Hall effect: dissociation of flat-bands-enabled excitonic insulator state.

Quantum anomalous Hall effect (QAHE) and quantum spin Hall effect (QSHE) are two interesting physical manifestations of 2D materials that have an intrinsic nontrivial band topology. In principle, they are ground-state equilibrium properties characterized by Fermi level lying in a topological gap, below which all the occupied bands are summed to a non-zero topological invariant. Here, we propose theoretical concepts and models of 'excited' QAHE (EQAHE) and EQSHE generated by dissociation of an excitonic insulator (EI) state with complete population inversion (CPI), a uniquemany-bodyground state enabled by two yin-yang flat bands (FBs) of opposite chirality hosted in a diatomic Kagome lattice. The two FBs have a trivial gap in between, i.e. the system is a trivial insulator in thesingle-particleground-state, but nontrivial gaps above and below, so that upon photoexcitation the quasi-Fermi levels of both electrons and holes will lie in a nontrivial gap achieved by the CPI-EI state, as demonstrated by exact diagonalization calculations. Then dissociation of singlet and triplet EI state will lead to EQAHE and EQSHE, respectively. Realizations of yin-yang FBs in real materials are also discussed.

Engineering a Robust Flat Band in III-V Semiconductor Heterostructures.

Electron states in semiconductor materials can be modified by quantum confinement. Adding to semiconductor heterostructures the concept of lateral geometry offers the possibility to further tailor the electronic band structure with the creation of unique flat bands. Using block copolymer lithography, we describe the design, fabrication, and characterization of multiorbital bands in a honeycomb In0.53Ga0.47As/InP heterostructure quantum well with a lattice constant of 21 nm. Thanks to an optimized surface quality, scanning tunnelling spectroscopy reveals the existence of a strong resonance localized between the lattice sites, signature of a p-orbital flat band. Together with theoretical computations, the impact of the nanopatterning imperfections on the band structure is examined. We show that the flat band is protected against the lateral and vertical disorder, making this industry-standard system particularly attractive for the study of exotic phases of matter.