Catalogue of flat-band stoichiometric materials.

Topological electronic flattened bands near or at the Fermi level are a promising route towards unconventional superconductivity and correlated insulating states. However, the related experiments are mostly limited to engineered materials, such as moiré systems1-3. Here we present a catalogue of the naturally occuring three-dimensional stoichiometric materials with flat bands around the Fermi level. We consider 55,206 materials from the Inorganic Crystal Structure Database catalogued using the Topological Quantum Chemistry website4,5, which provides their structural parameters, space group, band structure, density of states and topological characterization. We combine several direct signatures and properties of band flatness with a high-throughput analysis of all crystal structures. In particular, we identify materials hosting line-graph or bipartite sublattices-in either two or three dimensions-that probably lead to flat bands. From this trove of information, we create the Materials Flatband Database website, a powerful search engine for future theoretical and experimental studies. We use the database to extract a curated list of 2,379 high-quality flat-band materials, from which we identify 345 promising candidates that potentially host flat bands with charge centres that are not strongly localized on the atomic sites. We showcase five representative materials and provide a theoretical explanation for the origin of their flat bands close to the Fermi energy using the S-matrix method introduced in a parallel work6.

Design of Antiferromagnetic Second-Order Band Topology with Rotation Topological Invariants in Two Dimensions.

The existence of fractionally quantized topological corner charge serves as a key indicator for two-dimensional (2D) second-order topological insulators (SOTIs), yet it has not been experimentally observed in realistic materials. Here, based on effective model analysis and symmetry arguments, we propose a strategy for achieving SOTI phases with in-gap corner states in 2D systems with antiferromagnetic (AFM) order. We discover that the band topology originates from the interplay between intrinsic spin-orbital coupling and interlayer AFM exchange interactions. Using first-principles calculations, we show that the 2D AFM SOTI phase can be realized in (MnBi2Te4)(Bi2Te3)m films. Moreover, we demonstrate that the SOTI states are linked to rotation topological invariants under 3-fold rotation symmetry C3, resulting in fractionally quantized corner charge, i.e., n3|e| (mod e). Due to the great achievements in (MnBi2Te4)(Bi2Te3)m systems, our results providing reliable material candidates for experimentally accessible AFM SOTIs should draw intense attention.

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.

Ordered Assembly of DNA on Topological Insulator Bi2Se3 and Octadecylamine for a Sensitive Biosensor.

Controlling the assembly of DNA in order on a suitable electrode surface is of great significance for biosensors and disease diagnosis, but it is full of challenges. In this work, we creatively assembled DNA on the surface of octadecylamine (ODA)-modified topological insulator (Tls) Bi2Se3 and developed an electrochemical biosensor to detect biomarker DNA of coronavirus disease 2019 (COVID-19). A high-quality Bi2Se3 sheet was obtained from a single crystal synthesized in our lab. A uniform ODA layer was coated in argon by chemical vapor deposition (CVD). We observed and analyzed the assembly and mechanism of single-strand DNA (ssDNA) and double-strand DNA (dsDNA) on the Bi2Se3 surface through atomic force microscopy (AFM) and molecular dynamics (MD) simulations. The electrochemical signal revealed that the biosensor based on the DNA/ODA/Bi2Se3 electrode has a wide linear detection range from 1.0 × 10-12 to 1.0 × 10-8 M, with the limit of detection as low as 5 × 10-13 M. Bi2Se3 has robust surface states and improves the electrochemical signal-to-noise ratio, while the uniform ODA layer guides high-density ordered DNA, enhancing the sensitivity of the biosensor. Our work demonstrates that the ordered DNA/ODA/Bi2Se3 electrode surface has great application potential in the field of biosensing and disease diagnosis.

Straight and twisted open nodal-line phonon states in the CaI2 family of materials.

Based on first-principles calculations and symmetry analysis, we propose that trigonal CaI2 with the space group P3̄m1 possesses straight and twisted open nodal-line phonon states with linear dispersion. The symmetry analysis indicates that joint symmetry PT and rotational symmetry C3z protect the straight nodal lines along Γ-A and K-H while PT and mirror symmetry M010 (M110) maintain the twisted nodal lines that traverse Γ-M (Γ-K) and A-L (A-H). The calculated π Berry phase suggests that all the nodal lines are nontrivial and the corresponding drumhead-like surface states are clearly visible in the observation window, which is less than 6 THz, suggesting a significant chance for them to be measured using meV-resolution inelastic X-ray scattering. The distribution of the nodal lines in the Brillouin zone is also confirmed by the phononic tight-binding model. Furthermore, the isostructural compounds MgBr2 and MgI2 show similar phonon spectra and topological nontrivial surface states. This work provides promising candidates for investigating straight and twisted open nodal-line phonon states in a single material, which will facilitate future experimental observation.

Pressure-induced phase transitions and superconductivity in a quasi-1-dimensional topological crystalline insulator α-Bi4Br4.

Great progress has been achieved in the research field of topological states of matter during the past decade. Recently, a quasi-1-dimensional bismuth bromide, Bi4Br4, has been predicted to be a rotational symmetry-protected topological crystalline insulator; it would also exhibit more exotic topological properties under pressure. Here, we report a thorough study of phase transitions and superconductivity in a quasihydrostatically pressurized α-Bi4Br4 crystal by performing detailed measurements of electrical resistance, alternating current magnetic susceptibility, and in situ high-pressure single-crystal X-ray diffraction together with first principles calculations. We find a pressure-induced insulator-metal transition between ∼3.0 and 3.8 GPa where valence and conduction bands cross the Fermi level to form a set of small pockets of holes and electrons. With further increase of pressure, 2 superconductive transitions emerge. One shows a sharp resistance drop to 0 near 6.8 K at 3.8 GPa; the transition temperature gradually lowers with increasing pressure and completely vanishes above 12.0 GPa. Another transition sets in around 9.0 K at 5.5 GPa and persists up to the highest pressure of 45.0 GPa studied in this work. Intriguingly, we find that the first superconducting phase might coexist with a nontrivial rotational symmetry-protected topology in the pressure range of ∼3.8 to 4.3 GPa; the second one is associated with a structural phase transition from monoclinic C2/m to triclinic P-1 symmetry.

Weyl Monoloop Semi-Half-Metal and Tunable Anomalous Hall Effect.

Nodal monoloop, enjoying the cleanest scenario with a single loop, is recognized as the basic building block of intricate linked loops including chains, nets, and knots. Here, we explore the interplay of magnetic ordering and band topology in one system by introducing a brand-new quantum state, referred to as Weyl monoloop semi-half-metal, which is characterized by a single loop at the Fermi level stemming from the same spin channel. Such a nodal line Fermion, yielding 100% spin polarization, is protected by mirror (Mz) symmetry. As a prominent example, a realistic rutile-type metal fluorides LiV2F6 achieves the hitherto unmaterialized state, featuring fully spin-polarized ultraflat surface states. More interestingly, LiV2F6 has a "soft" ferromagnetic property, which is one of the desired systems to control the anomalous Hall effect by rotating the magnetization direction. Our findings offer a promising candidate for exploring the topology and magnetism with intriguing effects.

Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices.

Topological flat bands, such as the band in twisted bilayer graphene, are becoming a promising platform to study topics such as correlation physics, superconductivity, and transport. In this Letter, we introduce a generic approach to construct two-dimensional (2D) topological quasiflat bands from line graphs and split graphs of bipartite lattices. A line graph or split graph of a bipartite lattice exhibits a set of flat bands and a set of dispersive bands. The flat band connects to the dispersive bands through a degenerate state at some momentum. We find that, with spin-orbit coupling (SOC), the flat band becomes quasiflat and gapped from the dispersive bands. By studying a series of specific line graphs and split graphs of bipartite lattices, we find that (i) if the flat band (without SOC) has inversion or C_{2} symmetry and is nondegenerate, then the resulting quasiflat band must be topologically nontrivial, and (ii) if the flat band (without SOC) is degenerate, then there exists a SOC potential such that the resulting quasiflat band is topologically nontrivial. This generic mechanism serves as a paradigm for finding topological quasiflat bands in 2D crystalline materials and metamaterials.

Catalog of topological phonon materials.

Phonons play a crucial role in many properties of solid-state systems, and it is expected that topological phonons may lead to rich and unconventional physics. On the basis of the existing phonon materials databases, we have compiled a catalog of topological phonon bands for more than 10,000 three-dimensional crystalline materials. Using topological quantum chemistry, we calculated the band representations, compatibility relations, and band topologies of each isolated set of phonon bands for the materials in the phonon databases. Additionally, we calculated the real-space invariants for all the topologically trivial bands and classified them as atomic or obstructed atomic bands. We have selected more than 1000 "ideal" nontrivial phonon materials to motivate future experiments. The datasets were used to build the Topological Phonon Database.

2D Ladder Polyborane: An Ideal Dirac Semimetal with a Multi-Field-Tunable Band Gap.

Hydrogen, a simple and magic element, has attracted increasing attention for its effective incorporation within solids and powerful manipulation of electronic states. Here, we show that hydrogenation tackles common problems in two-dimensional borophene, e.g., stability and applicability. As a prominent example, a ladder-like boron hydride sheet, named as 2D ladder polyborane, achieves the desired outcome, enjoying the cleanest scenario with an anisotropic and tilted Dirac cone, that can be fully depicted by a minimal two-band tight-binding model. Introducing external fields, such as an electric field or a circularly polarized light field, can effectively induce distinctive massive Dirac fermions, whereupon four types of multi-field-driven topological domain walls hosting tunable chirality and valley indexes are further established. Moreover, the 2D ladder polyborane is thermodynamically stable at room temperature and supports highly switchable Dirac fermions, providing an ideal platform for realizing and exploring the various multi-field-tunable electronic states.

Optical bulk-boundary dichotomy in a quantum spin Hall insulator.

The bulk-boundary correspondence is a critical concept in topological quantum materials. For instance, a quantum spin Hall insulator features a bulk insulating gap with gapless helical boundary states protected by the underlying Z2 topology. However, the bulk-boundary dichotomy and distinction are rarely explored in optical experiments, which can provide unique information about topological charge carriers beyond transport and electronic spectroscopy techniques. Here, we utilize mid-infrared absorption micro-spectroscopy and pump-probe micro-spectroscopy to elucidate the bulk-boundary optical responses of Bi4Br4, a recently discovered room-temperature quantum spin Hall insulator. Benefiting from the low energy of infrared photons and the high spatial resolution, we unambiguously resolve a strong absorption from the boundary states while the bulk absorption is suppressed by its insulating gap. Moreover, the boundary absorption exhibits strong polarization anisotropy, consistent with the one-dimensional nature of the topological boundary states. Our infrared pump-probe microscopy further measures a substantially increased carrier lifetime for the boundary states, which reaches one nanosecond scale. The nanosecond lifetime is about one to two orders longer than that of most topological materials and can be attributed to the linear dispersion nature of the helical boundary states. Our findings demonstrate the optical bulk-boundary dichotomy in a topological material and provide a proof-of-principal methodology for studying topological optoelectronics.

Observation of Topological Edge States on α-Bi4Br4 Nanowires Grown on TiSe2 Substrates.

A time-reversal invariant two-dimensional (2D) topological insulator (TI) is characterized by the gapless helical edge states propagating along the perimeter of the system. However, the small band gap in the 2D TIs discovered so far hinders their applications. Recently, we predicted that single-layer Bi4Br4 is a 2D TI with a remarkable band gap and that α-Bi4Br4 crystals can host topological edge states at the step edges. Here we report the growth of α-Bi4Br4 nanowires with (102)-oriented top surfaces on the TiSe2 substrates and the direct observation of the predicted topological edge states at the step edges of the nanowires using scanning tunneling microscopy. The coupling between the edge states leads to the formation of surface states at the (102) top surfaces of the nanowires. Our work demonstrates the existence of topological edge states in α-Bi4Br4 and paves the way for developing α-Bi4Br4-based devices for a high-temperature quantum spin Hall effect.

Weyl Nodal Point-Line Fermion in Ferromagnetic Eu5Bi3.

On the basis of ab initio calculations and a low-energy effective k· p model, we propose a Weyl nodal point-line (WNPL) fermion, composed of 0D Weyl points and a 1D Weyl nodal line, in the ferromagnetic material Eu5Bi3. In the absence of spin-orbital coupling (SOC), the spin-up bands host a pair of triply degenerate points together with a bird-cage-like node structure. In the presence of SOC with (001) magnetization, each triplet point splits into a double Weyl point and a single Weyl point accompanied by two nodal rings, forming two sets of WNPL fermions near the Fermi level. The novel properties of the WNPL fermion are explored by revealing the unusual Berry curvature field and demonstrating the pinned chiral surface states with exotic Fermi arcs. Our work offers new ideas for exploring novel topological semimetal states with diverse band-crossing dimensions and provides a candidate for future experimental realization.

Fully Spin-Polarized Nodal Loop Semimetals in Alkaline Metal Monochalcogenide Monolayers.

Topological semimetals in ferromagnetic materials have attracted an enormous amount of attention due to potential applications in spintronics. Using first-principles density functional theory together with an effective lattice model, here we present a new family of topological semimetals with a fully spin-polarized nodal loop in alkaline metal monochalcogenide MX (M = Li, Na, K, Rb, or Cs; X = S, Se, or Te) monolayers. The half-metallic ferromagnetism can be established in MX monolayers, in which one nodal loop formed by two crossing bands with the same spin components is found at the Fermi energy. This nodal loop half-metal survives even when considering the spin-orbit coupling owing to the symmetry protection provided by the Mz mirror plane. The quantum anomalous Hall state and Weyl-like semimetal in this system can be also achieved by rotating the spin from the out-of-plane to the in-plane direction. The MX monolayers hosting rich topological phases thus offer an excellent platform for realizing advanced spintronic concepts.