Anomalous electrons in a metallic kagome ferromagnet.

Ordinary metals contain electron liquids within well-defined 'Fermi' surfaces at which the electrons behave as if they were non-interacting. In the absence of transitions to entirely new phases such as insulators or superconductors, interactions between electrons induce scattering that is quadratic in the deviation of the binding energy from the Fermi level. A long-standing puzzle is that certain materials do not fit this 'Fermi liquid' description. A common feature is strong interactions between electrons relative to their kinetic energies. One route to this regime is special lattices to reduce the electron kinetic energies. Twisted bilayer graphene1-4 is an example, and trihexagonal tiling lattices (triangular 'kagome'), with all corner sites removed on a 2 × 2 superlattice, can also host narrow electron bands5 for which interaction effects would be enhanced. Here we describe spectroscopy revealing non-Fermi-liquid behaviour for the ferromagnetic kagome metal Fe3Sn2 (ref. 6). We discover three C3-symmetric electron pockets at the Brillouin zone centre, two of which are expected from density functional theory. The third and most sharply defined band emerges at low temperatures and binding energies by means of fractionalization of one of the other two, most likely on the account of enhanced electron-electron interactions owing to a flat band predicted to lie just above the Fermi level. Our discovery opens the topic of how such many-body physics involving flat bands7,8 could differ depending on whether they arise from lattice geometry or from strongly localized atomic orbitals9,10.

Unconventional Flat Chern Bands and 2e Charges in Skyrmionic Moiré Superlattices.

The interplay of topological characteristics in real space and reciprocal space can lead to the emergence of unconventional topological phases. In this Letter, we implement a novel mechanism for generating higher-Chern flat bands on the basis of twisted bilayer graphene (TBG) coupled to topological magnetic structures in the form of the skyrmion lattice. In particular, we discover a scenario for generating |C| = 2 dispersionless electronic bands when the skyrmion periodicity and the moiré periodicity match. Following the Wilczek argument, the statistics of the charge-carrying excitations in this case is bosonic, characterized by electronic charge Q = 2e, which is even in units of electron charge e. The skyrmion coupling strength triggering the topological phase transition is realistic, with its lower bound estimated as 4 meV. The Hofstadter butterfly spectrum results in an unexpected quantum Hall conductance sequence ±2e2h,±4e2h,... for TBG with the skyrmion order.

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.

Multiple mobile excitons manifested as sidebands in quasi-one-dimensional metallic TaSe3.

Charge neutrality and their expected itinerant nature makes excitons potential transmitters of information. However, exciton mobility remains inaccessible to traditional optical experiments that only create and detect excitons with negligible momentum. Here, using angle-resolved photoemission spectroscopy, we detect dispersing excitons in the quasi-one-dimensional metallic trichalcogenide, TaSe3. The low density of conduction electrons and the low dimensionality in TaSe3 combined with a polaronic renormalization of the conduction band and the poorly screened interaction between these polarons and photo-induced valence holes leads to various excitonic bound states that we interpret as intrachain and interchain excitons, and possibly trions. The thresholds for the formation of a photo-hole together with an exciton appear as side valence bands with dispersions nearly parallel to the main valence band, but shifted to lower excitation energies. The energy separation between side and main valence bands can be controlled by surface doping, enabling the tuning of certain exciton properties.

Engineering SYK Interactions in Disordered Graphene Flakes under Realistic Experimental Conditions.

We model interactions following the Sachdev-Ye-Kitaev (SYK) framework in disordered graphene flakes up to 300 000 atoms in size (∼100 nm in diameter) subjected to an out-of-plane magnetic field B of 5-20 Tesla within the tight-binding formalism. We investigate two sources of disorder: (i) irregularities at the system boundaries, and (ii) bulk vacancies-for a combination of which we find conditions that could be favorable for the formation of the phase with Sachdev-Ye-Kitaev features under realistic experimental conditions above the liquid helium temperature.

Flat-Band-Induced Many-Body Interactions and Exciton Complexes in a Layered Semiconductor.

Interactions among a collection of particles generate many-body effects in solids that result in striking modifications of material properties. The heavy carrier mass that yields strong interactions and gate control of carrier density over a wide range makes two-dimensional semiconductors an exciting playground to explore many-body physics. The family of III-VI metal monochalcogenides emerges as a new platform for this purpose because of its excellent optical properties and the flat valence band dispersion. In this work, we present a complete study of charge-tunable excitons in few-layer InSe by photoluminescence spectroscopy. From the optical spectra, we establish that free excitons in InSe are more likely to be captured by ionized donors leading to the formation of bound exciton complexes. Surprisingly, a pronounced red shift of the exciton energy accompanied by a decrease of the exciton binding energy upon hole-doping reveals a significant band gap renormalization induced by the presence of the Fermi reservoir.

Mott versus Hybridization Gap in the Low-Temperature Phase of 1T-TaS_{2}.

We address the long-standing problem of the ground state of 1T-TaS_{2} by computing the correlated electronic structure of stacked bilayers using the GW+EDMFT method. Depending on the surface termination, the semi-infinite uncorrelated system is either band insulating or exhibits a metallic surface state. For realistic values of the on-site and inter-site interactions, a Mott gap opens in the surface state, but it is smaller than the gap originating from the bilayer structure. Our results are consistent with recent scanning tunneling spectroscopy measurements for different terminating layers, and with our own photoemission measurements, which indicate the coexistence of spatial regions with different gaps in the electronic spectrum. By comparison to exact diagonalization data, we clarify the interplay between Mott insulating and band insulating behavior in this archetypal layered system.

Crystal Field Effect and Electric Field Screening in Multilayer Graphene with and without Twist.

We address the intrinsic polarization and screening of an external electric field in a broad range of ordered and twisted configurations of multilayer graphene, using an ab initio approach combining density functional theory and the Wannier function formalism. We show that multilayer graphene is intrinsically polarized due to the crystal field effect, an effect that is often neglected in tight-binding models of twisted bilayer graphene and similar systems. This intrinsic polarization of the order of up to a few tens of millielectronvolts has different out-of-plane alignments in ordered and twisted graphene multilayers, while the in-plane potential modulation is found to be much stronger in twisted systems. We further investigate the dielectric permittivity ε in same multilayer graphene configurations at different electric field strengths. Our findings establish a deep insight into intrinsic and extrinsic polarization in graphene multilayers and provide parameters necessary for building accurate models of these systems.

Landau Levels as a Probe for Band Topology in Graphene Moiré Superlattices.

We propose Landau levels as a probe for the topological character of electronic bands in two-dimensional moiré superlattices. We consider two configurations of twisted double bilayer graphene (TDBG) that have very similar band structures, but show different valley Chern numbers of the flat bands. These differences between the AB-AB and AB-BA configurations of TDBG clearly manifest as different Landau level sequences in the Hofstadter butterfly spectra calculated using the tight-binding model. The Landau level sequences are explained from the point of view of the distribution of orbital magnetization in momentum space that is governed by the rotational C_{2} and time-reversal T symmetries. Our results can be readily extended to other twisted graphene multilayers and h-BN/graphene heterostructures thus establishing the Hofstadter butterfly spectra as a powerful tool for detecting the nontrivial valley band topology.

Moiré Flat Bands in Twisted Double Bilayer Graphene.

We investigate twisted double bilayer graphene (TDBG), a four-layer system composed of two AB-stacked graphene bilayers rotated with respect to each other by a small angle. Our ab initio band structure calculations reveal a considerable energy gap at the charge-neutrality point that we assign to the intrinsic symmetric polarization (ISP). We then introduce the ISP effect into the tight-binding parametrization and perform calculations on TDBG models that include lattice relaxation effects down to very small twist angles. We identify a narrow region around the magic angle characterized by a manifold of remarkably flat bands gapped out from other states even without external electric fields. To understand the fundamental origin of the magic angle in TDBG, we construct a continuum model that points to a hidden mathematical link to the twisted bilayer graphene model, thus indicating that the band flattening is a fundamental feature of TDBG and is not a result of external fields.

Artificial Neural Network Approach to the Analytic Continuation Problem.

Inverse problems are encountered in many domains of physics, with analytic continuation of the imaginary Green's function into the real frequency domain being a particularly important example. However, the analytic continuation problem is ill defined and currently no analytic transformation for solving it is known. We present a general framework for building an artificial neural network (ANN) that solves this task with a supervised learning approach. Application of the ANN approach to quantum Monte Carlo calculations and simulated Green's function data demonstrates its high accuracy. By comparing with the commonly used maximum entropy approach, we show that our method can reach the same level of accuracy for low-noise input data, while performing significantly better when the noise strength increases. The computational cost of the proposed neural network approach is reduced by almost three orders of magnitude compared to the maximum entropy method.

Hydrogen Bonding of Ammonia with (H,OH)-Si(001) Revealed by Experimental and Ab Initio Photoelectron Spectroscopy.

Combining experimental and ab initio core-level photoelectron spectroscopy (periodic DFT and quantum chemistry calculations), we elucidated how ammonia molecules bond to the hydroxyls of the (H,OH)-Si(001) model surface at a temperature of 130 K. Indeed, theory evaluated the magnitude and direction of the N 1s (and O 1s) chemical shifts according to the nature (acceptor or donor) of the hydrogen bond and, when confronted to experiment, showed unambiguously that the probe molecule makes one acceptor and one donor bond with a pair of hydroxyls. The consistency of our approach was proved by the fact that the identified adsorption geometries are precisely those that have the largest binding strength to the surface, as calculated by periodic DFT. Real-time core-level photoemission enabled measurement of the adsorption kinetics of H-bonded ammonia and its maximum coverage (0.37 ML) under 1.5 × 10-9 mbar. Experimental desorption free energies were compared to the magnitude of the adsorption energies provided by periodic DFT calculations. Minority species were also detected on the surface. As in the case of H-bonded ammonia, DFT core-level calculations were instrumental to attribute these minority species to datively bonded ammonia molecules, associated with isolated dangling bonds remaining on the surface, and to dissociated ammonia molecules, resulting largely from beam damage.

Manipulating Topological Domain Boundaries in the Single-Layer Quantum Spin Hall Insulator 1T'-WSe2.

We report the creation and manipulation of structural phase boundaries in the single-layer quantum spin Hall insulator 1T'-WSe2 by means of scanning tunneling microscope tip pulses. We observe the formation of one-dimensional interfaces between topologically nontrivial 1T' domains having different rotational orientations, as well as induced interfaces between topologically nontrivial 1T' and topologically trivial 1H phases. Scanning tunneling spectroscopy measurements show that 1T'/1T' interface states are localized at domain boundaries, consistent with theoretically predicted unprotected interface modes that form dispersive bands in and around the energy gap of this quantum spin Hall insulator. We observe a qualitative difference in the experimental spectral line shape between topologically "unprotected" states at 1T'/1T' domain boundaries and protected states at 1T'/1H and 1T'/vacuum boundaries in single-layer WSe2.

A novel quasi-one-dimensional topological insulator in bismuth iodide ß-Bi4I4.

Recent progress in the field of topological states of matter has largely been initiated by the discovery of bismuth and antimony chalcogenide bulk topological insulators (TIs; refs ,,,), followed by closely related ternary compounds and predictions of several weak TIs (refs ,,). However, both the conceptual richness of Z2 classification of TIs as well as their structural and compositional diversity are far from being fully exploited. Here, a new Z2 topological insulator is theoretically predicted and experimentally confirmed in the ß-phase of quasi-one-dimensional bismuth iodide Bi4I4. The electronic structure of ß-Bi4I4, characterized by Z2 invariants (1;110), is in proximity of both the weak TI phase (0;001) and the trivial insulator phase (0;000). Our angle-resolved photoemission spectroscopy measurements performed on the (001) surface reveal a highly anisotropic band-crossing feature located at the  point of the surface Brillouin zone and showing no dispersion with the photon energy, thus being fully consistent with the theoretical prediction.

Topological aspects of charge-carrier transmission across grain boundaries in graphene.

Dislocations and grain boundaries are intrinsic topological defects of large-scale polycrystalline samples of graphene. These structural irregularities have been shown to strongly affect electronic transport in this material. Here, we report a systematic investigation of the transmission of charge carriers across the grain-boundary defects in polycrystalline graphene by means of the Landauer-Büttiker formalism within the tight-binding approximation. Calculations reveal a strong suppression of transmission at low energies upon decreasing the density of dislocations with the smallest Burgers vector b = (1,0). The observed transport anomaly is explained from the point of view of resonant backscattering due to localized states of topological origin. These states are related to the gauge field associated with all dislocations characterized by b = (n,m) with n - m ≠ 3q (q ∈ Z). Our work identifies an important source of charge-carrier scattering caused by the topological defects present in large-area graphene samples produced by chemical vapor deposition.

Grain boundaries in graphene on SiC(0001Ì ) substrate.

Grain boundaries in epitaxial graphene on the SiC(0001̅) substrate are studied using scanning tunneling microscopy and spectroscopy. All investigated small-angle grain boundaries show pronounced out-of-plane buckling induced by the strain fields of constituent dislocations. The ensemble of observations determines the critical misorientation angle of buckling transition θc = 19 ± 2°. Periodic structures are found among the flat large-angle grain boundaries. In particular, the observed θ = 33 ± 2° highly ordered grain boundary is assigned to the previously proposed lowest formation energy structural motif composed of a continuous chain of edge-sharing alternating pentagons and heptagons. This periodic grain boundary defect is predicted to exhibit strong valley filtering of charge carriers thus promising the practical realization of all-electric valleytronic devices.

A guide to the design of electronic properties of graphene nanoribbons.

Graphene nanoribbons (GNRs) are one-dimensional nanostructures predicted to display a rich variety of electronic behaviors. Depending on their structure, GNRs realize metallic and semiconducting electronic structures with band gaps that can be tuned across broad ranges. Certain GNRs also exhibit a peculiar gapped magnetic phase for which the half-metallic state can be induced as well as the topologically nontrivial quantum spin Hall electronic phase. Because their electronic properties are highly tunable, GNRs have quickly become a popular subject of research toward the design of graphene-based nanostructures for technological applications. This Account presents a pedagogical overview of the various degrees of freedom in the atomic structure and interactions that researchers can use to tailor the electronic structure of these materials. The Account provides a broad picture of relevant physical concepts that would facilitate the rational design of GNRs with desired electronic properties through synthetic techniques. We start by discussing a generic model of zigzag GNR within the tight-binding model framework. We then explain how different modifications and extensions of the basic model affect the electronic band structures of GNRs. We classify the modifications based on the following categories: (1) electron-electron and spin-orbit interactions, (2) GNR configuration, which includes width and the crystallographic orientation of the nanoribbon (chirality), and (3) the local structure of the edge. We subdivide this last category into two groups: the effects of the termination of the π-electron system and the variations of electrostatic potential at the edge. This overview of the structure-property relationships provides a view of the many different electronic properties that GNRs can realize. The second part of this Account reviews three recent experimental methods for the synthesis of structurally well-defined GNRs. We describe a family of techniques that use patterning and etching of graphene and graphite to produce GNRs. Chemical unzipping of carbon nanotubes also provides a route toward producing chiral GNRs with atomically smooth edges. Scanning tunneling microscopy/spectroscopy investigations of these unzipped GNRs have revealed edge states and strongly suggest that these GNRs are magnetic. The third approach exploits the surface-assisted self-assembly of GNRs from molecular precursors. This powerful method can provide full control over the atomic structure of narrow nanoribbons and could eventually produce more complex graphene nanostructures.

Electronic transport in graphene with aggregated hydrogen adatoms.

Hydrogen adatoms and other species covalently bound to graphene act as resonant scattering centers affecting the electronic transport properties and inducing Anderson localization. We show that attractive interactions between adatoms on graphene and their diffusion mobility strongly modify the spatial distribution, thus fully eliminating isolated adatoms and increasing the population of larger size adatom aggregates. Such spatial correlation is found to strongly influence the electronic transport properties of disordered graphene. Our scaling analysis shows that such aggregation of adatoms increases conductance by up to several orders of magnitude and results in significant extension of the Anderson localization length in the strong localization regime. We introduce a simple definition of the effective adatom concentration x*, which describes the transport properties of both random and correlated distributions of hydrogen adatoms on graphene across a broad range of concentrations.

Observation of Kekulé vortices around hydrogen adatoms in graphene.

Fractional charges are one of the wonders of the fractional quantum Hall effect. Such objects are also anticipated in two-dimensional hexagonal lattices under time reversal symmetry-emerging as bound states of a rotating bond texture called a Kekulé vortex. However, the physical mechanisms inducing such topological defects remain elusive, preventing experimental realization. Here, we report the observation of Kekulé vortices in the local density of states of graphene under time reversal symmetry. The vortices result from intervalley scattering on chemisorbed hydrogen adatoms. We uncover that their 2π winding is reminiscent of the Berry phase π of the massless Dirac electrons. We can also induce a Kekulé pattern without vortices by creating point scatterers such as divacancies, which break different point symmetries. Our local-probe study thus confirms point defects as versatile building blocks for Kekulé engineering of graphene's electronic structure.

Electrical detection of the flat-band dispersion in van der Waals field-effect structures.

Two-dimensional flat-band systems have recently attracted considerable interest due to the rich physics unveiled by emergent phenomena and correlated electronic states at van Hove singularities. However, the difficulties in electrically detecting the flat-band position in field-effect structures are slowing down the investigation of their properties. In this work, we use indium selenide (InSe) as a flat-band system due to a van Hove singularity at the valence-band edge in a few-layer form of the material without the requirement of a twist angle. We investigate tunnelling photocurrents in gated few-layer InSe structures and relate them to ambipolar transport and photoluminescence measurements. We observe an appearance of a sharp change in tunnelling mechanisms due to the presence of the van Hove singularity at the flat band. We further corroborate our findings by studying tunnelling currents as a reliable probe for the flat-band position up to room temperature. Our results create an alternative approach to studying flat-band systems in heterostructures of two-dimensional materials.