Search

Materials with topological 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 moir\'e systems. Here we report a general way to construct one-dimensional (1D) flat bands in phosphorene nanoribbons (PNRs) with pentagonal nature: penta-hexa-PNRs and penta-dodeca-PNRs, wherein the corresponding flat bands are directly verified by using angle-resolved photoemission spectroscopy. We confirm that the observed 1D flat bands originate from the electronic 1D sawtooth 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. Our 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., Comment: 13 pages, 4 figures

Topological design of pi-electrons in zigzag-edged graphene nanoribbons (ZGNRs) leads to a wealth of magnetic quantum phenomena and exotic quantum phases. Symmetric ZGNRs typically exhibit antiferromagnetically coupled spin-ordered edge states. Eliminating cross-edge magnetic coupling in ZGNRs not only enables the realization of a new class of ferromagnetic quantum spin chains, enabling the exploration of quantum spin physics and entanglement of multiple qubits in the 1D limit, but also establishes a long-sought carbon-based ferromagnetic transport channel, pivotal for ultimate scaling of GNR-based quantum electronics. However, designing such GNRs entails overcoming daunting challenges, including simultaneous breaking of structural and spin symmetries, and designing elegant precursors for asymmetric fabrication of reactive zigzag edges. Here, we report a general approach for designing and fabricating such ferromagnetic GNRs in the form of Janus GNRs with two distinct edge configurations. Guided by Lieb's theorem and topological classification theory, we devised two JGNRs by asymmetrically introduced a topological defect array of benzene motifs to one zigzag edge, while keeping the opposing zigzag edge unchanged. This breaks structural symmetry and creates a sublattice imbalance within each unit cell, initiating a spin symmetry breaking. Three Z-shape precursors are designed to fabricate one parent ZGNR and two JGNRs with an optimal lattice spacing of the defect array for a complete quench of the magnetic edge states at the defective edge. Characterization via scanning probe microscopy/spectroscopy and first-principles density functional theory confirms the successful fabrication of Janus GNRs with ferromagnetic ground state delocalised along the pristine zigzag edge., Comment: 19 pages, 4 figures

We present here a method of probing the wave functions of a degenerate shell in a triangular graphene quantum dot, triangulene, using a localized substitutional impurity. We demonstrate its applicability to the example of aza-triangulenes. Using the analytical solution for degenerate states of an all-carbon triangulene as a basis for a triangulene containing a nitrogen impurity, we predict the structure of the zero energy shell in the presence of this impurity. We show that the impurity allows probing of the wave functions of a degenerate shell on a carbon site where it is located. We confirm our predictions by a comparison with the tight-binding and ab-initio calculation as well as with experiment.

Twisted bilayers of two-dimensional materials have emerged as a highly tunable platform for studying broken symmetry phases. While most interest has been focused on emergent states in systems whose constituent monolayers do not feature broken symmetry states, assembling monolayers that exhibit ordered states into twisted bilayers can also give rise to interesting phenomena. Here, we use large-scale first-principles density-functional theory calculations to study the atomic structure of twisted bilayer $\mathrm{{N}b{S}e_2}$ whose constituent monolayers feature a charge density wave. We find that different charge density wave states coexist in the ground state of the twisted bilayer: monolayer-like $3\times 3$ triangular and hexagonal charge density waves are observed in low-energy stacking regions, while stripe charge density waves are found in the domain walls surrounding the low-energy stacking regions. These predictions, which can be tested by scanning tunneling microscopy experiments, highlight the potential to create complex charge density wave ground states in twisted bilayer systems and can serve as a starting point for understanding superconductivity occurring at low temperatures.

We discuss coexistence of Kondo and spin excitation signals in tunneling spectroscopy in strongly correlated polyradical $\pi$-magnetic nanographenes on a metal surface. The Kondo signal is rationalized by a multi-orbital Kondo screening of the unpaired electrons. The fundamental processes are spin-flips of antiferromagnetic (AFM) order involving charged molecular multiplets. We introduce a~perturbative model, which provides simple rules to identify the presence of AFM channels responsible for Kondo screening. The Kondo regime is confirmed by numerical renormalization group calculations. This framework can be applied to similar strongly correlated open-shell systems., Comment: 43 pages (14 in main, 29 in SM), 20 figures (3 in main, 17 in SM)

Chemical activation of the intrinsically inert basal planes of transition metal dichalcogenides (TMDs) is crucial for developing high-efficiency electrocatalysts for energy technology applications. Here we report the discovery of an efficient TMD-based topological catalyst for hydrogen evolution reaction (HER), containing high-density single-atom reactive centers on a few-layer (7x7)-PtTe2-x superstructure with a Te-vacancy density of x. Compared with pristine Pt(111), PtTe2, and (2x2)-PtTe2-x, (7x7)-PtTe2-x exhibits superior HER performance owing to its substantially increased density of undercoordinated Pt sites, and displays exceptional catalytic stability when operating at high current densities. Our first-principles calculations confirm that multiple types of undercoordinated Pt sites on (7x7)-PtTe2-x exhibit favorable hydrogen adsorption Gibbs free energies, and that the reactive sites can further increase their population upon increasing hydrogen coverage. Both the (2x2)- and (7x7)-PtTe2-x are also shown to possess nontrivial band topology with robust edge states that may further facilitate HER.

The atomic doping of open-shell nanographenes enables the precise tuning of their electronic and magnetic state, which is crucial for their promising potential applications in optoelectronics and spintronics. Among this intriguing class of molecules, triangulenes stand out with their size-dependent electronic properties and spin states, which can also be influenced by the presence of dopant atoms and functional groups. However, the occurrence of Jahn-Teller distortions in such systems can have a crucial impact on their total spin and requires further theoretical and experimental investigation. In this study, we examine the nitrogen-doped aza-triangulene series via a combination of density functional theory and on-surface synthesis. We identify a general trend in the calculated spin states of aza-[n]triangulenes of various sizes, separating them into two symmetry classes, one of which features molecules that are predicted to undergo Jahn-Teller distortions that reduce their symmetry and thus their total spin. We link this behavior to the location of the central nitrogen atom relative to the two underlying carbon sublattices of the molecules. Consequently, our findings reveal that centrally-doped aza-triangulenes have one less radical than their undoped counterparts, irrespective of their predicted symmetry. We follow this by demonstrating the on-surface synthesis of {\pi}-extended aza-[5]triangulene, a large member of the higher symmetry class without Jahn-Teller distortions, via a simple one-step annealing process on Cu(111) and Au(111). Using scanning probe microscopy and spectroscopy combined with theoretical calculations, we prove that the molecule is positively charged on the Au(111) substrate, with a high-spin quintet state of S = 2, the same total spin as undoped neutral [5]triangulene., Comment: Main paper 18 pages, 5 figures. Removed hyphen from author name, addded funding information for one author

Patterning antidots ("voids") into well-defined antidot lattices creates an intriguing class of artificial structures for the periodic modulation of 2D electron systems, leading to anomalous transport properties and exotic quantum phenomena as well as enabling the precise bandgap engineering of 2D materials to address technological bottleneck issues. However, realizing such atomic-scale quantum antidots (QADs) is infeasible by current nanolithographic techniques. Here, we report an atomically-precise bottom-up fabrication of a series of atomic-scale QADs with elegantly engineered quantum states through a controllable assembly of a chalcogenide single vacancy (SV) in 2D PtTe2, a type-II Dirac semimetal. Te SVs as atomic-scale "antidots" undergo thermal migration and assembly into highly-ordered SV lattices spaced by a single Te atom, reaching the ultimate downscaling limit of antidot lattices. Increasing the number of SVs in QADs strengthens the cumulative repulsive potential and consequently enhances collective interference of multiple-pocket scattered quasiparticles inside QADs, creating multi-level quantum hole states with tunable gap from telecom to far-infrared regime. Moreover, precisely engineered quantum hole states of QADs are symmetry-protected and thus survive upon atom-by-atom oxygen substitutional doping. Therefore, SV-assembled QADs exhibit unprecedented robustness and property tunability, which not only holds the key to their future applications but also embody a wide variety of material technologies.

Open-shell benzenoid polycyclic aromatic hydrocarbons, known as magnetic nanographenes, exhibit unconventional p-magnetism arising from topological frustration or strong electronic-electron (e-e) interaction. Imprinting multiple strongly entangled spins into polyradical nanographenes creates a major paradigm shift in realizing non-trivial collective quantum behaviors and exotic quantum phases in organic quantum materials. However, conventional design approaches are limited by a single magnetic origin, which can restrict the number of correlated spins or the type of magnetic ordering in open-shell nanographenes. Here, we present a novel design strategy combing topological frustration and e-e interactions to fabricate the largest fully-fused open-shell nanographene reported to date, a 'butterfly'-shaped tetraradical on Au(111). We employed bond-resolved scanning tunneling microscopy and spin excitation spectroscopy to unambiguously resolve the molecular backbone and reveal the strongly correlated open-shell character, respectively. This nanographene contains four unpaired electrons with both ferromagnetic and anti-ferromagnetic interactions, harboring a many-body singlet ground state and strong multi-spin entanglement, which can be well described by many-body calculations. Furthermore, we demonstrate that the nickelocene magnetic probe can sense highly-correlated spin states in nanographene. The ability to imprint and characterize many-body strongly correlated spins in polyradical nanographenes not only presents exciting opportunities for realizing non-trivial quantum magnetism and phases in organic materials but also paves the way toward high-density ultrafast spintronic devices and quantum information technologies., Comment: 17 pages, 4 figures

Emergent quantum phenomena in two-dimensional van der Waal (vdW) magnets are largely governed by the interplay between the exchange and Coulomb interactions. The ability to tune the Coulomb interaction in such strongly correlated materials enables the precise control of spin-correlated flat-band states, bandgap (Eg) and unconventional magnetism, all of which are crucial for next-generation spintronics and magnonics applications. Here, we demonstrate a giant gate-tunable renormalization of spin-correlated flat-band states and bandgap in magnetic chromium tribromide (CrBr3) monolayers grown on graphene. Our gate-dependent scanning tunneling spectroscopy (STS) studies reveal that the inter-flat-band spacing and bandgap of CrBr3 can be continuously tuned by 120 meV and 240 meV respectively via electrostatic injection of carriers into the hybrid CrBr3/graphene system, equivalent to the modulation of the Cr on-site Coulomb repulsion energy by 500 meV. This can be attributed to the self-screening of CrBr3 arising from the gate-induced carriers injected into CrBr3, which dominates over the opposite trend from the remote screening of the graphene substrate. Precise tuning of the spin-correlated flat-band states and bandgap in 2D magnets via electrostatic modulation of Coulomb interactions not only provides new strategies for optimizing the spin transport channels but also may exert a crucial influence on the exchange energy and spin-wave gap, which could raise the critical temperature for magnetic order., Comment: 21 pages, 4 figures

Strain-induced pseudo magnetic fields offer the possibility of realizing zero magnetic field Quantum Hall effect in graphene, possibly up to room temperature, representing a promising avenue for lossless charge transport applications. Strain engineering on graphene has been achieved via random nanobubbles or artificial nanostructures on the substrate, but the highly localized and non-uniform pseudomagnetic fields can make spectroscopic probes of electronic structure difficult. Heterostructure engineering offers an alternative approach: By stacking graphene on top of another van der Waals material with large lattice mismatch at a desired twist angle, it is possible to generate large strain-induced pseudo magnetic fields uniformly over the entire heterostructure. Here, we report using nano-angle resolved photoemission spectroscopy (nano-ARPES) to probe the electronic bandstructure of a graphene/black phosphorus heterostructure (G/BP). By directly measuring the iso-energy contours of graphene and black phosphorus we determine a twist angle of 20-degrees in our heterostructure. High-resolution nano-ARPES of the graphene bands near the Fermi level reveals the emergence of flat bands located within the Dirac cone. The spacing of the flat bands is consistent with Landau level formation in graphene, and corresponds to a pseudo-field of 11.36 T. Our work provides a new way to study quantum Hall phases induced by strain in 2D materials and heterostructures.

The interplay of magnetism and topology lies at the heart of condensed matter physics, which offers great opportunities to design intrinsic magnetic topological materials hosting a variety of exotic topological quantum states including the quantum anomalous Hall effect (QAHE), axion insulator state, and Majorana bound states. Extending this concept to one-dimension (1D) systems offers additional rich quantum spin physics with great promise for molecular-scale spintronics. Despite recent progress in the discovery of symmetry-protected topological quantum phases in 1D graphene nanoribbons (GNRs), the rational design and realization of magnetic topological GNRs (MT-GNRs) represents a grand challenge, as one must tackle multiple dimensions of complexity including time-reversal symmetry (TRS), spatial symmetry (width, edge, end geometry) and many-electron correlations. Here, we devised a new route involving the real- and reciprocal-space descriptions by unifying the chemists and physicists perspectives, for the design of such MT-GNRs with non-trivial electronic topology and robust magnetic terminal. Classic Clar's rule offers a conceptually qualitative real-space picture to predict the transition from closed-shell to open-shell with terminal magnetism, and band gap reopening with possible non-trivial electronic topology in a series of wave-like GNRs, which are further verified by first principle calculations of band-structure topology in a momentum-space. With the advance of on-surface synthesis and careful design of molecular precursors, we have fabricated these MT-GNRs with observation of topological edge bands, whose terminal pi-magnetism can be directly captured using a single-nickelocene spin sensor. Moreover, the transition from strong anti-ferromagnetic to weak coupling (paramagnetism-like) between terminal spins can be controlled by tuning the length of MT-GNRs., Comment: 29 pages, 11 figures

We report an atomically-precise integration of individual nitrogen (N) dopant as an in-plane artificial nucleus in a graphene device by atomic implantation to probe its gate-tunable quantum states and correlation effects. The N dopant creates the characteristic resonance state in the conduction band, revealing a giant carrier-dependent energetic renormalization up to 350 meV with respect to the Dirac point, accompanied by the observation of long-range screening effects. Joint density functional theory and tight-binding calculations with modified perturbation potential corroborate experimental findings and highlight the short-range character of N-induced perturbation.

Non-invasive imaging of the atomic arrangement in two-dimensional (2D) Ruddlesden-Popper hybrid Perovskites (RPPs), as well as understanding the related effects is challenging, due to the insulating nature and softness of the organic layers which also obscure the underlying inorganic lattice. Here, we demonstrate a sub-angstrom resolution imaging of both soft organic layers and inorganic framework in a prototypical 2D lead-halide RPP crystal via combined tip-functionalized Scanning Tunneling Microscopy (STM) and non-contact Atomic Force Microscope (ncAFM) corroborated by theoretical simulations. STM measurements unveil the atomic reconstruction of the inorganic lead-halide lattice and overall twin-domain composition of the RPP crystal, while ncAFM measurements with a CO-tip enable non-perturbative visualization of the cooperative reordering of surface organic cations driven by their hydrogen bonding interactions with the inorganic lattice. Moreover, such a joint technique also allows for the atomic-scale imaging of the electrostatic potential variation across the twin-domain walls, revealing alternating quasi-one-dimensional (1D) electron and hole-channels at neighboring twin-boundaries, which may influence in-plane exciton transport and dissociation.

We report that mono-elemental black phosphorus presents a new electronic self-passivation scheme of single vacancy (SV). By means of low-temperature scanning tunneling microscopy and bond-resolved non-contact atomic force microscopy, we demonstrate that the local reconstruction and ionization of SV into negatively charged $\mathrm{SV}^-$ leads to the passivation of dangling bonds and thus the quenching of in-gap states, which can be achieved by mild thermal annealing or STM tip manipulation. SV exhibits a strong and symmetric Friedel oscillation (FO) pattern, while $\mathrm{SV}^-$ shows an asymmetric FO pattern with local perturbation amplitude reduced by one order of magnitude and a faster decay rate. The enhanced passivation by forming $\mathrm{SV}^-$ can be attributed to its weak dipole-like perturbation, consistent with density-functional theory and numerical calculations. Therefore, self-passivated $\mathrm{SV}^-$ is electronically benign and acts as a much weaker scattering center, which may hold the key to further enhance the charge mobility of BP and its analogs.

Progress in functional materials discovery has been accelerated by advances in high throughput materials synthesis and by the development of high-throughput computation. However, a complementary robust and high throughput structural characterization framework is still lacking. New methods and tools in the field of machine learning suggest that a highly automated high-throughput structural characterization framework based on atomic-level imaging can establish the crucial statistical link between structure and macroscopic properties. Here we develop a machine learning framework towards this goal. Our framework captures local structural features in images with Zernike polynomials, which is demonstrably noise-robust, flexible, and accurate. These features are then classified into readily interpretable structural motifs with a hierarchical active learning scheme powered by a novel unsupervised two-stage relaxed clustering scheme. We have successfully demonstrated the accuracy and efficiency of the proposed methodology by mapping a full spectrum of structural defects, including point defects, line defects, and planar defects in scanning transmission electron microscopy (STEM) images of various 2D materials, with greatly improved separability over existing methods. Our techniques can be easily and flexibly applied to other types of microscopy data with complex features, providing a solid foundation for automatic, multiscale feature analysis with high veracity.

The photon-like electronic dispersion of graphene bestows its charge carriers with unusual confinement properties that depend strongly on the geometry and strength of the surrounding potential. Here we report bottom-up synthesis of atomically-precise one-dimensional (1D) arrays of point charges aimed at exploring supercritical confinement of carriers in graphene for new geometries. The arrays were synthesized by arranging F4TCNQ molecules into a 1D lattice on back-gated graphene devices, allowing precise tuning of both the molecular charge state and the array periodicity. Dilute arrays of ionized F4TCNQ molecules are seen to behave like isolated subcritical charges but dense arrays show emergent supercriticality. In contrast to compact supercritical clusters, extended 1D charge arrays exhibit both supercritical and subcritical characteristics and belong to a new physical regime termed frustrated supercritical collapse. Here carriers in the far-field are attracted by a supercritical charge distribution, but have their fall to the center frustrated by subcritical potentials in the near-field, similar to the trapping of light by a dense cluster of stars in general relativity.

SnSe is a promising thermoelectric material with record-breaking figure of merit, \textit{i.e., ZT}. As a semiconductor, optimal electrical dosage is the key challenge to maximize \textit{ZT} in SnSe. However, to date a comprehensive understanding of the electronic structure and most critically, the self-hole doping mechanism in SnSe is still absent. Here, we report the highly anisotropic electronic structure of SnSe investigated by both angle-resolved photoemission spectroscopy and quantum transport, in which a unique "\textit{pudding-mold}" shaped valence band with quasi-linear energy dispersion is revealed. We prove that the electrical doping in SnSe is extrinsically controlled by the formation of SnSe$_{2}$ micro-domains induced by local phase segregation. Using different growth methods and conditions, we have achieved wide tuning of hole doping in SnSe, ranging from intrinsic semiconducting behaviour to typical metal with carrier density of $1.23\times 10^{18}$ cm$^{-3}$ at room temperature. The resulting multi-valley transport in $p$-SnSe is characterized by non-saturating weak localization along the armchair axis, due to strong intervalley scattering enhanced by in-plane ferroelectric dipole field of the puckering lattice. Strikingly, quantum oscillations of magnetoresistance reveal three-dimensional electronic structure with unusual interlayer coupling strength in $p$-SnSe, which is correlated to the interweaving of SnSe individual layers by unique point dislocation defects. Our results suggest that defect engineering may provide versatile routes in improving the thermoelectric performance of the SnSe family., Comment: 21 pages, 4 figures