Smectic pair-density-wave order in EuRbFe4As4.

The pair density wave (PDW) is a superconducting state in which Cooper pairs carry centre-of-mass momentum in equilibrium, leading to the breaking of translational symmetry1-4. Experimental evidence for such a state exists in high magnetic field5-8 and in some materials that feature density-wave orders that explicitly break translational symmetry9-13. However, evidence for a zero-field PDW state that exists independent of other spatially ordered states has so far been elusive. Here we show that such a state exists in the iron pnictide superconductor EuRbFe4As4, a material that features co-existing superconductivity (superconducting transition temperature (Tc) ≈ 37 kelvin) and magnetism (magnetic transition temperature (Tm) ≈ 15 kelvin)14,15. Using spectroscopic imaging scanning tunnelling microscopy (SI-STM) measurements, we show that the superconducting gap at low temperature has long-range, unidirectional spatial modulations with an incommensurate period of about eight unit cells. Upon increasing the temperature above Tm, the modulated superconductor disappears, but a uniform superconducting gap survives to Tc. When an external magnetic field is applied, gap modulations disappear inside the vortex halo. The SI-STM and bulk measurements show the absence of other density-wave orders, indicating that the PDW state is a primary, zero-field superconducting state in this compound. Both four-fold rotational symmetry and translation symmetry are recovered above Tm, indicating that the PDW is a smectic order.

Spin splitting of dopant edge state in magnetic zigzag graphene nanoribbons.

Spin-ordered electronic states in hydrogen-terminated zigzag nanographene give rise to magnetic quantum phenomena1,2 that have sparked renewed interest in carbon-based spintronics3,4. Zigzag graphene nanoribbons (ZGNRs)-quasi one-dimensional semiconducting strips of graphene bounded by parallel zigzag edges-host intrinsic electronic edge states that are ferromagnetically ordered along the edges of the ribbon and antiferromagnetically coupled across its width1,2,5. Despite recent advances in the bottom-up synthesis of GNRs featuring symmetry protected topological phases6-8 and even metallic zero mode bands9, the unique magnetic edge structure of ZGNRs has long been obscured from direct observation by a strong hybridization of the zigzag edge states with the surface states of the underlying support10-15. Here, we present a general technique to thermodynamically stabilize and electronically decouple the highly reactive spin-polarized edge states by introducing a superlattice of substitutional N-atom dopants along the edges of a ZGNR. First-principles GW calculations and scanning tunnelling spectroscopy reveal a giant spin splitting of low-lying nitrogen lone-pair flat bands by an exchange field (~850 tesla) induced by the ferromagnetically ordered edge states of ZGNRs. Our findings directly corroborate the nature of the predicted emergent magnetic order in ZGNRs and provide a robust platform for their exploration and functional integration into nanoscale sensing and logic devices15-21.

Engineering Small HOMO-LUMO Gaps in Polycyclic Aromatic Hydrocarbons with Topologically Protected States.

Topological phases in laterally confined low-dimensional nanographenes have emerged as versatile design tools that can imbue otherwise unremarkable materials with exotic band structures ranging from topological semiconductors and quantum dots to intrinsically metallic bands. The periodic boundary conditions that define the topology of a given lattice have thus far prevented the translation of this technology to the quasi-zero-dimensional (0D) domain of small molecular structures. Here, we describe the synthesis of a polycyclic aromatic hydrocarbon (PAH) featuring two localized zero modes (ZMs) formed by the topological junction interface between a trivial and nontrivial phase within a single molecule. First-principles density functional theory calculations predict a strong hybridization between adjacent ZMs that gives rise to an exceptionally small HOMO-LUMO gap. Scanning tunneling microscopy and spectroscopy corroborate the molecular structure of 9/7/9-double quantum dots and reveal an experimental quasiparticle gap of 0.16 eV, corresponding to a carbon-based small molecule long-wavelength infrared (LWIR) absorber.

Engineering Robust Metallic Zero-Mode States in Olympicene Graphene Nanoribbons.

Metallic graphene nanoribbons (GNRs) represent a critical component in the toolbox of low-dimensional functional materials technology serving as 1D interconnects capable of both electronic and quantum information transport. The structural constraints imposed by on-surface bottom-up GNR synthesis protocols along with the limited control over orientation and sequence of asymmetric monomer building blocks during the radical step-growth polymerization have plagued the design and assembly of metallic GNRs. Here, we report the regioregular synthesis of GNRs hosting robust metallic states by embedding a symmetric zero-mode (ZM) superlattice along the backbone of a GNR. Tight-binding electronic structure models predict a strong nearest-neighbor electron hopping interaction between adjacent ZM states, resulting in a dispersive metallic band. First-principles density functional theory-local density approximation calculations confirm this prediction, and the robust, metallic ZM band of olympicene GNRs is experimentally corroborated by scanning tunneling spectroscopy.

Automated Tip Conditioning for Scanning Tunneling Spectroscopy.

Scanning tunneling spectroscopy (STS), a technique that records the change in the tunneling current as a function of the bias (dI/dV) across the gap between a tip and the sample, is a powerful tool to characterize the electronic structure of single molecules and nanomaterials. While performing STS, the structure and condition of the scanning probe microscopy (SPM) tips are critical for reliably obtaining high quality point spectra. Here, we present an automated program based on machine learning models that can identify the Au(111) Shockley surface state in dI/dV point spectra and perform tip conditioning on clean or sparsely covered gold surfaces with minimal user intervention. We employed a straightforward height-based segmentation algorithm to analyze STM topographic images to identify tip conditioning positions and used 1789 archived dI/dV spectra to train machine learning models that can ascertain the condition of the tip by evaluating the quality of the spectroscopic data. Decision tree based ensemble and boosting models and deep neural networks (DNNs) have been shown to reliably identify tips in suitable conditions for STS. We expect the automated program to reduce operational costs and time, increase reproducibility in surface science studies, and accelerate the discovery and characterization of novel nanomaterials by STM. The strategies presented in this paper can readily be adapted to STM tip conditioning on a wide variety of other common substrates.

Covalent C-N Bond Formation through a Surface Catalyzed Thermal Cyclodehydrogenation.

The integration of substitutional dopants at predetermined positions along the hexagonal lattice of graphene-derived polycyclic aromatic hydrocarbons is a critical tool in the design of functional electronic materials. Here, we report the unusually mild thermally induced oxidative cyclodehydrogenation of dianthryl pyrazino[2,3-g]quinoxalines to form the four covalent C-N bonds in tetraazateranthene on Au(111) and Ag(111) surfaces. Bond-resolved scanning probe microscopy, differential conductance spectroscopy, along with first-principles calculations unambiguously confirm the structural assignment. Detailed mechanistic analysis based on ab initio density functional theory calculations reveals a stepwise mechanism featuring a rate determining barrier of only ΔE⧧ = 0.6 eV, consistent with the experimentally observed reaction conditions.

Orbitally Matched Edge-Doping in Graphene Nanoribbons.

A series of trigonal planar N-, O-, and S-dopant atoms incorporated along the convex protrusion lining the edges of bottom-up synthesized chevron graphene nanoribbons (cGNRs) induce a characteristic shift in the energy of conduction and valence band edge states along with a significant reduction of the band gap of up to 0.3 eV per dopant atom per monomer. A combination of scanning probe spectroscopy and density functional theory calculations reveals that the direction and the magnitude of charge transfer between the dopant atoms and the cGNR backbone are dominated by inductive effects and follow the expected trend in electronegativity. The introduction of heteroatom dopants with trigonal planar geometry ensures an efficient overlap of a p-orbital lone-pair centered on the dopant atom with the extended π-system of the cGNR backbone effectively extending the conjugation length. Our work demonstrates a widely tunable method for band gap engineering of graphene nanostructures for advanced electronic applications.

Temperature dependence of solid-state electron exchanges of mixed-valent ferrocenated Au monolayer-protected clusters.

Electron transfers (ETs) in mixed-valent ferrocene/ferrocenium materials are ordinarily facile. In contrast, the presence of ~1:1 mixed-valent ferrocenated thiolates in the organothiolate ligand shells of <2 nm diameter Au225, Au144, and Au25 monolayer-protected clusters (MPCs) exerts a retarding effect on ET between them at and below room temperature. Near room temperature, in dry samples, bimolecular rate constants for ET between organothiolate-ligated MPCs are diminished by the addition of ferrocenated ligands to their ligand shells. At lower temperatures (down to ~77 K), the thermally activated (Arrhenius) ET process dissipates, and the ET rates become temperature-independent. Among the Au225, Au144, and Au25 MPCs, the temperature-independent ET rates fall in the same order as at ambient temperatures: Au225 > Au144 > Au25. The MPC ET activation energy barriers are little changed by the presence of ferrocenated ligands and are primarily determined by the Au nanoparticle core size.

Transfer-Free Synthesis of Atomically Precise Graphene Nanoribbons on Insulating Substrates.

The rational bottom-up synthesis of graphene nanoribbons (GNRs) provides atomically precise control of widths and edges that give rise to a wide range of electronic properties promising for electronic devices such as field-effect transistors (FETs). Since the bottom-up synthesis commonly takes place on catalytic metallic surfaces, the integration of GNRs into such devices requires their transfer onto insulating substrates, which remains one of the bottlenecks in the development of GNR-based electronics. Herein, we report on a method for the transfer-free placement of GNRs on insulators. This involves growing GNRs on a gold film deposited onto an insulating layer followed by gentle wet etching of the gold, which leaves the nanoribbons to settle in place on the underlying insulating substrate. Scanning tunneling microscopy and Raman spectroscopy confirm that atomically precise GNRs of high density uniformly grow on the gold films deposited onto SiO2/Si substrates and remain structurally intact after the etching process. We have also demonstrated transfer-free fabrication of ultrashort channel GNR FETs using this process. A very important aspect of the present work is that the method can scale up well to 12 in. wafers, which is extremely difficult for previous techniques. Our work here thus represents an important step toward large-scale integration of GNRs into electronic devices.

Charge-Transfer Effects in Ligand Exchange Reactions of Au25 Monolayer-Protected Clusters.

Reported here are second-order rate constants of associative ligand exchanges of Au25L18 nanoparticles (L = phenylethanethiolate) of various charge states, measured by proton nuclear magnetic resonance at room temperature and below. Differences in second-order rate constants (M(-1) s(-1)) of ligand exchange (positive clusters ∼1.9 × 10(-5) versus negative ones ∼1.2 × 10(-4)) show that electron depletion retards ligand exchange. The ordering of rate constants between the ligands benzeneselenol > 4-bromobenzene thiol > benzenethiol reveals that exchange is accelerated by higher acidity and/or electron donation capability of the incoming ligand. Together, these observations indicate that partial charge transfer occurs between the nanoparticle and ligand during the exchange and that this is a rate-determining effect in the process.