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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Investigating the Electronic Structure of Prospective Water-Splitting Oxide BaCe 0.25 Mn 0.75 O 3-δ before and after Thermal Reduction

BaCe 0.25 Mn 0.75 O 3-δ (BCM), a non-stoichiometric oxide with a layered perovskite-like crystal structure, has recently emerged as a prospective contender for application in renewable energy harvesting by solar thermochemical hydrogen generation. Using solar-thermal energy and a reducing environment, oxygen vacancies can be created in high-temperature BCM, and the reduced crystal so obtained can, in turn, produce H 2 by stripping oxygen from H 2 O. Therefore, a first step toward understanding the working mechanism and optimizing the performance of BCM is a thorough and comparative analysis of the electronic structure of the pristine and the reduced material. In this paper, we probe the electronic structure of BCM using the combined effort of first-principles calculations and experimental O K-edge X-ray absorption spectroscopy (XAS). The computed projected density of states (PDOS) and orbital plots are used to propose a simplified model for orbital mixing between the oxygen and metal atoms. With the help of state-of-the-art simulations, we are able to find the origins of the XAS peaks and categorize them on the basis of contribution from Ce and Mn. For the reduced crystal, the calculations show that the change in electron density resulting from the reduction is strongly localized around the oxygen vacancy. Experimental measurements reveal a marked lowering of the first O K-edge peak in the reduced crystal. Using theoretical analysis, this is shown to result from lifting of spin degeneracy in the absorption peaks as well as from a diminished O 2p contribution to the frontier unoccupied orbitals, in accordance with the tight binding scheme. The simulated results serve as a reference for the extent of spectral change as a function of the percentage of oxygen vacancies in the reduced crystal. Here, our study paves the way for the investigation of the working mechanism of BCM and for computational and experimental efforts aimed at design and discovery of efficient water-splitting oxides.

08 HYDROGEN↗
DOE OSTI2025

Investigating Electron Conductivity Regimes in the Bacterial Cytochrome Wire OmcS

The anaerobic bacterium Geobacter sulfurreducens produces extracellular, electronically conductive cytochrome polymer wires that are conductive over micron length scales. Structure models from cryo-electron microscopy data show OmcS wires form a linear chain of hemes along the protein wire axis, which is proposed as the structural basis supporting their electronic properties. However, the mechanism by which this heme arrangement supports long-range electronic conduction remains unknown. Structure models from cryo-electron microscopy data show these wires form a linear chain of hemes along the protein wire axis, which is proposed as the structural basis supporting their electronic properties. Existing computational models using static heme redox potentials and coupling energies fail to explain experimental observations, predicting conductances 10,000 to 100,000 times lower than measured values. Here, we investigate how dynamic disorder affects site energies, interheme coupling, and long-range electronic conductivity within these cytochrome wires. We introduce an approach to extract charge carrier site information directly from Kohn–Sham density functional theory, without employing projector schemes, and show that site and coupling energies are highly sensitive to changes in interheme geometry and the surrounding electrostatic environment. Unlike models that incorporate dynamic disorder as a thermally averaged quantity, our quantum charge carrier model incorporates proxies for dynamic disorder through decoherence corrections, yielding predicted diffusion coefficient closer to what is expected from experiment and comparable with other organic-based electronic materials. Based on these simulations, we propose that the instantaneous fluctuations of the local electrostatic environment can transiently lift energy degeneracies and delocalize charge carriers. Furthermore, these studies reveal how incorporating dynamic fluctuations associated with the environment resolves the discrepancy between theory and experiment in microbial cytochrome wires and highlight design principles for bioinspired, heme-based conductive materials.

Bioinorganic chemistry↗
DOE OSTI2023

Frontier Orbital Degeneracy: A New Concept for Tailoring the Magnetic State in Organic Semiconductor Adsorbates

Kondo resonances in molecular adsorbates are an important building block for applications in the field of molecular spintronics. Here, we introduce the novel concept of using frontier orbital degeneracy for tailoring the magnetic state, which is demonstrated for the case of the organic semiconductor 1,4,5,8,9,11-Hexaazatriphenylenehexacarbonitrile (HATCN, C 18 N 12 ) on Ag(111). Low-temperature scanning tunneling microscopy/spectroscopy (LT-STM/STS) measurements reveal the existence of two types of adsorbed HATCN molecules with distinctly different appearances and magnetic states, as evident from the presence or absence of an Abrikosov-Suhl-Kondo resonance. Our DFT results show that HATCN on Ag(111) supports two almost isoenergetic states, both with one excess electron transferred from the Ag surface, but with magnetic moments of either 0 or 0.65 μ B . Therefore, even though all molecules undergo charge transfer of one electron from the Ag substrate, they exist in two different molecular magnetic states that resemble a free doublet or an entangled spin state. We explain how the origin of this behavior lies in the twofold degeneracy of the lowest unoccupied molecular orbitals of gas phase HATCN, lifted upon adsorption and charge-transfer from Ag(111). In conclusion, our combined STM and DFT study introduces a new pathway to tailoring the magnetic state of molecular adsorbates on surfaces, with significant potential for spintronics and quantum information science.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Multi-Dimensional Spectroscopy with Intense Entangled Beams: Entanglement-Enabled Phase Matching in a Collinear Beam Geometry

The experimental realization of quantum molecular spectroscopy with entangled photons remains challenging owing to the low signal-to-noise ratio resulting from the use of low-flux entangled photons. High-flux entangled photons via intense entangled beams can be used to improve the signal-to-noise ratio, but the presence of unentangled photons contaminates the quantum signal stemming from entangled photons. Here, we demonstrate how intense entangled beams can be used in multi-dimensional spectroscopy while retaining the advantage of photon entanglement. Our approach is broadly applicable to odd-ordered nonlinear spectroscopies, and it generates purely quantum spectroscopic signals. The proposed approach allows the recording of desired phase-matched signals even in a collinear beam geometry, which lifts the requirement of complicated beam geometry setups for phase matching in multi-dimensional spectroscopies.

Absorption spectroscopy↗
DOE OSTI2020

Fundamentals of Using Cracked Film Lithography to Pattern Transparent Conductive Metal Grids for Photovoltaics

The fundamentals of using cracked film lithography (CFL) to fabricate metal grids for transparent contacts in solar cells were studied. The underlying physics of drying-induced cracks were well-predicted by an empirical correlation relating crack spacing to capillary pressure. CFL is primarily controlled by varying the crack template thickness, which establishes a three-way tradeoff between the areal density of cracks, crack width, and spacing between cracks, which in turn determine final grid transmittance, grid sheet resistance, and the semiconductor resistance for a given solar cell. Since CFL uses a lift-off process, an additional constraint is that the metal thickness must be less than 1/3 of the crack template thickness. Furthermore, the transmittance/grid sheet resistance/wire spacing tradeoffs measured in this work were used to calculate solar cell performance: CFL-patterned grids should outperform screen-printed grids for narrow cells (0.5–2 cm wide) and/or cells with high semiconductor sheet resistance (=100 O/sq), making CFL attractive for monolithically integrated thin-film photovoltaic modules.

14 SOLAR ENERGY↗
DOE OSTI2022

Noncovalent Surface Modification of Metal–Organic Frameworks: Unscrambling Adsorption Properties via Isothermal Titration Calorimetry

Despite the importance of noncovalent interactions in the utilization of metal–organic frameworks (MOFs), using these interactions to functionalize MOFs has rarely been explored. The ease of functionalization and potential for surface-selective functionalization makes modification via noncovalent interactions promising for the creation of porous photocatalytic assemblies. Here, using isothermal titration calorimetry, photoluminescence measurements, and desorption experiments, we have explored the nature and magnitude of the interactions of [Ru(bpy) 2 (bpy-R)] 2+ -functionalized dyes with the surface of MIL-96, where R = C 3 , C 8 , C 12 , and C 18 alkyl chains of either straight-chain or cyclic conformations. The orientation of the dyes appears to be flat against the surface with respect to the long alkyl chains, and the surface concentration approaches a monolayer at high initial concentrations of dye. Strangely, the dodecyl-functionalized dye, despite having a smaller interaction energy and larger footprint than either octyl-functionalized dye, achieves the highest maximum surface concentration. Based on photoluminescence spectra, desorption experiments, and ITC data, we believe this is due to the core of the dye being lifted from the surface as the chain length increases. Our understanding of these interactions is important for further utilization of this method for the functionalization of the internal and external surface areas of MOFs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Double Quantum Dots with Quenched Charging Energy in PbTe Nanowires

Here, we investigate double quantum dots defined by electrostatic gating in semiconductor PbTe nanowire devices. We perform transport measurements to obtain charge stability diagrams distinguished by negligible separation between paired triple points and by the spin degeneracy of all transport resonances at zero magnetic field. We show a 4-fold splitting of high-bias stability diagram triangles in an applied magnetic field to illustrate the lifting of this spin degeneracy. We also identify patterns of narrow transport resonances in these high-bias triangles and discuss their possible physical origins. Our results represent a step toward the realization of PbTe-based spin qubits.

PbTe nanowire↗
DOE OSTI2025

Hybrid MBE Route to Adsorption-Controlled Growth of BaTiO 3 Membranes with Robust Polarization Switching

Freestanding ferroelectric membranes are promising for flexible electronics, nonvolatile memory, photonics, and spintronics, but their synthesis is challenged by the need for reproducibility with precise stoichiometric control. Here, we demonstrate the adsorption-controlled growth of single-crystalline, epitaxial BaTiO 3 films by hybrid molecular beam epitaxy (MBE) on a binary oxide sacrificial layer. Using a simple water-droplet lift-off method, we obtained submillimeter- to millimeter-sized membranes that retained crystallinity, as confirmed by high-resolution X-ray diffraction, and exhibited robust tetragonal symmetry, as verified by Raman spectroscopy. Impedance spectroscopy confirmed a high dielectric constant of ∼1340, reflecting the robust dielectric response of the membranes. Ferroelectric functionality was revealed by piezoresponse force microscopy (PFM) and further verified by polarization-electric field (P-E) loop measurements with Positive-Up-Negative-Down (PUND). The P-E loops exhibited a remnant polarization of ∼5 μC cm –2 and a coercive field of ∼63 kV cm –1 . Furthermore, these results were interpreted in relation to c- and a-domain configurations.

Raman spectroscopy↗
DOE OSTI2020

Spin Transport in Ferromagnet-InSb Nanowire Quantum Devices

Signatures of Majorana zero modes (MZMs), which are the building blocks for fault-tolerant topological quantum computing, have been observed in semiconductor nanowires (NW) with strong spin-orbital-interaction (SOI), such as InSb and InAs NWs with proximity-induced superconductivity. Realizing topological superconductivity and MZMs in this most widely-studied platform also requires eliminating spin degeneracy, which is realized by applying a magnetic field to induce a helical gap. Yet, the applied field can adversely impact the induced superconducting state in the NWs and also places geometric restrictions on the device, which can affect scaling of future MZM-based quantum registers. These challenges could be circumvented by integrating magnetic elements with the NWs. With this motivation, in this work we report the first experimental investigation of spin transport across InSb NWs, which are enabled by devices with ferromagnetic (FM) contacts. We determine signatures of spin polarization and spin-dependent transport in the quasi-one-dimensional ballistic regime. Moreover, we show that electrostatic gating tunes the observed magnetic signal and also reveals a transport regime where the device acts as a spin filter. These results open an avenue towards developing MZM devices in which spin degeneracy is lifted locally, without the need of an applied magnetic field. They further provide a path for realizing spin-based devices that leverage spin-orbital states in quantum wires.

1D ballistic spin transport↗
DOE OSTI2021

Atomic-Scale Investigation of Oxidation at the Black Phosphorus Surface

Black phosphorus (BP) exhibits extraordinary electronic properties that are desirable for a wide variety of electronic and optoelectronic applications. However, applications of BP are hindered by its rapid degradation in ambient conditions. Despite significant advances that have been made in understanding the degradation mechanism, no consensus has yet been reached on how BP oxidation occurs at the atomic scale as experimental studies have been mostly restricted to averaged effects of degradation over a micron- to millimeter-sized region. Here, BP oxidation is investigated using scanning tunneling microscopy/spectroscopy (STM/S). Introducing O 2 gas to the BP surface in ultrahigh vacuum at a pressure of 10 –5 mbar for 1 min creates two new types of defects on the surface. We identify these defects as dangling atomic oxygen and phosphorus multivacancies using density functional theory simulations. In addition to the structural changes to the surface, the electronic structure is also drastically altered by the introduction of oxygen. The 300 meV band gap of BP is lifted due to dosing. This change in the electronic structure is reversible through STM tip manipulation. As a result, these are the first experimental results showing the atomic-scale oxidation of BP, an important step toward understanding the degradation process

2D materials↗
DOE OSTI2025

Magnetic La 0.7 Sr 0.3 MnO 3 Membranes Synthesized by Etching a Sr 3 Al 2 O 6 Sacrificial Layer Using an Intermediary Manganite Protection Layer

The integration of perovskite oxides onto flexible substrates has witnessed significant advancements owing to the development of an epitaxial lift-off technique utilizing a Sr 3 Al 2 O 6 sacrificial layer. However, Sr 3 Al 2 O 6 is susceptible to instability in both air and high-temperature oxygen atmospheres, potentially leading to degradation during the growth of the functional oxide layer. In this study, we investigate the use of an oxygen-deficient La 0.7 Sr 0.3 MnO 3 as capping layer, and demonstrate its ability to stabilize Sr 3 Al 2 O 6 films in ambient air. We successfully synthesized freestanding La 0.7 Sr 0.3 MnO 3 membranes by etching this sacrificial layer and transferring them onto flexible polymer substrates. Importantly, the magnetic properties of the La 0.7 Sr 0.3 MnO 3 films are preserved in these membranes. Furthermore, our results underline that employing a thin manganite capping layer ensures both high structural quality and the preservation of functional properties in the resulting membranes.

Deposition↗
DOE OSTI2020

The Bonding Nature and Adhesion of Polyacrylic Acid Coating on Li-Metal for Li Dendrite Prevention

The success of polyacrylic acid (PAA) to suppress Li dendrite growth suggests that the mechanical properties of polymer-based coatings, including the modulus, toughness, and interfacial adhesion are important design criteria. However, the measurement of the adhesion of thin PAA, as well as other polymer coatings to the reactive Li-metal anode surface is limited experimentally and challenging computationally. In this paper, a strategy was proposed to estimate the adhesion and delamination of the PAA(polymer)/Li interface, based on the bonding nature at the simpler PAA (oligomer)/Li interfaces using density functional theory calculations. It has been shown that the carboxylic acid groups in PAA reacted strongly with metallic Li, which significantly enhances the interfacial adhesion through the Li–O bonds formation, Li ionization and its incorporation into PAA, and –H or –OH termination of Li after decomposition of the COOH functional group. During delamination, it was found that the most likely PAA delamination route involved breaking partial Li–O bonds and lifting some ionized Li atoms from the Li-metal, especially for the Li atoms that showed a charge closer to +1 or are bonded with two O atoms from PAA. Based on the average bonding energies from PAA(oligomer)/Li interface delamination calculations, the work of separation, W sep , of the PAA(polymer)/Li interface was estimated to be ~1.0 (J/m 2 ). The high W sep of PAA (polymer)/Li was comparable with the Li 2 O/Li interface and higher than Li 2 CO 3 /Li and LiF/Li interfaces. This order correlated well with the areal density of Li–O bonds, which can serve as a descriptor for the interfacial adhesion. Furthermore, this computational approach can be applied to other interfaces with polymer-based coatings.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Hierarchical, Self-Assembled Metasurfaces via Exposure-Controlled Reflow of Block Copolymer-Derived Nanopatterns

Here, nanopatterning for the fabrication of optical metasurfaces entails a need for high-resolution approaches like electron beam lithography that cannot be readily scaled beyond prototyping demonstrations. Block copolymer thin film self-assembly offers an attractive alternative for producing periodic nanopatterns across large areas, yet the pattern feature sizes are fixed by the polymer molecular weight and composition. Here, a general strategy is reported that overcomes the limitation of fixed feature size by treating the copolymer thin film as a hierarchical resist, in which the nanoscale pattern motif is defined by self-assembly. Feature sizes can then be tuned by thermal reflow controlled locally by irradiative crosslinking or chemical alteration using lithographic ultraviolet light or electron beam exposure. Using blends of polystyrene-block-poly(methylmethacrylate) (PS-b-PMMA) with PS and PMMA homopolymer, we demonstrate both self-assembled PS grating and hexagonal hole patterns; exposure-controlled reflow is then used to reduce hole diameter by as much as 50% or increase PS grating linewidth by more than 180%. Transferring these nanopatterns, or their inverse obtained by a lift-off approach, into silicon yields structural colors that may be prescriptively controlled based on nanoscale feature size. Furthermore, patterned exposure enables area-selective feature size control, yielding uniform structural color patterns across centimeter square areas. Electron beam lithography is also used to show that the lithographic resolution of this selective-area control can be extended to the nanoscale dimensions of the self-assembled features. The exposure-controlled reflow approach demonstrated here takes a pivotal step towards fabricating complex, hierarchical optical metasurfaces using scalable self-assembly methods.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2026

Role of Surface Hydroxyls and Lattice Oxygen in Governing Selectivity and Restructuring During Acetic Acid Conversion on Fe 3 O 4 (001)

Understanding the reactivity of carboxylic acids on metal oxide surfaces is critical for elucidating ketonization mechanisms relevant to biomass upgrading. Here, we investigate the adsorption and thermal decomposition of acetic acid (CH 3 COOH) on Fe 3 O 4 (001) using scanning tunneling microscopy (STM), temperature-programmed reaction spectroscopy (TPRS), and X-ray photoelectron spectroscopy (XPS). At room temperature, acetic acid adsorbs dissociatively to form ordered bidentate acetate (CH 3 COO) overlayer that lifts the (√2 × √2)R 45° surface reconstruction. TPRS reveals ketene (CH 2 CO) as the dominant product, along with CO, CO 2 , and H 2 O, the latter evolving via a Mars–van Krevelen (MvK) mechanism. Isotopic labeling shows preferential CO 2 formation from the carboxyl carbon and a more balanced CO/CO 2 ratio from the methyl carbon, suggesting distinct oxidation pathways. STM imaging reveals embedded acetate intermediates filling surface oxygen vacancies created in MvK steps. Upon product formation completion (~700 K), extensive surface etching is observed, with pits elongated along the octahedral Fe rows. Approximately 20% of the surface oxygen is removed, consistent with vacancy formation stoichiometry inferred from product distributions. These findings demonstrate that carboxylate-induced restructuring of Fe 3 O 4 (001) involves both surface healing and reduction processes, offering mechanistic insights relevant to ketonization and broader carboxylic acid chemistry on metal oxides.

acetic acid↗
DOE OSTI2025

Electrical Control of the Nuclear Spin States of Rare-Earth Adatoms

Rare-earth adatoms on surfaces have been studied for potential atomic-scale magnetic storage, quantum sensing, and quantum computing applications. Despite accumulating experimental efforts, a comprehensive description of the electronic configurations of the adatoms remains elusive. Here, we investigate two charge states and several electronic configurations, including 5d and 6s valence shells, for a Sm adatom on a MgO substrate using multiconfigurational ab initio methods, for the possibility of using the Sm nuclear spin levels as qubits. For the configurations in a neutral charge state, we find that the electronic ground state is a singlet, and thus the hyperfine interaction associated with the 147 Sm nucleus is absent, which may greatly enhance nuclear spin coherence time. The degeneracy of the nuclear levels is lifted by the nuclear quadrupole interaction. We show that the splitting of the nuclear levels can be controlled by a static electric field, and that Rabi oscillations between the nuclear levels can be induced by a time-dependent electric field. For the configurations in a singly charged state, electronic Kramers doublets are formed. The electronic configurations including an unpaired 6s orbital exhibit a strong hyperfine Stark effect due to a large Fermi contact contribution to the hyperfine interaction. In these configurations, electric-field-induced Rabi oscillations between the electronic-nuclear levels can occur at frequencies up to 3 orders of magnitude higher than those for the neutral charge state. The proposed system may be experimentally observed within scanning tunneling microscopy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Current-Driven Symmetry Breaking and Spin–Orbit Polarization in Chiral Wires

The spin dynamics of electrons in chiral molecular systems remains a topic of intense interest, particularly regarding whether geometric chirality inherently induces spin polarization in current-carrying electrons. In this work, we employ ab initio real-time time-dependent density functional theory (rt-TDDFT) to directly simulate the interplay among charge current, spin, and orbital. This realtime tracking extends beyond perturbative treatments, and we analyze how nonequilibrium currents effectively lift the symmetry constraints of screw rotation and time-reversal symmetry. We find that the emergence of spin and orbital angular momenta is dynamically correlated with a concomitant loss of translational (linear) momentum, which we interpret as an intrinsic consequence of current-driven symmetry lowering. The implications of this mechanism for chirality-induced spin selectivity and spintronics device design are discussed.

chiral wire↗
DOE OSTI2023

Sulfur Lone Pairs Control Topology in Heterotrimetallic Complexes: An Experimental and Theoretical Study

Heterotrimetallic complexes with (N 2 S 2 )M metallodithiolates, M = Ni 2+ , [Fe(NO)] 2+ , and [Co(NO)] 2+ , as bidentate chelating ligands to a central trans-Cr(NO)(MeCN) unit were characterized as the first members of a new class, NiCrNi, FeCrFe, CoCrCo. The complexes exhibit a cisoid structural topology, ascribed to the stereoactivity of the available lone pair(s) on the sulfur donors, resulting in a dispersed, electropositive pocket from the N/N and N/S hydrocarbon linkers wherein the Cr-NO site is housed. Computational studies explored alternative isomers (transoid and inverted cisoid) that suggest a combination of electronic and steric effects govern the geometrical selectivity. Electrostatic potential maps readily display the dominant electronegative potential from the sulfurs which force the NO to the electropositive pocket. The available S lone pairs work in synergy with the π-withdrawing ability of NO to lift Cr out of the S 4 plane toward the NO and stabilize the geometry. The metallodithiolate ligands bound to Cr(NO) thus find structural consistency across the three congeners. Although the dinitrosyl [(bme-dach)Co(NO)-Mo(NO)(MeCN)-(bme-dach)Co(MeCN)][PF 6 ] 2 (CoMoCo') analogue displays chemical noninnocence and a partial Mo–Co bond toward (N 2 S 2 )Co'(NCCH 3 ) in an “asymmetric butterfly” topology, the stability of the {Cr(NO)} 5 unit prohibits such bond rearrangement. Magnetism and EPR studies illustrate spin coupling across the sulfur thiolate sulfur bridges.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Fermi-Level Engineering of Nitrogen Core-Doped Armchair Graphene Nanoribbons

Substitutional heteroatom doping of bottom-up engineered 1D graphene nanoribbons (GNRs) is a versatile tool for realizing low-dimensional functional materials for nanoelectronics and sensing. Previous efforts have largely relied on replacing C–H groups lining the edges of GNRs with trigonal planar N atoms. This type of atomically precise doping, however, only results in a modest realignment of the valence band (VB) and conduction band (CB) energies. Here, we report the design, bottom-up synthesis, and spectroscopic characterization of nitrogen core-doped 5-atom-wide armchair GNRs (N2-5-AGNRs) that yield much greater energy-level shifting of the GNR electronic structure. Here, the substitution of C atoms with N atoms along the backbone of the GNR introduces a single surplus π-electron per dopant that populates the electronic states associated with previously unoccupied bands. First-principles DFT-LDA calculations confirm that a sizable shift in Fermi energy (∼1.0 eV) is accompanied by a broad reconfiguration of the band structure, including the opening of a new band gap and the transition from a direct to an indirect semiconducting band gap. Scanning tunneling spectroscopy (STS) lift-off charge transport experiments corroborate the theoretical results and reveal the relationship among substitutional heteroatom doping, Fermi-level shifting, electronic band structure, and topological engineering for this new N-doped GNR.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗