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At least 127 records · Page 7

Majorana bound states with chiral magnetic textures

The aim of this Tutorial is to give a pedagogical introduction into realizations of Majorana fermions, usually termed as Majorana bound states (MBSs), in condensed matter systems with magnetic textures. We begin by considering the Kitaev chain model of “spinless” fermions and show how two “half” fermions can appear at chain ends due to interactions. By considering this model and its two-dimensional generalization, we emphasize intricate relation between topological superconductivity and possible realizations of MBS. We further discuss how “spinless” fermions can be realized in more physical systems, e.g., by employing the spin-momentum locking. Next, we demonstrate how magnetic textures can be used to induce synthetic or fictitious spin–orbit interactions, and, thus, stabilize MBS. We describe a general approach that works for arbitrary textures and apply it to skyrmions. We show how MBS can be stabilized by elongated skyrmions, certain higher order skyrmions, and chains of skyrmions. We also discuss how braiding operations can be performed with MBS stabilized on magnetic skyrmions. Furthermore, this Tutorial is aimed at students at the graduate level.

36 MATERIALS SCIENCE↗

Size and Stoichiometry Effects on the Reactivity of MoCy Nanoparticles Towards Ethylene

Molybdenum carbides are promising catalysts alternative to Pt-group metals for the hydrogenation of unsaturated hydrocarbons. Nanostructuring has been shown to be an efficient way to boost the catalytic activity of these materials with MoCy nanoparticles (NPs) exhibiting a good performance when encapsulated inside zeolites or dispersed on inert supports such as carbon or gold. In this work, we focus on a systematic DFT study of the interaction of MoCy NPs with ethylene (C 2 H 4 ), as a general and simple approach for examining binding and activation of C≡C bonds. Models for 14 NPs, with a Mo/C ratio in the 0.67 to 2.00 range, have been built following a cascade procedure. Several chemical descriptors, including the adsorption energy, structural NPs distortion, C≡C deformation, and C 2 H 4 attachment energy have been analyzed along with a meticulous geometric and electronic characterization of bare NPs and C2H4 binding. The present results show that 1:1 stoichiometric Mo 6 C 6 , Mo 12 C 12 , and Mo 24 C 24 , and the non-stochiometric Mo 4 C 6 , Mo 8 C 12 (MetCar), and Mo 14 C 13 (Nanocube) are excellent systems for the binding and activation of ethylene, exhibiting a much bigger reactivity than a bulk δ-MoC(001) surface with a similar Mo:C ratio. In addition, C 2 H 4 binding on the NPs with a Mo/C < 1.08 is advantageous since, apart from a rather large adsorption energy, implies low energy values for NPs deformation (from 0.00 to 0.31 eV), C≡C distortion (from 0.30 to 0.52 eV), and C 2 H 4 attachment (from -2.12 to -2.58 eV). These theoretical results point to the ideal MoCy size and composition for C 2 H 4 binding, providing a background for further experimental studies aimed at the preparation of MoCy NPs as hydrogenation catalysts.

36 MATERIALS SCIENCE↗

Advances in atomistic modeling and understanding of drying shrinkage in cementitious materials

Despite more than a century of research, drying shrinkage still causes unwanted stresses and cracks in our concrete infrastructures. This is partly due to the lack of understanding of the underlying mechanisms governing the drying shrinkage in cementitious materials. Inspired by the tremendous impact of atomistic simulations on materials science, we expect such innovative simulation techniques to hold a key to unlocking the enigmatic nature of drying shrinkage at the nanoscale. In this treatise, we first introduce basic physics concepts and atomistic simulation methods in detail. Afterward, we discuss the progress brought by atomistic simulations in understanding the drying shrinkage in cementitious materials and other nanoporous and nanolayered systems. This review also highlights important remaining fundamental questions and practical issues regarding drying shrinkage and delineates how atomistic simulations can help resolve them.

36 MATERIALS SCIENCE↗

Nondestructive Photo-Cross-Linking of Microphase-Separated Diblock Polymers through Coumarin Dimerization

The effect of long-wavelength ultraviolet photocrosslinking on microphase-separated coumarin-containing block polymers was studied by photo-rheometry and small-angle X-ray scattering. This model system consisted of three photocrosslinkable diblock polymers of poly(methoxyethyl acrylate)-b-poly(hexyl methacrylate-co-coumarin methacrylate) with different volume fractions of the crosslinkable coumarin-containing block, which microphase separated into lamellar and cylindrical morphologies. All polymers stiffened upon exposure to 365 nm light, with much greater relative increases in moduli recorded for lamellae-forming polymers (ca. 3200% increase) compared to the cylinder-forming polymer (ca. 550% increase). Disordering transitions that were evident in uncrosslinked samples were no longer observed after crosslinking in the ordered state, and domain sizes were found to remain stable to heating. The photocrosslinking reaction only proceeded under active irradiation, indicating a high degree of spatiotemporal control over curing in this system. Finally, at constant concentration of couamarin within the crosslinkable block, the cure rate was largely independent of polymer composition, suggesting a constant local concentration of coumarin moieties within the segregated crosslinkable domains. Lastly, these findings establish a set of specific structure-property relationships governing the phase-selective photocrosslinking of diblock polymers that can guide the design of robust nanostructured materials.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Multimodal X-ray nano-spectromicroscopy analysis of chemically heterogeneous systems

Abstract Understanding the nanoscale chemical speciation of heterogeneous systems in their native environment is critical for several disciplines such as life and environmental sciences, biogeochemistry, and materials science. Synchrotron-based X-ray spectromicroscopy tools are widely used to understand the chemistry and morphology of complex material systems owing to their high penetration depth and sensitivity. The multidimensional (4D+) structure of spectromicroscopy data poses visualization and data-reduction challenges. This paper reports the strategies for the visualization and analysis of spectromicroscopy data. We created a new graphical user interface and data analysis platform named XMIDAS (X-ray multimodal image data analysis software) to visualize spectromicroscopy data from both image and spectrum representations. The interactive data analysis toolkit combined conventional analysis methods with well-established machine learning classification algorithms (e.g. nonnegative matrix factorization) for data reduction. The data visualization and analysis methodologies were then defined and optimized using a model particle aggregate with known chemical composition. Nanoprobe-based X-ray fluorescence (nano-XRF) and X-ray absorption near edge structure (nano-XANES) spectromicroscopy techniques were used to probe elemental and chemical state information of the aggregate sample. We illustrated the complete chemical speciation methodology of the model particle by using XMIDAS. Next, we demonstrated the application of this approach in detecting and characterizing nanoparticles associated with alveolar macrophages. Our multimodal approach combining nano-XRF, nano-XANES, and differential phase-contrast imaging efficiently visualizes the chemistry of localized nanostructure with the morphology. We believe that the optimized data-reduction strategies and tool development will facilitate the analysis of complex biological and environmental samples using X-ray spectromicroscopy techniques.

36 MATERIALS SCIENCE↗

Modeling Catalyzed Growth of Single-Wall Carbon Nanotubes (Final Report)

Single-walled carbon nanotubes (SWCNTs) are among the most promising nanostructures because of their special and unusual physico-chemical properties that make them strong candidates for a variety of applications. Since their discovery, chemical vapor deposition (CVD) methods have become the preferred synthesis method. CVD uses a carbon-containing precursor species, which is decomposed over a catalyst yielding C atoms that eventually evolve in carbon nanostructures. CVD temperatures are in the order of 1000K or lower, and pressures in the range of 1-5 atm, although some processes use higher pressures. Depending on the nature of the catalyst, and on the conditions of pressure, temperature, and presence of other inert compounds, the resultant nanostructures may include nanofibers, nano-onions, multiple-, or single-wall carbon nanotubes, among others. When the CVD synthesis process is appropriately tuned, however, it is possible to obtain only SWCNTs, which are geometrically characterized by their diameter and by their chiral angle. The chiral indexes (n,m) determine the degree of helical twist of the graphite lattice along the nanotube axis, where the term chirality is derived from the left and right-handed helicity of the tubes defined by their chiral indexes (n,m) and (m,n) respectively. The main goal of this research is to build fundamental understanding that will help elucidating the nature and structure of the actual catalyst in a combined catalyst/support system, which we claim is essential especially when the catalyst is of nanodimensions. Given that we are considerably advanced in the understanding of selective single-walled carbon nanotube catalyst synthesis, we take this process as a case study. Thus, we focus on the understanding of the selective growth of SWCNTs on supported nanocatalysts in systems where the catalyst synthesis takes place in the same reactor preceding the nanotube synthesis. Once we understand what type of catalyst structure would be necessary for this specific growth, we will try to elucidate the catalytic synthesis process that leads to such catalytic structure. Thus, our aim of controlling nanostructure synthesis may start to be delineated.

36 MATERIALS SCIENCE↗

Morphology and chemical behavior of model CsO x /Cu 2 O/Cu(111) nanocatalysts for methanol synthesis: Reaction with CO 2 and H 2

Cs is a promoter of Cu-based catalysts for the synthesis of alcohols from CO 2 hydrogenation. Scanning tunneling microscopy and ambient-pressure x-ray photoelectron spectroscopy were used to study the morphology and chemical properties of surfaces generated by the deposition of cesium on Cu 2 O/Cu(111) and Cu(111) substrates. CsO x nanostructures were formed after Cs metal was deposited on Cu 2 O/Cu(111) at 300 K. The formed CsO x protrude over the surface of copper oxide by 2–4 Å, with the dimension at the base of the nanostructures being in the range of 1–3 nm. Heating to elevated temperature induced significant changes in the size and dispersion of the CsO x nanostructures, and there was a clear reconstruction of the copper oxide substrate, which then exhibited long range order with a hexagonally packed structure. The as-deposited and annealed surfaces of CsO x /Cu 2 O/Cu(111) were more reactive toward CO 2 than plain Cu 2 O/Cu(111) or clean Cu(111). Yet, none of them were stable in the presence of H 2 , which fully reduced the copper oxide at 400–450 K. In CsO x /Cu(111), the CsO x nanoclusters were dispersed all over the metallic copper in no particular order. The CsO x species had an average width of 2 nm and ~1 Å height. The CsO x /Cu(111) systems exhibited the highest activity for the binding and dissociation of CO 2 , indicating that the CsO x -copper interface plays a key role in alcohol synthesis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Scattering theory of frequency-entangled biphoton states facilitated by cavity polaritons

The use of quantum light to probe exciton properties in semiconductor and molecular nanostructures typically occurs in the low-intensity regime. A substantial enhancement of exciton-photon coupling can be achieved with photonic cavities, where excitons hybridize with cavity modes to form polariton states. Here, to provide a theoretical framework for interpreting emerging experimental efforts in this direction, we develop a scattering theory describing the interaction of frequency-entangled photon pairs with cavity polariton and bipolariton states under various coupling regimes. Employing the Tavis-Cummings model in combination with our scattering approach, we present a quantitative analysis of how the interaction of the entangled photon pair with the polariton or bipolariton modifies its joint spectral amplitude (JSA). Specifically, we examine the effects of the cavity-mode steady-state population, exciton-cavity coupling strength, and different forms of the input photon JSA. Our results show that the entanglement entropy of the scattered photons is highly sensitive to the interplay between the input JSA and the spectral line shapes of the polariton resonances, emphasizing the cavity filtering effects. We suggest that biphoton-scattering quantum light spectroscopy best serves as a sensitive probe of polariton and bipolariton states in the photon-vacuum cavity state. Our approach is not only robust to various regimes of cavity-exciton coupling, but also amenable to extensions beyond the Tavis-Cummings model, enabling the representation of a broad class of molecular systems and solid state quantum materials.

36 MATERIALS SCIENCE↗

Dynamic Binary Complexes (DBC) as Super-Adjustable Viscosity Modifiers for Hydraulic Fracturing Fluids

In the preceding project year two, we refined three DBC formulations from a selection of over 50 different chemistries. The optimization study primarily encompassed testing for (i) reversibility extent, (ii) performance in the presence of chemical additives, (iii) adhesion and friction behavior during displacement in wellbores and pipelines, (iv) corrosion protection performance, and (v) injection performance with model fracture systems at the laboratory scale. Highly promising results obtained from all these tests signify the significant potential of DBCs in enhancing hydrocarbon recovery from unconventional reservoirs. The primary activities in the third project year included publishing experimental findings across multiple articles and conducting outreach initiatives. Throughout the year, we undertook tasks such as replicating experimental results, further optimizing various formulations and their associated experimental sets, and conducting additional tests to address missing components based on reviewer feedback and suggestions. We also explored the surfactant and friction-reduction aspects of selected formulations through drag reduction tests. In addition, we constructed an improved fracturing performance setup and performed flow injection tests. The specific DBC formulations focused on during this project period were A8/B1, A12/B5, and A10/B12. We also obtained results for additional DBC formulations and a select few commercial fracturing fluids for the purpose of comparison. Within the project's scope, we aim to enhance the experimental findings with the development of various models. The first two years focused on two key aspects: (i) the creation of a high-fidelity hydraulic fracturing model for non-Newtonian fluids to gain insights into the implementation of DBC fluids in fracking environments, and (ii) the development of a multiphase flow simulator for estimating total production, fluid saturation in the reservoir, and the creation of a fracture propagation model and kinetic Monte Carlo (kMC) models for diverse applications. In the third year, we delved into the fundamental nanostructural properties of DBCs, exploring aspects such as material chemistry, pH tunability, and control of DBC formation and stability. Subsequently, in the extension year, we conducted a systematic investigation of various building blocks containing primary, secondary, and tertiary amine functional groups to understand their impact on rheological and viscoelastic properties. Furthermore, we explored a Dissipative Particle Dynamics (DPD) model to simulate self-assembly processes with precision, creating a high-fidelity representation of relevant nanostructures. The tasks performed this year with the significant results obtained have been discussed in Section 2.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A lyotropic liquid crystal-templated nanofiltration membrane with thermo- and pH-responsive 3D transport pathway

We produce controlled nanostructured membranes from cross-linking of self-assembled diacrylated poloxamers. At sufficiently high concentrations, poloxamers form lyotropic liquid crystals (LLCs), such as lamellar (L α ), cubic packing of spherical micelles, and hexagonal packing of rod-like micelles in water (H 1 ). We use the H 1 phase as a template to produce orderly packed nanofibrous membranes. The obtained membrane has a continuous 3D transport pathway and can alter its nanofiltration (NF) properties in response to changes in temperature and pH. The formulation includes Pluronic P84-diacrylate (P84DA), a thermoresponsive component that acts as both macromer and structure-directing amphiphile. P84DA facilitates changes in membrane pore size with temperature due to its thermoresponsiveness when it is in contact with water. Furthermore, the precursor contains acrylic acid (AAc) as the charged component, which upon copolymerization with P84DA, not only enables ion separation through Donnan exclusion but also imparts pH-responsive behavior for the separation of ionic species. The membrane performance is studied and compared with a commercial NF membrane (NF270). We show that the synthesized NF membrane has separation properties adjustable with temperature and pH with exceptional resistance to fouling by various solutes due to its highly hydrophilic surface. Furthermore, the membrane shows an outstanding sulfate over chloride ion selectivity, which is a requirement for salt fractionation applications. Deducted from separate experiments, the ideal chloride/sulfate selectivity for magnesium cation is about 2.38 at low ionic strengths. This study is done on a model system to show the capability of incorporating pH-responsiveness in LLC templated membranes, in which the pH-responsive range can be designed by changing the charged groups of comonomer in the formulation.

36 MATERIALS SCIENCE↗

Self-assembled nanofiltration membranes with thermo- and pH-responsive behavior

We produce controlled nanostructured membranes from cross-linking of self-assembled diacrylated poloxamers. At sufficiently high concentrations, poloxamers form lyotropic liquid crystals (LLCs), such as lamellar (L α ), cubic packing of spherical micelles, and hexagonal packing of rod-like micelles in water (H 1 ). We use the H 1 phase as a template to produce orderly packed nanofibrous membranes. The obtained membrane has a continuous 3D transport pathway and can alter its nanofiltration (NF) properties in response to changes in temperature and pH. The formulation includes Pluronic P84-diacrylate (P84DA), a thermoresponsive component that acts as both macromer and structure-directing amphiphile. P84DA facilitates changes in membrane pore size with temperature due to its thermoresponsiveness when it is in contact with water. Furthermore, the precursor contains acrylic acid (AAc) as the charged component, which upon copolymerization with P84DA, not only enables ion separation through Donnan exclusion but also imparts pH-responsive behavior for the separation of ionic species. The membrane performance is studied and compared with a commercial NF membrane (NF270). We show that the synthesized NF membrane has separation properties adjustable with temperature and pH with exceptional resistance to fouling by various solutes due to its highly hydrophilic surface. Furthermore, the membrane shows an outstanding sulfate over chloride ion selectivity, which is a requirement for salt fractionation applications. Deducted from separate experiments, the ideal chloride/sulfate selectivity for magnesium cation is about 2.38 at low ionic strengths. This study is done on a model system to show the capability of incorporating pH-responsiveness in LLC templated membranes, in which the pH-responsive range can be designed by changing the charged groups of comonomer in the formulation.

36 MATERIALS SCIENCE↗

Unveiling Structural Heterogeneity and Imbalance of Gold Decahedral Nanoparticles using Four-dimensional Scanning Transmission Electron Microscopy

Multi-twinned structures have been observed in technologically important crystal systems, for example diamond cubic and face-centered cubic (FCC) lattices, that include materials such as diamond, silicon, a wide range of noble metals, and their nanoscale counterparts. Beyond atomic building blocks, the special arrangements also occur in the self-assembly of nanoparticles (NP) and μm-sized colloidal particles and occupy parts of their phase diagrams. Spanning a wide range of length scales, the universality of the structures arises when the systems attempt to achieve multitwinned structures by overcoming geometric misfits during minimizing surface energies with entirely {111} or close-packing facets. While it is fundamental to understand how strain is sustained upon twinned structures and symmetry breaking, the knowledge will be paramount in practical aspects such as guiding and controlling the thin film growth, anisotropic NP growth, and self-assembly of NPs. Au decahedral (Dh) NP, as the most prevalent multi-twinned model system, fits five tetrahedral motifs into a circle by sharing an axis resulting in a geometric misfit angle of 7.35°, or a disclination with power of -7.35°. Postulating how Au FCC lattice adopts the misfit, theoretical models have been developed to address the underlying lattice symmetry and inhomogeneous strain distribution separately. Yet, experimental reports regarding the former have been limited due to the relatively large X-ray beam sizes that do not fit the sizes of NPs. On the other hand, though the latter has been widely adapted in the thermodynamics of small (<10 nm) multi-twinned nanoparticles, previous literature has shown that, at edge length of 17 nm, the theory’s is invalidated by shear strain that is observed in a defect-free Au Dh NP by high-resolution transmission electron microscopy (HR-TEM) imaging. Though the advancement of aberrationcorrected scanning transmission electron microscopy (AC-STEM) imaging and ab initio calculation techniques brings new opportunities, along with challenges in complicated image analysis and limitation in particle size (usually below 10 nm), the gap between nanoscale and mesoscale has never been extended to gain insight from atomic system with straightforward interaction potentials.

4D-STEM↗

Crystallization pathways and interfacial drivers for the formation of hierarchical architectures

The development of structural hierarchy on various length scales during crystallization process is ubiquitous in biological systems and is also observed in synthetic nanomaterials. The driving forces for the formations of complex architectures range from local interfacial interactions, that modify interfacial speciation, local supersaturation, and nucleation barriers, to macroscopic interparticle forces. Although it is enticing to interpret the formation of hierarchical architectures as the assembly of independently nucleated building blocks, often crystallization pathways follow monomer-by-monomer addition with structural complexity arising from interfacial chemical coupling and strongly correlated fluctuation dynamics in the electric double layers. Here, the mechanism of the development of structural hierarchy through heterogeneous nucleation, coupled interfacial nucleation and assembly, and oriented attachment of independently nucleated particles is discussed. In this article, the emphasis is made on the discussion of the underlying interfacial forces and chemical coupling that drives crystallization pathways towards the formation of structural hierarchy.

36 MATERIALS SCIENCE↗

Assembly of short amphiphilic peptoids into nanohelices with controllable supramolecular chirality

Abstract A long-standing challenge in bioinspired materials is to design and synthesize synthetic materials that mimic the sophisticated structures and functions of natural biomaterials, such as helical protein assemblies that are important in biological systems. Herein, we report the formation of a series of nanohelices from a type of well-developed protein-mimetics called peptoids. We demonstrate that nanohelix structures and supramolecular chirality can be well-controlled through the side-chain chemistry. Specifically, the ionic effects on peptoids from varying the polar side-chain groups result in the formation of either single helical fiber or hierarchically stacked helical bundles. We also demonstrate that the supramolecular chirality of assembled peptoid helices can be controlled by modifying assembling peptoids with a single chiral amino acid side chain. Computational simulations and theoretical modeling predict that minimizing exposure of hydrophobic domains within a twisted helical form presents the most thermodynamically favorable packing of these amphiphilic peptoids and suggests a key role for both polar and hydrophobic domains on nanohelix formation. Our findings establish a platform to design and synthesize chiral functional materials using sequence-defined synthetic polymers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Transport of Delocalized Excitons through DNA-Based Molecular Photonic Wires

Molecular photonic wires conduct electronic energy via their rapid transport properties. In photosynthesis, nature achieves efficient transport across large distances using delocalized excitons, generated by strong excitonic coupling between chromophores. How, or even whether, delocalization facilitates long-distance energy transport in synthetic systems has been challenging to experimentally test and optimize. Thus, far, studies have been limited to strongly coupled, heterogeneous chromophore aggregates or weakly coupled chromophore monomers. Here, in this work, we employed DNA nanostructures to engineer molecular photonic wires constructed from a series of excitonically coupled indocarbocyanine chromophores─achieving the intermediate and strong coupling regimes. Using time-resolved fluorescence spectroscopy and complementary simulations, we demonstrated that an intermediate intermolecular electronic coupling (∼ k B T ) enables up to 40% faster exciton transport as compared to strongly coupled chromophores. The delocalized excitons generated in the intermediate coupling regime exhibited properties conducive to rapid diffusivity, similar to their monomeric counterparts. Thus, intermediate excitonic coupling, analogous to natural systems, achieves long-distance exciton transport with the high chromophore density required for energy capture.

DNA origami↗

Antineoplastic activity of Salmonella Typhimurium outer membrane nanovesicles

Highlights: • ST-OMVs is a promising antitumor monotherapy or as an adjuvant to chemotherapies. • ST-OMVs downregulated Ki-67 and upregulated CD49b immune-expression. • ST-OMVs downregulated angiogenesis by inhibiting VEGF gene expression. • ST-OMVs increased tumor cells apoptosis and autophagy (increased caspase-3and Beclin1). Nano-sized Gram-negative bacterial outer membrane vesicles possess unique structural and immunostimulatory effects that could be exploited to regress tumors by alerting the host immune system and reversing the immunosuppressive tumor microenvironment. The current study was conducted to investigate the antitumor activity of the outer membrane vesicles (ST-OMVs) of Salmonella Typhimurium ATCC 14028, in vitro in human colorectal carcinoma (HTC116), breast cancer (MCF-7), and hepatocellular carcinoma (HepG2) cell lines and in vivo in Ehrlich solid carcinoma-bearing mice model either as a mono-immunotherapy or as an adjuvant to a commonly used conventional chemotherapy. In addition, we investigated the safety of ST-OMVs. Adult Swiss albino female mice with transplanted Ehrlich solid carcinoma were treated with either ST-OMVs, paclitaxel or a combination of both. Tumor volume, growth inhibition rate, quantitative RT-PCR of Bax and VEGF genes expression, histopathology and immune-expression of caspase-3, Beclin-1, CD49b and Ki-67 were all analyzed. Our results showed that ST-OMVs significantly decreased tumor volume, significantly increased tumor growth inhibition rate, up-regulated the immunohistochemical expression of caspase-3, Beclin-1, and CD49b (enhanced recruitment of NK cells). Furthermore, ST-OMVs down-regulated the expression of Ki-67, increased Bax gene expression and decreased VEGF gene expression as detected by qRT-PCR analysis. Histologically, ST-OMVs promoted apoptosis, decreased tumor invasion and mitotic activities. Moreover, ST-OMVs showed a remarkable cytotoxic activity in various investigated in vitro cancer cell lines. Our findings demonstrate potential antitumor activity of ST-OMVs that might be used as a promising safe antitumor immunotherapy or an adjuvant to conventional chemotherapeutic drugs, resolving some of their problems.

60 APPLIED LIFE SCIENCES↗

Solution of the Schrödinger equation for quasi-one-dimensional materials using helical waves

We formulate and implement a spectral method for solving the Schrödinger equation, as it applies to quasi-one-dimensional materials and structures. This allows for computation of the electronic structure of important technological materials such as nanotubes (of arbitrary chirality), nanowires, nanoribbons, chiral nanoassemblies, nanosprings and nanocoils, in an accurate, efficient and systematic manner. Our work is motivated by the observation that one of the most successful methods for carrying out electronic structure calculations of bulk/crystalline systems — the plane-wave method — is a spectral method based on eigenfunction expansion. Our scheme avoids computationally onerous approximations involving periodic supercells often employed in conventional plane-wave calculations of quasi-one-dimensional materials, and also overcomes several limitations of other discretization strategies, e.g., those based on finite differences and atomic orbitals. The basis functions in our method — called helical waves (or twisted waves) — are eigenfunctions of the Laplacian with symmetry adapted boundary conditions, and are expressible in terms of plane waves and Bessel functions in helical coordinates. We describe the setup of fast transforms to carry out discretization of the governing equations using our basis set, and the use of matrix-free iterative diagonalization to obtain the electronic eigenstates. Miscellaneous computational details, including the choice of eigensolvers, use of a preconditioning scheme, evaluation of oscillatory radial integrals and the imposition of a kinetic energy cutoff are discussed. We have implemented these strategies into a computational package called HelicES (Helical Electronic Structure). We demonstrate the utility of our method in carrying out systematic electronic structure calculations of various quasi-one-dimensional materials through numerous examples involving nanotubes, nanoribbons and nanowires. We also explore the convergence properties of our method, and assess its accuracy and computational efficiency by comparison against reference finite difference, transfer matrix method and plane-wave results. We anticipate that our method will find applications in computational nanomechanics and multiscale modeling, for carrying out transport calculations of interest to the field of semiconductor devices, and for the discovery of novel chiral phases of matter that are of relevance to the burgeoning quantum hardware industry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗