Carbon Nanotubes and Related Nanomaterials: Critical Advances and Challenges for Synthesis toward Mainstream Commercial Applications

Advances in the synthesis and scalable manufacturing of single-walled carbon nanotubes (SWCNTs) remain critical to realizing many important commercial applications. Here we review recent breakthroughs in the synthesis of SWCNTs and highlight key ongoing research areas and challenges. A few key applications that capitalize on the properties of SWCNTs are also reviewed with respect to the recent synthesis breakthroughs and ways in which synthesis science can enable advances in these applications. While the primary focus of this review is on the science framework of SWCNT growth, we draw connections to mechanisms underlying the synthesis of other 1D and 2D materials such as boron nitride nanotubes and graphene.

Strike a balance: optimization of backbone torsion parameters of AMBER polarizable force field for simulations of proteins and peptides

Based on the AMBER polarizable model (ff02), we have re-optimized the parameters related to the main-chain (Phi, Psi) torsion angles by fitting to the Boltzmann-weighted average quantum mechanical (QM) energies of the important regions (i.e., beta, P(II), alpha(R), and alpha(L) regions). Following the naming convention of the AMBER force field series, this release will be called ff02pol.rl The force field has been assessed both by energetic comparison against the QM data and by the replica exchange molecular dynamics simulations of short alanine peptides in water. For Ace-Ala-Nme, the simulated populations in the beta, P(II) and alpha(R) regions were approximately 30, 43, and 26%, respectively. For Ace-(Ala)(7)-Nme, the populations in these three regions were approximately 24, 49, and 26%. Both were in qualitative agreement with the NMR and CD experimental conclusions. In comparison with the previous force field, ff02pol.rl demonstrated good balance among these three important regions. The optimized torsion parameters, together with those in ff02, allow us to carry out simulations on proteins and peptides with the consideration of polarization.

Helically chiral polymers: a class of ligands for asymmetric catalysis

Helically chiral polymers from achiral monomers containing N and P atoms have been shown to be ligands for transition metals such as Pd and Rh. The Rh complex of the phosphane-containing polyisocyanate p(18-co-17) was an active albeit hardly enantioselective catalyst in the asymmetric hydrogenation of the dehydro amino acid N-acetamidocinnamic acid (15% enantiomeric excess). The most active catalyst obtained until now was the Pd-complexed polymethacrylate Pd-p12, which catalyzes the allylic substitution reaction of 1,3-diphenylprop-2-enyl acetate with dimethyl malonate even at -20 degrees C in quantitative yield, although again the enantioselectivity was unsatisfactory. The most successful application of a helically chiral polymer in asymmetric catalysis with respect to both reactivity and enantioselectivity is the polymethacrylate p(5-co-8). Its palladium complex catalyzes the above-mentioned reaction at 0 degrees C with quantitative yield and 60% enantiomeric excess.

An In-tether Chiral Center Modulates the Helicity, Cell Permeability, and Target Binding Affinity of a Peptide

The addition of a precisely positioned chiral center in the tether of a constrained peptide is reported, yielding two separable peptide diastereomers with significantly different helicity, as supported by circular dichroism (CD) and NMR spectroscopy. Single crystal X-ray diffraction analysis suggests that the absolute configuration of the in-tether chiral center in helical form is R, which is in agreement with theoretical simulations. The relationship between the secondary structure of the short peptides and their biochemical/biophysical properties remains elusive, largely because of the lack of proper controls. The present strategy provides the only method for investigating the influence of solely conformational differences upon the biochemical/biophysical properties of peptides. The significant differences in permeability and target binding affinity between the peptide diastereomers demonstrate the importance of helical conformation.

Stapled Peptides-A Useful Improvement for Peptide-Based Drugs

Peptide-based drugs, despite being relegated as niche pharmaceuticals for years, are now capturing more and more attention from the scientific community. The main problem for these kinds of pharmacological compounds was the low degree of cellular uptake, which relegates the application of peptide-drugs to extracellular targets. In recent years, many new techniques have been developed in order to bypass the intrinsic problem of this kind of pharmaceuticals. One of these features is the use of stapled peptides. Stapled peptides consist of peptide chains that bring an external brace that force the peptide structure into an α-helical one. The cross-link is obtained by the linkage of the side chains of opportune-modified amino acids posed at the right distance inside the peptide chain. In this account, we report the main stapling methodologies currently employed or under development and the synthetic pathways involved in the amino acid modifications. Moreover, we report the results of two comparative studies upon different kinds of stapled-peptides, evaluating the properties given from each typology of staple to the target peptide and discussing the best choices for the use of this feature in peptide-drug synthesis.

Computational fluid dynamic simulations of image-based stented coronary bifurcation models

One of the relevant phenomenon associated with in-stent restenosis in coronary arteries is an altered haemodynamics in the stented region. Computational fluid dynamics (CFD) offers the possibility to investigate the haemodynamics at a level of detail not always accessible within experimental techniques. CFD can quantify and correlate the local haemodynamics structures which might lead to in-stent restenosis. The aim of this work is to study the fluid dynamics of realistic stented coronary artery models which replicate the complete clinical procedure of stent implantation. Two cases of pathologic left anterior descending coronary arteries with their bifurcations are reconstructed from computed tomography angiography and conventional coronary angiography images. Results of wall shear stress and relative residence time show that the wall regions more prone to the risk of restenosis are located next to stent struts, to the bifurcations and to the stent overlapping zone for both investigated cases. Considering a bulk flow analysis, helical flow structures are generated by the curvature of the zone upstream from the stent and by the bifurcation regions. Helical recirculating microstructures are also visible downstream from the stent struts. This study demonstrates the feasibility to virtually investigate the haemodynamics of patient-specific coronary bifurcation geometries.

Helicity conservation by flow across scales in reconnecting vortex links and knots

The conjecture that helicity (or knottedness) is a fundamental conserved quantity has a rich history in fluid mechanics, but the nature of this conservation in the presence of dissipation has proven difficult to resolve. Making use of recent advances, we create vortex knots and links in viscous fluids and simulated superfluids and track their geometry through topology-changing reconnections. We find that the reassociation of vortex lines through a reconnection enables the transfer of helicity from links and knots to helical coils. This process is remarkably efficient, owing to the antiparallel orientation spontaneously adopted by the reconnecting vortices. Using a new method for quantifying the spatial helicity spectrum, we find that the reconnection process can be viewed as transferring helicity between scales, rather than dissipating it. We also infer the presence of geometric deformations that convert helical coils into even smaller scale twist, where it may ultimately be dissipated. Our results suggest that helicity conservation plays an important role in fluids and related fields, even in the presence of dissipation.

Investigation of the role of tryptophan residues in cationic antimicrobial peptides to determine the mechanism of antimicrobial action

AIMS

To understand the effects of Trp residues in linear antimicrobial peptides with α-helical conformations on cell permeation ability and membrane transduction efficacy.

METHODS AND RESULTS

A series of L-K6 analogues were designed and synthesized by replacing Ile or Leu with Trp at different positions on the hydrophobic face of L-K6. The antimicrobial and haemolytic activity and secondary structure of the designed Trp-containing peptides were assessed. In addition, the role of Trp in membrane disruption for these designed peptides was investigated. I1W, I4W and L5W demonstrated stronger activity than the other peptides against both Gram-positive and Gram-negative bacteria. All of the tested peptides preferentially interacted with negatively charged vesicles composed of phosphatidylglycerol (PG)/cardiolipin (CL) or PG/CL/phosphatidylethanolamine, and, to a lesser extent, with zwitterionic vesicles. I1W, I4W and L5W caused calcein release at 2·5 μmol l(-1) .

CONCLUSIONS

The position of Trp, rather than the number of Trp residues, in these peptides was an important factor in the antimicrobial activity. Trp residues were deeply inserted into negatively charged membranes but were largely exposed in aqueous buffer solution.

SIGNIFICANCE AND IMPACT OF THE STUDY

These Trp-containing peptides may represent good candidates for new antibiotic agents and for use in new therapeutic approaches.

Cys-Cys and Cys-Lys Stapling of Unprotected Peptides Enabled by Hypervalent Iodine Reagents

Easy access to a wide range of structurally diverse stapled peptides is crucial for the development of inhibitors of protein-protein interactions. Herein, we report bis-functional hypervalent iodine reagents for two-component cysteine-cysteine and cysteine-lysine stapling yielding structurally diverse thioalkyne linkers. This stapling method works with unprotected natural amino acid residues and does not require pre-functionalization or metal catalysis. The products are stable to purification and isolation. Post-stapling modification can be accessed via amidation of an activated ester, or via cycloaddition onto the formed thioalkyne group. Increased helicity and binding affinity to MDM2 was obtained for a i,i+7 stapled peptide.

Self-Assembled Helical Arrays for the Stabilization of the Triplet State

Room-temperature phosphorescence of metal and heavy atom-free organic molecules has emerged as an area of great potential in recent years. A rational design played a critical role in controlling the molecular ordering to impart efficient intersystem crossing and stabilize the triplet state to achieve room-temperature ultralong phosphorescence. However, in most cases, the strategies to strengthen phosphorescence efficiency have resulted in a reduced lifetime, and the available nearly degenerate singlet-triplet energy levels impart a natural competition between delayed fluorescence and phosphorescence, with the former one having the advantage. Herein, an organic helical assembly supports the exhibition of an ultralong phosphorescence lifetime. In contrary to other molecules, 3,6-phenylmethanone functionalized 9-hexylcarbazole exhibits a remarkable improvement in phosphorescence lifetime (>4.1 s) and quantum yield (11 %) owing to an efficient molecular packing in the crystal state. A right-handed helical molecular array act as a trap and exhibits triplet exciton migration to support the exceptionally longer phosphorescence lifetime.

Chiral Nanostructures from Helical Copolymer-Metal Complexes: Tunable Cation-π Interactions and Sergeants and Soldiers Effect

Poly(phenylacetylene) (PPA) copolymers containing (R)- or (S)-MPA as minor chiral pendant can be forced to selectively adopt the right- o left-handed helix, in the presence of small amounts of Na(+) or Ag(+) ("Sergeants and Soldiers Effect") by addition of a donor cosolvent. The helical sense depends exclusively on the chiral monomer/donor cosolvent ratio, and this allows a perfect on/off tuning of the helicity of the copolymer. When the amount of the donor cosolvent is low, the metal ion complex is stabilized by a cation-π interaction, which is selectively cleaved when the amount of cosolvent is higher. Macroscopically chiral nanospheres and nanotubes composed by helical copolymers with P or M helical sense are also described. Our results demonstrate that it is possible to obtain the two enantiomeric helical structures (P and M helicities) and the corresponding nanospheres and nanotubes from a single helical copolymer, by controlled activation/deactivation of the Sergeant and Soldiers Effect with a donor cosolvent.

Role of helicity on the anticancer mechanism of action of cationic-helical peptides

In the present study, the 26-residue amphipathic α-helical peptide A12L/A20L (Ac-KWKSFLKTFKSLKKTVLHTLLKAISS-amide) with strong anticancer activity and specificity was used as the framework to study the effects of helicity of α-helical anticancer peptides on biological activities. Helicity was systematically modulated by introducing d-amino acids to replace the original l-amino acids on the non-polar face or the polar face of the helix. Peptide helicity was measured by circular dichroism spectroscopy and was demonstrated to correlate with peptide hydrophobicity and the number of d-amino acid substitutions. Biological studies showed that strong hemolytic activity of peptides generally correlated with high hydrophobicity and helicity. Lower helicity caused the decrease of anti-HeLa activity of peptides. By introducing d-amino acids to replace the original l-amino acids on the non-polar face or the polar face of the helix, we improved the therapeutic index of A12L/A20L against HeLa cells by 9-fold and 22-fold, respectively. These results show that the helicity of anticancer peptides plays a crucial role for biological activities. This specific rational approach of peptide design could be a powerful method to improve the specificity of anticancer peptides as promising therapeutics in clinical practices.

Helicity is the only integral invariant of volume-preserving transformations

We prove that any regular integral invariant of volume-preserving transformations is equivalent to the helicity. Specifically, given a functional I defined on exact divergence-free vector fields of class C(1) on a compact 3-manifold that is associated with a well-behaved integral kernel, we prove that I is invariant under arbitrary volume-preserving diffeomorphisms if and only if it is a function of the helicity.

Bamboo-like π-Nanotubes with Tunable Helicity and Circularly Polarized Luminescence

We report the fabrication of an exotic bamboo-like π-nanotube via the hierarchical self-assembly of a dipeptide-substituted naphthalenediimide gelator with tunable helicity and circularly polarized luminescence (CPL). It was found that in the presence of trifluoroacetic acid (TFA) the gelator molecules self-assembled into a bamboo-like π-nanotube, which is composed of truncated nanocones and CPL active. When defining the diameter ratio of the lower to upper edge of each nanocone as a parameter to express the helicity of different nanotubes, it was found that both the helicity and CPL of these nanotubes can be adjusted by the amount of TFA. Moreover, the helicity of the nanotube can be conveyed to the achiral quantum dots (QDs) and produce a hybrid nanotube/QDs CPL active materials with adjustable dissymmetry factor. This work finds a new type self-assembled bamboo-like π-nanotube and unveils their helicity and CPL control.

Surface Physical Activity and Hydrophobicity of Designed Helical Peptide Amphiphiles Control Their Bioactivity and Cell Selectivity

G(IIKK)₃I-NH₂ has been recently shown to be highly effective at killing bacteria and inhibiting cancer cell growth while remaining benign to normal host mammalian cells. The aim of this work is to evaluate how residue substitutions of Ala (A), Val (V), Glu (E), and Lys (K) for the N-terminal Gly (G) or C-terminal Ile (I) of G(IIKK)₃I-NH₂ affect the physiochemical properties and bioactivity of the variants. All substitutions caused the reduction of peptide hydrophobicity, while N-terminal substitutions had a less noticeable effect on the surface activity and helix-forming ability than C-terminal substitutions. N-terminal variants held potent anticancer activity but exhibited reduced hemolytic activity; these actions were related to the maintenance of their moderate surface pressures (12-16 mN m^-1), while their hydrophobicity was reduced. Thus, N-terminal substitutions enhanced the cell selectivity of the mutants relative to the control peptide G(IIKK)₃I-NH₂. In contrast, C-terminal variants exhibited lower anticancer activity and much lower hemolytic activity except for G(IIKK)₃V-NH₂. These features were correlated well with their lower surface pressures (≤10 mN m^-1) and decreased hydrophobicity. In spite of its very low helical content, the C-terminal variant G(IIKK)₃V-NH₂ still displayed potent anticancer activity while retaining high hemolytic activity as well, again correlating well with its relatively high surface pressure and hydrophobicity. These results together indicated that surface activity governs the anticancer activity of the peptides, but hydrophobicity influences their hemolytic activity. In contrast, helicity appears to be poorly correlated to their bioactivity. This work has demonstrated that N-terminal modifications provide a useful strategy to optimize the anticancer activity of helical anticancer peptides (ACPs) against its potential toxicity to mammalian host cells.

Current and Future Applications of Computational Fluid Dynamics in Coronary Artery Disease

Hemodynamics interacts with the cellular components of human vessels, influencing function and healthy status. Locally acting hemodynamic forces have been associated-by a steadily increasing amount of scientific evidence-with nucleation and evolution of atherosclerotic plaques in several vascular regions, resulting in the formulation of the 'hemodynamic risk hypothesis' of the atherogenesis. At the level of coronary arteries, however, the complexity of both anatomy and physiology made the study of this vascular region particularly difficult for researchers. Developments in computational fluid dynamics (CFD) have recently allowed an accurate modelling of the intracoronary hemodynamics, thus offering physicians a unique tool for the investigation of this crucial human system by means of advanced mathematical simulations. The present review of CFD applications in coronary artery disease was set to concisely offer the medical reader the theoretical foundations of quantitative intravascular hemodynamics-reasoned schematically in the text in its basic (i.e., pressure and velocity) and derived quantities (e.g., fractional flow reserve, wall shear stress and helicity)-along with its current implications in clinical research. Moreover, attention was paid in classifying computational modelling derived from invasive and non-invasive imaging modalities with unbiased remarks on the advantages and limitations of each procedure. Finally, an extensive description-aided by explanatory figures and cross references to recent clinical findings-was presented on the role of near-wall hemodynamics, in terms of shear stress, and of intravascular flow complexity, in terms of helical flow.

Wall Shear Stress Directional Abnormalities in BAV Aortas: Toward a New Hemodynamic Predictor of Aortopathy?

The bicuspid aortic valve (BAV) generates wall shear stress (WSS) abnormalities in the ascending aorta (AA) that may be responsible for the high prevalence of aortopathy in BAV patients. While previous studies have analyzed the magnitude and oscillatory characteristics of the total or streamwise WSS in BAV AAs, the assessment of the circumferential component is lacking despite its expected significance in this highly helical flow environment. This gap may have hampered the identification of a robust hemodynamic predictor of BAV aortopathy. The objective of this study was to perform a global and component-specific assessment of WSS magnitude, oscillatory and directional characteristics in BAV AAs. The WSS environments were computed in the proximal and middle convexity of tricuspid aortic valve (TAV) and BAV AAs using our previous valve-aorta fluid-structure interaction (FSI) models. Component-specific WSS characteristics were investigated in terms of temporal shear magnitude (TSM) and oscillatory shear index (OSI). WSS directionality was quantified in terms of mean WSS vector magnitude and angle, and angular dispersion index (D_α). Local WSS magnitude and multidirectionality were captured in a new shear magnitude and directionality index (SMDI) calculated as the product of the mean WSS magnitude and D_α. BAVs subjected the AA to circumferential TSM overloads (2.4-fold increase vs. TAV). TAV and BAV AAs exhibited a unidirectional circumferential WSS (OSI < 0.04) and an increasingly unidirectional longitudinal WSS between the proximal (OSI > 0.21) and middle (OSI < 0.07) sections. BAVs generated mean WSS vectors skewed toward the anterior wall and WSS angular distributions exhibiting decreased uniformity in the proximal AA (0.27-point increase in D_α vs. TAV). SMDI was elevated in all BAV AAs but peaked in the proximal LR-BAV AA (3.6-fold increase vs. TAV) and in the middle RN-BAV AA (1.6-fold increase vs. TAV). This analysis demonstrates the significance of the circumferential WSS component and the existence of substantial WSS directional abnormalities in BAV AAs. SMDI abnormality distributions in BAV AAs follow the morphotype-dependent occurrence of dilation in BAV AAs, suggesting the predictive potential of this metric for BAV aortopathy.

Hierarchy of Asymmetry at Work: Chain-Dependent Helix-to-Helix Interactions in Supramolecular Polymers

A detailed investigation of the hierarchy of asymmetry operating in the self-assembly of achiral (1) and chiral ((S)-2 and (R)-3) 1,3,5-triphenylbenzenetricarboxamides (TPBAs) is reported. The aggregation of these TPBAs is conditioned by the point chirality at the peripheral side chains for (S)-2 and (R)-3. An efficient helix-to-helix interaction that goes further in the organization of fibrillar bundles is experimentally detected and theoretically supported only for the achiral TPBA 1. The effective interdigitation of the achiral aliphatic side chains produces a social self-sorting to form preferentially heterochiral macromolecular aggregates.

Controlling Ultra-Large Optical Asymmetry in Amorphous Molecular Aggregations

Although ultra-large optical asymmetry appears in crystalline materials, distractions from the mesoscopic ordering often causes inauthenticity in chiropticity. In amorphous materials, however, it remains challenging and elusive to achieve large chiropticity. Herein, we report the quantitative control of chiral amplification, on amorphous supramolecular structures of cholesteryl-linked bis(dipyrrinato)zinc(II), to an exceptionally high level. A proper chiral packing of the building block at several molecular scale considerably contributes to the absorptive dissymmetry factor g_abs , although the system is overall disordered. The intense and tunable aggregation strength renders a variable g_abs value up to +0.10 and +0.31 in the solution and in film state. On this basis, a superior ON-OFF switching of chiropticity is realized under external stimuli. This work establishes a general design principle to control over ultra-large optical asymmetry on a wider scope of chiral materials.

Enantiomeric Effect of d-Amino Acid Substitution on the Mechanism of Action of α-Helical Membrane-Active Peptides

V13K, a 26-residue peptide, has been shown to have strong antimicrobial activity, negligible hemolytic activity, and significant anticancer activity. In the present work, V13K was used as the framework to investigate the influence of helicity, as influenced by d-amino acid substitutions in the center of the peptide polar and non-polar faces of the amphipathic helix, on biological activity. The antibacterial and anticancer activities of the peptides were investigated. Atomic force microscopy and other biophysical methods were used to investigate the effect of peptide helicity on biological activity. The results showed the importance of suitable and rational modification of membrane-active peptides, based on helicity, in optimizing potential biological activity.

Magnetic Skyrmions with Unconventional Helicity Polarization in a Van Der Waals Ferromagnet

Skyrmion helicity, which defines the spin swirling direction, is a fundamental parameter that may be utilized to encode data bits in future memory devices. Generally, in centrosymmetric ferromagnets, dipole skyrmions with helicity of -π/2 and π/2 are degenerate in energy, leading to equal populations of both helicities. On the other hand, in chiral materials where the Dzyaloshinskii-Moriya interaction (DMI) prevails and the dipolar interaction is negligible, only a preferred helicity is selected by the type of DMI. However, whether there is a rigid boundary between these two regimes remains an open question. Herein, the observation of dipole skyrmions with unconventional helicity polarization in a van der Waals ferromagnet, Fe_{5- δ} GeTe₂ , is reported. Combining magnetometry, Lorentz transmission electron microscopy, electrical transport measurements, and micromagnetic simulations, the short-range superstructures in Fe_{5- δ} GeTe₂ resulting in a localized DMI contribution, which breaks the degeneracy of the opposite helicities and leads to the helicity polarization, is demonstrated. Therefore, the helicity feature in Fe_{5- δ} GeTe₂ is controlled by both the dipolar interaction and DMI that the former leads to Bloch-type skyrmions with helicity of ±π/2 whereas the latter breaks the helicity degeneracy. This work provides new insights into the skyrmion topology in van der Waals materials.

Helicity Modulation Improves the Selectivity of Antimicrobial Peptoids

The modulation of conformational flexibility in antimicrobial peptides (AMPs) has been investigated as a strategy to improve their efficacy against bacterial pathogens while reducing their toxicity. Here, we synthesized a library of helicity-modulated antimicrobial peptoids by the position-specific incorporation of helix-inducing monomers. The peptoids displayed minimal variations in hydrophobicity, which permitted the specific assessment of the effect of conformational differences on antimicrobial activity and selectivity. Among the moderately helical peptoids, the most dramatic increase in selectivity was observed in peptoid 17, providing more than a 20-fold increase compared to fully helical peptoid 1. Peptoid 17 had potent broad-spectrum antimicrobial activity that included clinically isolated multi-drug-resistant pathogens. Compared to pexiganan AMP, 17 showed superior metabolic stability, which could potentially reduce the dosage needed, alleviating toxicity. Dye-uptake assays and high-resolution imaging revealed that the antimicrobial activity of 17 was, as with many AMPs, mainly due to membrane disruption. However, the high selectivity of 17 reflected its unique conformational characteristics, with differential interactions between bacterial and erythrocyte membranes. Our results suggest a way to distinguish different membrane compositions solely by helicity modulation, thereby improving the selectivity toward bacterial cells with the maintenance of potent and broad-spectrum activity.

Stimuli-Responsive Chiroptical Switching

"Chirality" governs many fundamental properties in chemistry and biochemistry. While early investigations on stereochemistry are primarily dedicated to static chirality, there is an increasing interest in the field of dynamic chirality (chiral switches). These chiral switches are essential in controlling the directionality in molecular motors. Dynamic chiralities are equally crucial in switchable stereoselectivity, switchable asymmetric catalysis and enantioselective separation. Herein, we limit our discussion to recent advances on stimuli-induced chiroptical switching of axial, helical, and planar chirality in response to external stimuli. We also discuss a few examples of applications of the switchable chirality.

Characterization of Excitonic Nature in Raman Spectra Using Circularly Polarized Light

We propose a technique of Raman spectroscopy to characterize the excitonic nature and to evaluate the relative contribution of the two kinds of electron/exciton-phonon interactions that are observed in two-dimensional transition-metal dichalcogenides (TMDCs). In the TMDCs, the electron/exciton-phonon interactions mainly originate from the deformation potential (DP) or the Fröhlich interaction (FI) which give the mutually different Raman tensors. Using a circularly polarized light, the relative proportion of the DP and the FI can be defined by the ratio of helicity-polarized intensity that is observed by MoS₂. By this analysis, we show that the excitonic FI interaction gradually increases with decreasing temperature, contributes equally to DP at ∼230 K, and dominates at lower temperatures. The excitonic effect in the Raman spectra is confirmed by modulating the dielectric environment for the exciton and by changing the laser power.

Chirality-Induced Propagation Velocity Asymmetry

The spin-dependent propagation of electrons in helical nanowires is investigated. We show that the interplay of spin angular momentum and nanowire chirality, under spin-orbit interaction, lifts the symmetry between left and right propagating electrons, giving rise to a velocity asymmetry. The study is based on a microscopic tight-binding model that takes into account the spin-orbit interaction. The continuity equation for the spin-dependent probability density is derived, including the spin nonconserving terms, and quantum dynamics calculations are performed to obtain the electron propagation dynamics. The calculations are applied to the inorganic double-helix SnIP, a quasi-1D material that constitutes a semiconductor with a band gap of ∼1.9 eV. The results, nevertheless, have general validity due to symmetry considerations. The relation of the propagation velocity asymmetry with the phenomena ascribed to the chiral-induced spin selectivity effect is examined.