Predictions of a topological electronic structure in the skutterudite ${\mathrm{TPn}}_3$ family ($T=\text{transition metal}$, $Pn=\text{pnictogen}$) are investigated via magnetoresistance, quantum oscillation, and angle-resolved photoemission experiments on $\mathrm{Rh}{\mathrm{Sb}}_3$, a semimetal with low carrier density. Electronic band structure calculations and symmetry analysis of $\mathrm{Rh}{\mathrm{Sb}}_3$ indicate this material to be a zero-gap semimetal protected by symmetry with inverted valence and conduction bands that touch at the $\mathrm{\Gamma }$ point close to the Fermi level. Transport experiments reveal an unsaturated linear magnetoresistance that approaches a factor of 200 at 60 T magnetic fields and quantum oscillations observable up to 150 K that are consistent with a large Fermi velocity ($\sim 1.3\times {10}^6$ m/s), high carrier mobility [$\sim 14$ ${\mathrm{m}}^2/\left(\mathrm{V}\mathrm{s}\right)$], and the existence of a small three-dimensional hole pocket. A very small, sample-dependent effective mass falls to values as low as 0.018(2) of the bare electron mass and scales with the Fermi wave vector. This, together with a nonzero Berry's phase and the location of the Fermi level in the linear region of the valence band, suggests $\mathrm{Rh}{\mathrm{Sb}}_3$ as representative of a material family of topological semimetals with symmetry-enforced Fermi degeneracy at the high-symmetry points.

Single crystals were grown and characterized to investigate the physical properties and magnetic ground state of $\mathrm{Ba}{\mathrm{Nd}}_2\mathrm{Pt}{\mathrm{O}}_5$, a candidate to host physics of the Shastry-Sutherland model. Analysis of single crystal x-ray diffraction data yields an updated crystal structure, similar to the prior report but now in space group $P4$/mbm. Magnetization and specific heat measurements reveal an antiferromagnetic transition at ${\mathrm{T}}_N=1.9\mathrm{K}$ and a large magnetic anisotropy with in-plane magnetization much larger than out-of-plane magnetization. Single crystal neutron diffraction at zero field reveals a propagation vector of $\left(\frac{1}{2}\frac{1}{2}\frac{1}{2}\right)$ for the magnetic ground state as compared to the $\left(\frac{1}{2}\frac{1}{2}0\right)$ wave vector observed in the related body-centered material $\mathrm{Ba}{\mathrm{Nd}}_2\mathrm{Zn}{\mathrm{O}}_5$. The ground state is found to be a fully compensated antiferromagnet with diffraction data well fitted within the magnetic space group $P_{\mathrm{S}}\text{−}1$ (BNS setting #2.7). The ordered moment is mostly in the basal plane with nearest neighbors forming ferromagnetic dimers, however it also has a finite out-of-plane component unlike the related easy-plane materials $\mathrm{Ba}{\mathrm{Nd}}_2\mathrm{Zn}{\mathrm{O}}_5$ and $\mathrm{Ba}{\mathrm{Nd}}_2\mathrm{Zn}{\mathrm{S}}_5$. Field-induced transitions are observed below $T_{\mathrm{N}}$ when the field is applied within the basal plane, and in-plane anisotropy of the associated critical fields is observed. The magnetization is strongly impacted by misalignment of the field away from high symmetry directions. These results suggest complex magnetic structures may arise in the field-induced states, and they highlight the need for extreme care when studying this and related Shastry-Sutherland materials.

Transient binding between associating macromolecules can cause qualitative changes to chain dynamics, including modes of conformational relaxation and diffusion, through tethering effects imparted by long-range connectivity. In this work, the role of binding on short-time segmental dynamics in associative polymer gels is investigated by neutron spin-echo (NSE) measurements on a class of model artificial coiled-coil proteins with a systematically varied architecture, probing timescales of 0.1–130 ns, and length scales close to the molecular radius of gyration. The results illustrate effects of transient cross-linking on chain dynamics on different timescales, manifested in changes in segmental relaxation behavior with variations in strand length, chain concentration, and sticker distribution (endblock- vs midblock-functionalized). In all gels, a short-time cooperative diffusion mode is seen over all wave vectors, analogous to a semidilute solution, with no transitions seen at any known structural length scale. However, the diffusion coefficients are found to decrease with increasing junction density across all gels, with the strand length and number of stickers per chain in each gel appearing to play a relatively minor role. The slowing of cooperative diffusion with junction density contrasts with classical predictions of a greater restoring force for fluctuation dissipation due to the increased elasticity, suggesting additional effects of the coiled-coil junctions such as an enhancement in local viscosity that slows dynamics. Notably, the relaxation rates for all gels can be rescaled by the interjunction spacing inferred from small-angle neutron scattering, where they collapse onto a master curve suggestive of self-similar dynamics even in networks with different strand lengths and chain architectures. On long timescales (but shorter than the junction exchange time), a slowing of network relaxation is observed, resulting in a nondecaying plateau in the spin-echo amplitude attributed to a freezing of chain dynamics due to tethering. A characteristic length scale corresponding to the extent of dynamic fluctuations is estimated for each gel, which appears to be smaller than the interjunction spacing but similar to the correlation blob size of the overlapping strands. The results indicate an important role of transient binding on molecular-scale dynamics in associative polymer gels, even on timescales shorter than the junction exchange time, in addition to its effects on long-range self-diffusion previously observed.

Low-dimensional materials can display enhanced electronic, magnetic, and quantum properties. We use the topological scaling algorithm to identify all sufficiently metastable materials in the Materials Project database to identify bulk crystals with one-dimensional (1D) structural motifs: Five hundred fifty-one crystals that are within 50 meV ${\mathrm{atom}}^{-1}$ of the thermodynamic hull display 1D motifs, where 293 of these contain $d$-valence elements, which we focus on in this work. After exfoliating nanowires from 263 of these materials and calculating their thermodynamic stability using density functional theory, 103 nanowires meet per-atom and per-Ångström thermodynamic stability criteria. We illustrate for three nanowire systems that a variety of local minima can be present in these systems, demonstrating one case of a Peierls distortion. The wires display a broad diversity of electronic and magnetic properties of these nanowires, with 14 metals, 7 half-metals, and 82 semiconductors and insulators, and 41 nanowires displaying magnetic moments ranging from 0.1 to $5{\mu }_B$ per $d$-valence species when assuming ferromagnetic order. A subset of these chains are investigated for the impact of magnetic ordering, identifying 1D ${\mathrm{FeCl}}_3$ to be most stable in an antiferromagnetic state. The electronic and magnetic properties of the identified 1D materials could enable applications in spintronic and quantum devices.

Antiferroelectricity is a state of matter that has so far eluded a clear-cut definition. Even in the best-known material realization, ${\mathrm{PbZrO}}_3$, the physical nature of the driving force towards an antipolar order has not been settled yet. Here, by building a Landau-like continuum Hamiltonian from first principles via an exact long-wave approach, we reconcile the existing theories in terms of a single physical mechanism. In particular, we find that a formerly overlooked trilinear coupling between tilts, tilt gradients, and polarization provides a surprisingly accurate description of the energetics and structure of the antiferroelectric ground state of ${\mathrm{PbZrO}}_3$. We discuss the relevance of our findings to other ferrielectric and incommensurate polar structures that were recently observed in perovskites.

Pressure is a unique tuning parameter for probing the properties of materials, and it has been particularly useful for studies of electronic materials such as high-temperature cuprate superconductors. Here we report the effects of quasihydrostatic compression produced by a neon pressure medium on the structures of bismuth-based high-${\mathit{T}}_{\mathit{c}}$ cuprate superconductors with the nominal composition ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Ca}}_{n-1}{\mathrm{Cu}}_n{\mathrm{O}}_{2n+4+\delta }$ ($n=1,2,3$) up to 155 GPa. The structures of all three compositions obtained by synchrotron x-ray diffraction can be described as pseudotetragonal over the entire pressure range studied. We show that previously reported pressure-induced distortions and structural changes arise from the large strains that can be induced in these layered materials by nonhydrostatic stresses. The pressure-volume equations of state (EOS) measured under these quasihydrostatic conditions cannot be fit to single phenomenological formulation over the pressure ranges studied, starting below 20 GPa. This intrinsic anomalous compression as well as the sensitivity of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Ca}}_{n-1}{\mathrm{Cu}}_n{\mathrm{O}}_{2n+4+\delta }$ to deviatoric stresses provide explanations for the numerous inconsistencies in reported EOS parameters for these materials. We conclude that the anomalous compressional behavior of all three compositions is a manifestation of the changes in electronic properties that are also responsible for the remarkable nonmonotonic dependence of ${\mathit{T}}_{\mathit{c}}$ with pressure, including the increase in ${\mathit{T}}_{\mathit{c}}$ at the highest pressures studied so far for each. Transport and spectroscopic measurements up to megabar pressures are needed to fully characterize these cuprates and explore higher possible critical temperatures in these materials.

Here we present $\mathrm{Yb}{\mathrm{V}}_3{\mathrm{Sb}}_4$ and $\mathrm{Eu}{\mathrm{V}}_3{\mathrm{Sb}}_4$, two compounds exhibiting slightly distorted vanadium-based kagome nets interleaved with zigzag chains of divalent ${\mathrm{Yb}}^{2+}$ and ${\mathrm{Eu}}^{2+}$ ions. Single crystal growth methods are reported alongside magnetic, electronic, and heat capacity measurements. $\mathrm{Yb}{\mathrm{V}}_3{\mathrm{Sb}}_4$ is a nonmagnetic metal with no collective phase transitions observed between 60 mK and 300 K. Conversely, $\mathrm{Eu}{\mathrm{V}}_3{\mathrm{Sb}}_4$ is a magnetic kagome metal exhibiting easy-plane ferromagneticlike order below $T_{\text{C}}=32$ K with hints of modulated spin texture under low field. With $\mathrm{Yb}{\mathrm{V}}_3{\mathrm{Sb}}_4$ and $\mathrm{Eu}{\mathrm{V}}_3{\mathrm{Sb}}_4$ we demonstrate another direction for the discovery and development of vanadium-based kagome metals while incorporating the chemical and magnetic degrees of freedom offered by a rare-earth sublattice.

The enthalpy change involved in metal oxide reduction is a key quantity in various processes related to energy conversion and storage and is of particular interest for computational prediction. Often this prediction involves the simulation of a high-temperature reduction process with a 0-K methodology like density functional theory (DFT), and it is not infrequent for the high temperature and 0-K stable crystal structures to differ. This introduces a conundrum with regard to the choice of crystal structure to utilize in the computation, with approaches in the literature varying and experimental validation remaining scarce. In this work, we address both the crystal structure conundrum and the experimental validation, and then apply the insights we gain to guide a high-throughput search for new materials for solar thermochemical water-splitting applications. By computing the $\mathrm{DFT}+U$ oxygen-vacancy formation energy ($\mathrm{\Delta }{E}_{vf}$) of a selection of $AB{\text{O}}_3$ compounds and comparing different crystal structures for each composition, we highlight the issues that arise when the structure utilized in the computation is dynamically unstable at 0 K, namely the presence of an artificial lowering of $\mathrm{\Delta }{E}_{vf}$, and the lack of convergence of $\mathrm{\Delta }{E}_{vf}$ with cell size. We solve these limitations by identifying and employing a suitable surrogate dynamically stable structure. We then validate the predictive power of our calculations against appositely generated experimental measurements of reduction enthalpy for a series of Hubbard $U$ values, finding an accuracy ranging between 0.2–0.6 eV/O. In light of such conclusions, we revise and expand a previous a high-throughput DFT study on $AB{\mathrm{O}}_3$ perovskite oxides. We provide a list of candidate STCH materials, highlight trends with redox-active cation and structural distortion, and identify ${\mathrm{Mn}}^{4+}$, ${\mathrm{Mn}}^{3+}$, and ${\mathrm{Co}}^{3+}$ as the most promising redox-active cations.

Ytterbium-doped $\mathrm{CsPb}{\mathrm{Cl}}_3$ is the leading candidate for a quantum-cutting coating on silicon solar cells to increase their efficiencies and durability by converting each incident ultraviolet and blue photon with energies $>2.5$ eV to two 1.25-eV near-infrared (NIR) photons. This approach can potentially increase silicon solar cell efficiencies above the Quessier limit. While photoluminescence quantum yields (PLQYs) approaching 200% have been demonstrated with thin films made using colloidal particle synthesis and nanocrystal dispersions, there is increased interest in physical vapor deposition as a large-area scalable method. We investigated the effect of Yb concentration and the annealing environment on the film structure, morphology, and optical properties, including the NIR PLQY. We found that subtle differences in the postdeposition annealing protocol significantly affect PLQY. Specifically, the highest PLQY ($\sim 70\%$) is achieved by annealing the films in an ${\mathrm{N}}_2$-filled glovebox first, followed by a second annealing step in air, both at $350{}^{\circ }\mathrm{C}$. X-ray photoelectron spectroscopy reveals that this approach anneals bulk defects, brings Yb to the surface, and forms a passivating oxide layer on the surface whose major component appears to be ${\mathrm{Yb}}_2{\mathrm{O}}_3$. Both surface oxidation and Yb segregation to the surface suppress grain growth during annealing. In addition, annealing only in air stops Yb segregation toward the surface. Annealing in ${\mathrm{N}}_2$ brings Yb to the surface but does not form a robust oxide. In contrast, annealing in ${\mathrm{N}}_2$, followed by annealing in air, brings Yb toward the surface and forms a passivating oxide, resulting in the highest PLQY.

Parametrized tight-binding models fit to first-principles calculations can provide an efficient and accurate quantum mechanical method for predicting properties of molecules and solids. However, well-tested parameter sets are generally only available for a limited number of atom combinations, making routine use of this method difficult. Furthermore, many previous models consider only simple two-body interactions, which limits accuracy. To tackle these challenges, we develop a density functional theory database of nearly 1 000 000 materials, which we use to fit a universal set of tight-binding parameters for 65 elements and their binary combinations. We include both two-body and three-body effective interaction terms in our model, plus self-consistent charge transfer, enabling our model to work for metallic, covalent, and ionic bonds with the same parameter set. To ensure predictive power, we adopt a learning framework where we repeatedly test the model on new low-energy crystal structures and then add them to the fitting data set, iterating until predictions improve. We distribute the materials database and tools developed in this paper publicly.

The electrostatic self-assembly of charged Brownian objects typically occurs in cases of short-range interactions. The objects form Coulombic materials that are close-packed and have long-range order. Here, we present a system in which two kinds of non-Brownian millimeter-sized beads tribocharge differently, experience long-range electrostatic interactions, and still form ordered two-dimensional structures. We provide a complete characterization of the kinetics of formation of these materials, as the total number of beads is held constant and the relative number of beads that tribocharge negatively or positively is modified. We agitate the beads by shaking the dish in which they are contained. We show that the beads commonly adopt a transient structure that we call a rosette. A rosette consists of a central bead surrounded by six close-packed neighbors of a different kind. The symmetry of the final structure depends on the relative number of negatively and positively charged beads, and it is not necessarily the same as that of the transient structure. Our results bear important implications in the de novo design of Coulombic materials given our ability to isolate transient structures, identify the moment of their appearance, and quantify the impact of agitation, tribocharging, and Coulombic energy minimization on their persistence.

High-performance permanent magnets have a wide range of applications in various fields of the information age. One distinct feature of permanent magnet materials is significant magnetic anisotropy, which is mainly affected by spin-orbit coupling (SOC). Focusing on materials containing $3d$ transition elements with specific Wyckoff positions, where certain partially occupied orbital multiplets can significantly enhance the effect of SOC, we perform a highly efficient search for permanent magnet materials in the inorganic crystal structure database. According to common standards of permanent magnets, we identify 19 potential permanent magnet materials. Among these candidates, 14 materials have already been discussed in previous studies, and we finally propose five new permanent magnet candidates. As examples, the detailed magnetic properties of two candidates among these five new proposed materials are presented. We believe that these potential permanent magnet materials deserve further experimental study.

An outstanding challenge in synthesis and theory is to develop molecular materials at ambient conditions that exhibit highly efficient energy transfer. Here we demonstrate the potential of a recently synthesized, highly conductive amorphous material—a nickel tetrathiafulvalene-tetrathiolate (NiTTFtt) polymer—to become an exciton condensate—a Bose-Einstein condensate of particle-hole pairs, known as excitons, that supports dissipationless flow of excitation energy. While exciton condensates have recently been realized in ordered materials, we show by advanced electronic structure calculations that this highly correlated phenomenon can potentially be realized in molecularly tailored, amorphous materials. In contrast to the Bechgaard salts that support superconductivity at compressed geometries requiring high pressures, we show that the recently synthesized, amorphous NiTTFtt polymer exhibits the computational signature of exciton condensation at experimentally realizable geometries, occurring at ambient pressures. Results suggest that superfluidity in this system and related systems—including van der Waals structures, molecular metals with extended-TTF dithiolate ligands, and Bechgaard salts—may occur via a nontraditional excitonic mechanism tuneable according to system composition, geometry, size, and charge. This study prompts further experimental investigation of the rational design of molecularly scaled exciton condensates with potential applications to efficient transport in technologically relevant materials.

Terrace-sized, single-orientation graphene can be grown on top of a carbon buffer layer on silicon carbide by thermal decomposition. Despite its homogeneous appearance, a surprisingly large variation in electron transport properties is observed. Here, we employ aberration-corrected low-energy electron microscopy to study a possible cause of this variability. We characterize the morphology of stacking domains between the graphene and the buffer layer of three different high-quality samples to capture the range of possible behavior. Similar to the case of twisted bilayer graphene, the lattice mismatch between the graphene layer and the buffer layer at the growth temperature causes a moiré pattern with domain boundaries between AB and BA stackings. We analyze this moiré pattern to characterize the relative strain and to count the number of edge dislocations. Furthermore, we show that epitaxial graphene on silicon carbide in general is close to a phase transition, causing intrinsic disorder in the form of the coexistence of anisotropic stripe domains and isotropic trigonal domains. Using adaptive geometric phase analysis, we determine the precise relative strain variation caused by these domains in different samples. We observe that the step edges of the SiC substrate influence the orientation of the domains and we discuss which aspects of the growth process influence these effects by comparing samples from different sources.

We present the growth and basic magnetic and transport properties of ${\mathrm{Cr}}_{1+x}{\mathrm{Pt}}_{5-x}\mathrm{P}$. We show that single crystals can readily be grown from a high-temperature solution created by adding dilute quantities of Cr to Pt-P based melts. Like other 1–5–1 compounds, ${\mathrm{Cr}}_{1+x}{\mathrm{Pt}}_{5-x}\mathrm{P}$ adopts a tetragonal P4/mmm structure composed face-sharing ${\mathrm{CrPt}}_3$ like slabs that are broken up along the $c$ axis by sheets of P atoms. EDS and x-ray diffraction measurements both suggest ${\mathrm{Cr}}_{1+x}{\mathrm{Pt}}_{5-x}\mathrm{P}$ has mixed occupancy between Cr and Pt atoms, similar to what is found in the closely related compound ${\mathrm{CrPt}}_3$, giving real compositions of ${\mathrm{Cr}}_{1.5}{\mathrm{Pt}}_{4.5}\mathrm{P}$ $(x=0.5)$. We report that ${\mathrm{Cr}}_{1.5}{\mathrm{Pt}}_{4.5}\mathrm{P}$ orders ferromagnetically at ${\mathit{T}}_C=464.5$ K with a saturated moment of $\approx 2.1{\mu }_{\mathit{B}}/\mathrm{Cr}$ at 1.8 K. Likely owing to the strong spin-orbit coupling associated with the large quantity of high Z, Pt atoms, ${\mathrm{Cr}}_{1.5}{\mathrm{Pt}}_{4.5}\mathrm{P}$ has exceptionally strong planar anisotropy with estimated anisotropy fields of 345 kOe and 220 kOe at 1.8 K and 300 K, respectively. The resistance of ${\mathrm{Cr}}_{1.5}{\mathrm{Pt}}_{4.5}\mathrm{P}$ has a metallic temperature dependence with relatively weak magnetoresistance. Electronic band structure calculations show that ${\mathrm{CrPt}}_5\mathrm{P}$ has a large peak in the density of states near the Fermi level, which is split into spin majority and minority bands in the ferromagnetic state. Furthermore, the calculations suggest substantial hybridization between $\mathrm{Cr}\text{−}3d$ and $\mathrm{Pt}\text{−}5d$ states near the Fermi level, in agreement with the experimentally measured anisotropy.

Solute segregation is a crucial means of stabilizing nanostructured alloys, and at very small grain sizes, this requires consideration of triple junctions (TJs), which attain a meaningful volume fraction and thus become relevant for bulk material behavior. Here, the solute segregation spectra for grain boundary (GB) and TJ sites are calculated for a large number of dilute Al-based binary systems with available interatomic potentials. A defect-identifying algorithm is applied to quantify the average GB thickness and classify the intergranular site spectra into GB and junction subspectra. The algorithm is also applied to a hybrid electronic-level database for GB segregation of various solutes in Al, yielding polycrystalline TJ solute segregation spectra from first principles. The results suggest that TJ segregation is alloy or interatomic potential dependent and can exhibit either boundary or junction preference. With these spectra as inputs, the spectral GB segregation model gives quantitative predictions of segregation as a function of grain size, temperature, and total solute concentration, suitable for alloy screening and design.

Tellurium is a gyrotropic, $p$-type Weyl semiconductor with remarkable electronic, optical, and transport properties. It has been argued that some of these properties might stem from Weyl nodes at crossing points in the band structure and their nontrivial topological textures. However, Weyl nodes in time-reversal invariant semiconductors are split up in energy, rather than in momentum, and located deep below (far above) the top (bottom) of the valence (conduction) band, challenging such an interpretation. Here, instead, we use a four-band$\mathbf{k}·\mathbf{p}$ Hamiltonian for $p$-type tellurium to show how the k-dependent spin-orbit interaction mixes up the top two (Weyl node free) and bottom two (Weyl-node-containing) valence bands, generating a 3D hedgehog orbital magnetic texture at the uppermost valence band, already accessible to transport at the lowest doping. Hedgehog textures are important signatures of Weyl fermion physics, in general, and in the context of condensed matter physics arise form the carriers' wave packet rotation being locked to their propagation wave vector. For spatially dispersive media, such an induced hedgehog texture/carrier rotation stabilizes two nonreciprocal and antisymmetric components to the Hall transport within different weak-localization (antilocalization) relaxation regimes: the anomalous and planar Hall effects, usually forbidden by time-reversal symmetry. Our AC magnetotransport measurements on Sn-doped tellurium confirm the theoretical predictions and our paper demonstrates how Weyl signatures generally appear in transport on enantiomorphic materials with natural optical activity.

Nanotube encapsulation is a powerful technique for coaxing solids into unconventional configurations. By synthesizing materials within the interior confines of hollow nanotubes, lower dimensional morphologies, such as one-dimensional chains or nanoribbons, are favored. We have used carbon nanotube encapsulation to realize ultranarrow, atomically precise $\mathrm{Hf}{\mathrm{Te}}_2$ nanoribbons. A local, electron-beam-stimulated transition from the metallic 1T phase to the previously unreported semiconducting 1H phase is observed. We study computationally how charging can drive the phase transition and the stability of the different atomic configurations.

Broadband ferromagnetic resonance is measured in single crystalline Fe films of varying thickness sandwiched between MgO layers. An exhaustive magnetic characterization of the films (exchange constant, cubic, uniaxial and surface anisotropies) is enabled by the study of the uniform and the first perpendicular standing spin wave modes as a function of applied magnetic field and film thickness. Additional measurements of nonreciprocal spin-wave propagation allow us to separate each of the two interface contributions to the total surface anisotropy. The results are consistent with the model of a quasi-bulk film interior and two magnetically different top and bottom interfaces, a difference ascribed to different oxidation states.

A puckered sheet is a freestanding crystalline membrane with an embedded array of bistable buckled units. Recent work has shown that the bistable units behave like spins in a two-dimensional compressible Ising antiferromagnet with, however, a coupling to flexural phonons. At finite temperature, this purely mechanical system displays Ising-like phase transitions, which drive anomalous thermal expansion. Here, we show that geometry can be used to control phase behavior: curvature produces a radius-dependent “external field” that encourages alignment between neighboring “spins,” disrupting the ordered checkerboard ground state of antialigned neighbors. The effective field strength scales as the inverse of the radius of curvature. We identify this effective field theoretically with both a discrete real space model and a nonlinear continuum elastic model. We then present molecular dynamics simulations of puckered sheets in cylindrical geometries at zero and finite temperature, probing the influence of curvature on the stability of configurations and phase transitions. Our work demonstrates how curvature and temperature can be used to design and operate a responsive and tunable metamaterial at either the macroscale or nanoscale.