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Landau predicted that transverse sound propagates in a Fermi liquid with sufficiently strong Fermi liquid interactions, unlike a classical fluid which cannot support shear oscillations. Previous attempts to observe this unique collective mode yielded inconclusive results due to contributions from single particle excitations. Here, we have microfabricated acoustic cavities with a micron-scale path length that is suitable for direct detection of this sound mode. The interference fringes of these acoustic Fabry-Perot cavities can be used to determine both the real and imaginary parts of the acoustic impedance. We report a null-result in this search as no clear interference fringe has been observed in the Fermi liquid, indicating the attenuation of TZS is likely above 2000 cm^-1. We provide theoretical justification for why the sound mode may yet exist but not being directly detectable due to high attenuation.

We consider the Atiyah-Patodi-Singer (APS) index theorem corresponding to the chiral symmetry of a continuum formulation of staggered fermions called Kähler-Dirac fermions, which have been recently investigated as an ingredient in lattice constructions of chiral gauge theories. We point out that there are two notions of chiral symmetry for Kähler-Dirac fermions, both having a mixed perturbative anomaly with gravity leading to index theorems on closed manifolds. By formulating these theories on a manifold with boundary, we find the APS index theorems corresponding to each of these symmetries, necessary for a complete picture of anomaly inflow, using a recently discovered physics-motivated proof. We comment on a fundamental difference between the nature of these two symmetries by showing that a sensible local, symmetric boundary condition only exists for one of the two symmetries. This sheds light on how these symmetries behave under lattice discretization, and in particular on their use for recent symmetric-mass generation proposals.

We analyze the phases of theories which only have a microscopic $\mathbb{Z}_N$ 1-form symmetry, starting with a topological BF theory and deforming it in accordance with microscopic symmetry. These theories have a well-defined notion of confinement. Prototypical examples are pure $SU(N)$ gauge theories and $\mathbb{Z}_N$ lattice gauge theories. Our analysis shows that the only generic phases are in $d=2$, only the confined phase; in $d=3$, both the confined phase and the topological BF phase; and in $d=4$, the confined phase, the topological BF phase, and a phase with a massless photon. We construct a $\mathbb{Z}_N$ lattice gauge theory with a deformation which, surprisingly, produces up to $(N-1)$ photons. We give an interpretation of these findings in terms of two competing pictures of confinement -- proliferation of monopoles and proliferation of center vortices -- and conclude that the proliferation of center vortices is a necessary but insufficient condition for confinement, while that of monopoles is both necessary and sufficient.

Chemotactic active particles, such as bacteria and cells, exhibit an adaptive run-and-tumble motion, giving rise to complex emergent behaviors in response to external chemical fields. This motion is generated by the conversion of internal chemical energy into self-propulsion, allowing each agent to sustain a steady-state far from thermal equilibrium and perform works. The rate of entropy production serves as an indicates of how extensive these agents operate away from thermal equilibrium, providing a measure for estimating maximum obtainable power. Here we present the general framework for calculating the entropy production rate created by such population of agents from the first principle, using the minimal model of bacterial adaptive chemotaxis, as they execute the most basic collective action -- the mass transport.

Anisotropic aerogel possesses structure which exhibits a strong influence over the composition and orientation of the order parameter of imbibed superfluid $^3$He. Computational studies have identified stretched aerogel with plane-like structures and compressed aerogel with nematic-like structures. Studies of the B phase of superfluid $^3$He in stretched aerogel display an enhanced nuclear magnetic susceptibility likely caused by Andreev bound states near plane-like impurity sites. We report further details on the influence of these planar structures on both magnetic and orbital orientation transitions. The orbital orientation transitions appear in both the B and A phases of stretched and compressed aerogels. These transitions result from a crossover of the superfluid coherence length with long and short length scale structure with the coherence length and are consequently magnetic field independent. Additionally, the apparent temperature-independence of the susceptibility of the B phase equal to that of the A phase in stretched aerogel, is in marked contrast with the field dependence of the superfluid A to B phase transition, indicating that it is a near-isentropic transition.

The homogeneous precession domain (HPD) of superfluid $^{3}$He has recently been identified as a detection medium which might provide sensitivity to the axion-nucleon coupling $g_{aNN}$ competitive with, or surpassing, existing experimental proposals. In this work, we make a detailed study of the statistical and dynamical properties of the HPD system in order to make realistic projections for a full-fledged experimental program. We include the effects of clock error and measurement error in a concrete readout scheme using superconducting qubits and quantum metrology. This work also provides a more general framework to describe the statistics associated with the axion gradient coupling through the treatment of a transient resonance with a non-stationary background in a time-series analysis. Incorporating an optimal data-taking and analysis strategy, we project a sensitivity approaching $g_{aNN} \sim 10^{-12}$ GeV$^{-1}$ across a decade in axion mass.

To study gapped phases of $4$d gauge theories, we introduce the temporal gauging of $\mathbb{Z}_N$ $1$-form symmetry in $4$d quantum field theories (QFTs), thereby defining effective $3$d QFTs with $\widetilde{\mathbb{Z}}_N\times \mathbb{Z}_N$ $1$-form symmetry. In this way, spatial fundamental Wilson and 't Hooft loops are simultaneously genuine line operators. Assuming a mass gap and Lorentz invariant vacuum of the $4$d QFT, the $\widetilde{\mathbb{Z}}_N\times \mathbb{Z}_N$ symmetry must be spontaneously broken to an order-$N$ subgroup $H$, and we can classify the $4$d gapped phases by specifying $H$. This establishes the $1$-to-$1$ correspondence between the two classification schemes for gapped phases of $4$d gauge theories: One is the conventional Wilson-'t Hooft classification, and the other is the modern classification using the spontaneous breaking of $4$d $1$-form symmetry enriched with symmetry-protected topological states.

Nuclear magnetic resonance measurements of the magnetic susceptibility of superfluid $^3$He imbibed in anisotropic aerogel reveal anomalous behavior at low temperatures. Although the frequency shift clearly identifies a low-temperature phase as the $B$ phase, the magnetic susceptibility does not display the expected decrease associated with the formation of the opposite-spin Cooper pairs. This susceptibility anomaly appears to be the predicted high-field behavior corresponding to the Ising-like magnetic character of surface Andreev bound states within the planar aerogel structures.

We perform cluster aggregation simulations to model the structure of anisotropic aerogel. By biasing the diffusion process, we are able to obtain two distinct types of globally anisotropic aerogel structures which we call "nematic", with long strands along the anisotropy axis, and "planar", with long strands in planes perpendicular to the anisotropy axis. We calculate the auto-correlation function, the structure factor, and the angular dependence of the free-path distribution for these samples. The calculated structure factor from simulated aerogels can be compared with data from small-angle X-ray scattering (SAXS) of lab-grown aerogel allowing us to classify the spatial structure of the lab-grown samples. We find that the simulated "nematic" aerogel has a structure factor consistent with lab-grown, axially-compressed silica aerogel while the simulated "planar" aerogel has a structure factor consistent with lab-grown "stretched" silica aerogel. Unexpectedly, compressing previously isotropic silica aerogel leads to the formation of long strands along the compression axis while stretching silica aerogel leads to formation of planes perpendicular to the stretching axis. We discuss the implication of this determination on experiments of superfluid $^3$He in anisotropic aerogel, in particular the orbital analog of the spin-flop transition.

Anomalies are a powerful way to gain insight into possible lattice regularizations of a quantum field theory. In this work, we argue that the continuum anomaly for a given symmetry can be matched by a manifestly-symmetric, local, lattice regularization in the same spacetime dimensionality only if (i) the symmetry action is offsite, or (ii) if the continuum anomaly is reproduced exactly on the lattice. We consider lattice regularizations of a class of prototype models of QCD: the (1+1)-dimensional asymptotically-free Grassmannian nonlinear sigma models (NLSMs) with a $\theta$ term. Using the Grassmannian NLSMs as a case study, we provide examples of lattice regularizations in which both possibilities are realized. For possibility (i), we argue that Grassmannian NLSMs can be obtained from $\mathrm{SU}(N)$ antiferromagnets with a well-defined continuum limit, reproducing both the infrared physics of $\theta$ vacua and the ultraviolet physics of asymptotic freedom. These results enable the application of new classical algorithms to lattice Monte Carlo studies of these quantum field theories, and provide a viable realization suited for their quantum simulation. On the other hand, we show that, perhaps surprisingly, the conventional lattice regularization of $\theta$ vacua due to Berg and Lüscher reproduces the anomaly exactly on the lattice, providing a realization of the second possibility.

Monitoring chemical reactions in solutions at the scale of individual entities is challenging: single particle detection requires small confocal volumes which are hardly compatible with Brownian motion, particularly when long integration times are necessary. Here, we propose a real-time (10 Hz) holography-based nm-precision 3D tracking of single moving nanoparticles. Using this localization, the confocal collection volume is dynamically adjusted to follow the moving nanoparticle and allow continuous spectroscopic monitoring. This concept is applied to the study galvanic exchange in freely-moving colloïdal silver nanoparticles with gold ions generated in-situ. While the Brownian trajectory reveals particle size, spectral shifts dynamically reveal composition changes and transformation kinetics at the single object level, pointing at different transformation kinetics for free and tethered particles.

Axions and axion-like particles may couple to nuclear spins like a weak oscillating effective magnetic field, the "axion wind." Existing proposals for detecting the axion wind sourced by dark matter exploit analogies to nuclear magnetic resonance (NMR) and aim to detect the small transverse field generated when the axion wind resonantly tips the precessing spins in a polarized sample of material. We describe a new proposal using the homogeneous precession domain (HPD) of superfluid helium-3 as the detection medium, where the effect of the axion wind is a small shift in the precession frequency of a large-amplitude NMR signal. We argue that this setup can provide broadband detection of multiple axion masses simultaneously, and has competitive sensitivity to other axion wind experiments such as CASPEr-Wind at masses below $10^{-7}$ eV by exploiting precision frequency metrology in the readout stage.

While the $\theta$ dependence of field theories is $2\pi$ periodic, the ground-state wavefunctions at $\theta$ and $\theta+2\pi$ often belong to different classes of symmetry-protected topological states. When this is the case, a continuous change of the $\theta$ parameter can introduce an interface that supports a nontrivial field theory localized on the wall. We consider the $2$d $\mathbb{C}P^{N-1}$ sigma model as an example and construct a weak-coupling setup of this interface theory by considering the small $S^1$ compactification with nonzero winding $\theta$ parameter and a suitable symmetry-twisted boundary condition. This system has $N$ classical vacua connected by fractional instantons, but the anomaly constraint tells us that the fractional-instanton amplitudes should vanish completely to have $N$-fold degeneracy at the quantum level. We show how this happens in this purely bosonic system, uncovering that the integration over the zero modes annihilates the fractional instanton amplitudes, which is sharp contrast to what happens when the $\theta$ angle is constant. Moreover, we provide another explanation of this selection rule by showing that the $N$ perturbative vacua acquire different charges under the global symmetry with the activation of the winding $\theta$ angle. We also demonstrate a similar destructive interference between instanton effects in the $\mathbb{C}P^{N-1}$ quantum mechanics with the Berry phase.

Although the equilibrium composition of many alloy surfaces is well understood, the rate of transient surface segregation during annealing is not known, despite its crucial effect on alloy corrosion and catalytic reactions occurring on overlapping timescales. In this work, CuNi bimetallic alloys representing (100) surface facets are annealed in vacuum using atomistic simulations to observe the effect of vacancy diffusion on surface separation. We employ multi-timescale methods to sample the early transient, intermediate, and equilibrium states of slab surfaces during the separation process, including standard MD as well as three methods to perform atomistic, long-time dynamics: parallel trajectory splicing (ParSplice), adaptive kinetic Monte Carlo (AKMC), and kinetic Monte Carlo (KMC). From nanosecond (ns) to second timescales, our multiscale computational methodology can observe rare stochastic events not typically seen with standard MD, closing the gap between computational and experimental timescales for surface segregation. Rapid diffusion of a vacancy to the slab is resolved by all four methods in tens of ns. Stochastic re-entry of vacancies into the subsurface, however, is only seen on the microsecond timescale in the two KMC methods. Kinetic vacancy trapping on the surface and its effect on the segregation rate are discussed. The equilibrium composition profile of CuNi after segregation during annealing is estimated to occur on a timescale of seconds as determined by KMC, a result directly comparable to nanoscale experiments.

In this work, we use a minimal model to introduce a framework for controlling self-assembly under the influence of time-dependent driving forces. We develop a mean-field thermodynamic framework that predicts the conditions required to reliably self-assemble a desired spatial pattern under time-varying external fields. We also calculate the entropy production associated with the time-dependent self-assembly process and examine how it can be used to predict conditions under which the external time-varying signal is reliably encoded as a spatial pattern in the self-assembling material. While the results in this work are developed in the context of a minimal one-dimensional model, we anticipate that the framework can be used to establish guidelines for controlling self-assembly in more complex scenarios.

The discovery of superfluidity in 3He in 1971, published in 1972, [1, 2] has influenced a wide range of investigations that extend well beyond fermionic superfluids, including electronic quantum ma- terials, ultra-cold gases and degenerate neutron matter. Observation of thermodynamic transitions from the 3He Fermi liquid to two other liquid phases, A and B-phases, along the melting curve of liquid and solid 3He, discovered by Osheroff, Richardson, and Lee, were the very first indications of 3He superfluidity leading to their Nobel prize in 1996. This is a brief retrospective specifically focused on the AB transition.

Spin current and spin torque generation through the spin-orbit interactions in solids, of bulk or interfacial origin, is at the heart of spintronics research. The realization of spin-orbit torque (SOT) driven magnetic dynamics and switching in diverse magnetic heterostructures also pave the way for developing SOT magnetoresistive random access memory and other novel SOT memory and logic devices. Of scientific and technological importance are accurate and efficient SOT quantification techniques, which have been abundantly developed in the last decade. In this article, we summarize popular techniques to experimentally quantify SOTs in magnetic heterostructures at micro- and nano-scale. For each technique, we give an overview of its principle, variations, strengths, shortcomings, error sources, and any cautions in usage. Finally, we discuss the remaining challenges in understanding and quantifying the SOTs in heterostructures.

The interplay between unconventional superconductivity and quantum critical ferromagnetism in the U-Ge compounds represents an open problem in strongly correlated electron systems. Sample quality can have a strong influence on both of these ordered states in the compound UCoGe, as is true for most unconventional superconductors. We report results of a new approach at UCoGe crystal growth using a floating-zone method with potential for improvements of sample quality and size as compared with traditional means such as Czochralski growth. Single crystals of the ferromagnetic superconductor UCoGe were produced using an ultra-high vacuum electron-beam floating-zone refining technique. Annealed single crystals show well-defined signatures of bulk ferromagnetism and superconductivity at $T_c \sim$2.6 K and $T_s \sim$0.55 K, respectively, in the resistivity and heat capacity. Scanning electron microscopy of samples with different surface treatments shows evidence of an off-stoichiometric uranium rich phase of UCoGe collected in cracks and voids that might be limiting sample quality.

Understanding the role of non-equilibrium driving in self-organization is crucial for developing a predictive description of biological systems, yet it is impeded by their complexity. The actin cytoskeleton serves as a paradigm for how equilibrium and non-equilibrium forces combine to give rise to self-organization. Motivated by recent experiments that show that actin filament growth rates can tune the morphology of a growing actin bundle crosslinked by two competing types of actin binding proteins, we construct a minimal model for such a system and show that the dynamics are subject to a set of thermodynamic constraints that relate the non-equilibrium driving, bundle morphology, and molecular fluxes. The thermodynamic constraints reveal the importance of correlations between these molecular fluxes, and offer a route to estimating microscopic driving forces from microscopy experiments.

An anomalous optical second-harmonic generation (SHG) signal was previously reported in Sr$_2$IrO$_4$ and attributed to a hidden odd-parity bulk magnetic state. Here we investigate the origin of this SHG signal using a combination of bulk magnetic susceptibility, magnetic-field-dependent SHG rotational anisotropy, and overlapping wide-field SHG imaging and atomic force microscopy measurements. We find that the anomalous SHG signal exhibits a two-fold rotational symmetry as a function of in-plane magnetic field orientation that is associated with a crystallographic distortion. We also show a change in SHG signal across step edges that tracks the bulk antiferromagnetic stacking pattern. While we do not rule out the existence of hidden order in Sr$_2$IrO$_4$, our results altogether show that the anomalous SHG signal in parent Sr$_2$IrO$_4$ originates instead from a surface-magnetization-induced electric-dipole process that is enhanced by strong spin-orbit coupling.

We studied the electronic structure of PtPb$_{4}$ using laser angle-resolved photoemission spectroscopy(ARPES) and density functional theory(DFT) calculations. This material is closely related to PtSn$_{4}$, which exhibits exotic topological properties such as Dirac node arcs. Fermi surface(FS) of PtPb$_{4}$ consists of two electron pockets at the center of the Brillouin zone(BZ) and several hole pockets around the zone boundaries. Our ARPES data reveals significant Rashba splitting at the $\Gamma$ point in agreement with DFT calculations. The presence of Rashba splitting may render this material of potential interest for spintronic applications.

We propose a scheme of decomposition of the total relativistic energy in solids to intra- and interatomic contributions. The method is based on a variation of the speed of light from its value in relativistic theory to infinity (a non-relativistic limit). As an illustration of the method, we tested such decomposition in the case of a spin-orbit interaction variation for decomposition of the magnetic anisotropy energy (MAE) in CoPt. We further studied the \alpha''-Fe16N2 magnet doped by Bi, Sb, Co and Pt atoms. It has been found that the addition of Pt atoms can enhance the MAE by as large as five times while Bi and Sb substitutions double the total MAE. Using the proposed technique we demonstrate the spatial distribution of these enhancements. Our studies also suggest that Sb, Pt and Co substitutions could be synthesized by experiments.

Organic semiconductors exhibit properties of individual molecules and extended crystals simultaneously. The strongly bound excitons they host are typically described in the molecular limit, but excitons can delocalize over many molecules, raising the question of how important the extended crystalline nature is. Using accurate Green's function based methods for the electronic structure and non-perturbative finite difference methods for exciton-vibration coupling, we describe exciton interactions with molecular and crystal degrees of freedom concurrently. We find that the degree of exciton delocalization controls these interactions, with thermally activated crystal phonons predominantly coupling to delocalized states, and molecular quantum fluctuations predominantly coupling to localized states. Based on this picture, we quantitatively predict and interpret the temperature and pressure dependence of excitonic peaks in the acene series of organic semiconductors, which we confirm experimentally, and we develop a simple experimental protocol for probing exciton delocalization. Overall, we provide a unified picture of exciton delocalization and vibrational effects in organic semiconductors, reconciling the complementary views of finite molecular clusters and periodic molecular solids.

Point defects in hexagonal boron nitride have emerged as a promising quantum light source due to their bright and photostable room temperature emission. In this work, we study the incorporation of quantum emitters during chemical vapor deposition growth on a nickel substrate. Combining a range of characterization techniques, we demonstrate that the incorporation of quantum emitters is limited to (001) oriented nickel grains. Such emitters display improved emission properties in terms of brightness and stability. We further utilize these emitters and integrate them with a compact optical antenna enhancing light collection from the sources. The hybrid device yields average saturation count rates of ~2.9 x106 cps and an average photon purity of ~90%. Our results advance the controlled generation of spatially distributed quantum emitters in hBN and demonstrate a key step towards on-chip devices with maximum collection efficiency.

Luminescent colloidal CdSe nanorings are a new type of semiconductor structure that have attracted interest due to the potential for unique physics arising from their non-trivial toroidal shape. However, the exciton properties and dynamics of these materials with complex topology are not yet well understood. Here, we use a combination of femtosecond vibrational spectroscopy, temperature-resolved photoluminescence (PL), and single particle measurements to study these materials. We find that on transformation of CdSe nanoplatelets to nanorings, by perforating the center of platelets, the emission lifetime decreases and the emission spectrum broadens due to ensemble variations in the ring size and thickness. The reduced PL quantum yield of nanorings (~10%) compared to platelets (~30%) is attributed to an enhanced coupling between: (i) excitons and CdSe LO-phonons at 200 cm-1 and (ii) negatively charged selenium-rich traps which give nanorings a high surface charge (~-50 mV). Population of these weakly emissive trap sites dominates the emission properties with an increased trap emission at low temperatures relative to excitonic emission. Our results provide a detailed picture of the nature of excitons in nanorings and the influence of phonons and surface charge in explaining the broad shape of the PL spectrum and the origin of PL quantum yield losses. Furthermore, they suggest that the excitonic properties of nanorings are not solely a consequence of the toroidal shape but are also a result of traps introduced by puncturing the platelet center.

In the majority of molecular optimization tasks, predictive machine learning (ML) models are limited due to the unavailability and cost of generating big experimental datasets on the specific task. To circumvent this limitation, ML models are trained on big theoretical datasets or experimental indicators of molecular suitability that are either publicly available or inexpensive to acquire. These approaches produce a set of candidate molecules which have to be ranked using limited experimental data or expert knowledge. Under the assumption that structure is related to functionality, here we use a molecular fragment-based graphical autoencoder to generate unique structural fingerprints to efficiently search through the candidate set. We demonstrate that fragment-based graphical autoencoding reduces the error in predicting physical characteristics such as the solubility and partition coefficient in the small data regime compared to other extended circular fingerprints and string based approaches. We further demonstrate that this approach is capable of providing insight into real world molecular optimization problems, such as searching for stabilization additives in organic semiconductors by accurately predicting 92% of test molecules given 69 training examples. This task is a model example of black box molecular optimization as there is minimal theoretical and experimental knowledge to accurately predict the suitability of the additives.

We characterize the nanosecond pulse switching performance of the three-terminal magnetic tunnel junctions (MTJs), driven by the spin Hall effect (SHE) in the channel, at a cryogenic temperature of 3 K. The SHE-MTJ devices exhibit reasonable magnetic switching and reliable current switching by as short pulses as 1 ns of $<10^{12}$ A/m$^{2}$ magnitude, exceeding the expectation from conventional macrospin model. The pulse switching bit error rates reach below $10^{-6}$ for < 10 ns pulses. Similar performance is achieved with exponentially decaying pulses expected to be delivered to the SHE-MTJ device by a nanocryotron device in parallel configuration of a realistic memory cell structure. These results suggest the viability of the SHE-MTJ structure as a cryogenic memory element for exascale superconducting computing systems.

The critical field for superfluid $^3$He in axially compressed, anisotropic silica aerogel is shown to be the result of an anisotropic distribution of magnetic impurities affecting the superfluid $A$ phase. The critical field results from the fact that the $A$ phase is suppressed relative to the $B$ phase which is immune to the effects of magnetic impurities. In the absence of magnetic quasiparticle scattering in anisotropic aerogel, we find that the relative symmetry of $A$ and $B$ phase order parameters is the same as in isotropic aerogel, just as it is in pure superfluid $^3$He. These results are of potential importance for understanding unconventional superconductivity.

We explore an opportunity to induce and control tetragonal distortion in materials. The idea involves formation of a binary alloy from parent compounds having body-centered and face-centered symmetries. The concept is illustrated in the case of FeNi$_{1-x}$Co$_x$ magnetic alloy formed by substitutional doping of the L1$_0$ FeNi magnet with Co. Using electronic structure calculations we demonstrate that the tetragonal strain in this system can be controlled by concentration and it reaches maximum for $x=0.5$. This finding is then applied to create a large magnetocrystalline anisotropy (MAE) in FeNi$_{1-x}$Co$_x$ system by considering an interplay of the tetragonal distortion with electronic concentration and chemical anisotropy. In particular, we identify a new ordered FeNi$_{0.5}$Co$_{0.5}$ system with MAE larger by a factor 4.5 from the L1$_0$ FeNi magnet.

We present a study of the pulsed current switching characteristics of spin-valve nanopillars with in-plane magnetized dilute permalloy and undiluted permalloy free layers in the ballistic regime at low temperature. The dilute permalloy free layer device switches much faster: the characteristic switching time for a permalloy free (Ni0.83Fe0.17) layer device is 1.18 ns, while that for a dilute permalloy ([Ni0.83Fe0.17]0.6Cu0.4) free layer device is 0.475 ns. A ballistic macrospin model can capture the data trends with a reduced spin torque asymmetry parameter, reduced spin polarization and increased Gilbert damping for the dilute permalloy free layer relative to the permalloy devices. Our study demonstrates that reducing the magnetization of the free layer increases the switching speed while greatly reducing the switching energy and shows a promising route toward even lower power magnetic memory devices compatible with superconducting electronics.

The formation possibility of a new (Zr0.25Nb0.25Ti0.25V0.25)C high-entropy ceramic (ZHC-1) was first analyzed by the first-principles calculations and thermodynamical analysis and then it was successfully fabricated by hot pressing sintering technique. The first-principles calculation results showed that the mixing enthalpy of ZHC-1 was 5.526 kJ/mol and the mixing entropy of ZHC-1 was in the range of 0.693R-1.040R. The thermodynamical analysis results showed that ZHC-1 was thermodynamically stable above 959 K owing to its negative mixing Gibbs free energy. The experimental results showed that the as-prepared ZHC-1 (95.1% relative density) possessed a single rock-salt crystal structure, some interesting nanoplate-like structures and high compositional uniformity from nanoscale to microscale. By taking advantage of these unique features, compared with the initial metal carbides (ZrC, NbC, TiC and VC), it showed a relatively low thermal conductivity of 15.3 + - 0.3 W/(m.K) at room temperature, which was due to the presence of solid solution effects, nanoplates and porosity. Meanwhile, it exhibited the relatively high nanohardness of 30.3 + - 0.7 GPa and elastic modulus of 460.4 + - 19.2 GPa and the higher fracture toughness of 4.7 + - 0.5 MPa.m1/2, which were attributed to the solid solution strengthening mechanism and nanoplate pullout and microcrack deflection toughening mechanism.

Single photon emitters (SPEs) in solids have emerged as promising candidates for quantum photonic sensing, communications, and computing. Defects in hexagonal boron nitride (hBN) exhibit high-brightness, room-temperature quantum emission, but their large spectral variability and unknown local structure significantly challenge their technological utility. Here, we directly correlate hBN quantum emission with the material's local strain using a combination of photoluminescence (PL), cathodoluminescence (CL) and nano-beam electron diffraction. Across 40 emitters and 15 samples, we observe zero phonon lines(ZPLs) in PL and CL ranging from 540-720 nm. CL mapping reveals that multiple defects and distinct defect species located within an optically-diffraction-limited region can each contribute to the observed PL spectra. Local strain maps indicate that strain is not required to activate the emitters and is not solely responsible for the observed ZPL spectral range. Instead, four distinct defect classes are responsible for the observed emission range. One defect class has ZPLs near 615 nm with predominantly matched CL-PL responses; it is not a strain-tuned version of another defect class with ZPL emission centered at 580 nm. A third defect class at 650 nm has low visible-frequency CL emission; and a fourth defect species centered at 705 nm has a small, ~10 nm shift between its CL and PL peaks. All studied defects are stable upon both electron and optical irradiation. Our results provide an important foundation for atomic-scale optical characterization of color centers, as well as a foundation for engineering defects with precise emission properties.

Superfluid 3He has a rich spectrum of collective modes with both massive and massless excitations. The masses of these modes can be precisely measured using acoustic spectroscopy and fit to theoretical models. Prior comparisons of the experimental results with theory did not include strong-coupling effects beyond the weak-coupling-plus BCS model, so-called non-trivial strong-coupling corrections. In this work we utilize recent strong-coupling calculations to determine the Higgs masses and find consistency between experiments that relate them to a sub-dominant $f$-wave pairing strength.

Single-photon emitters in gallium nitride (GaN) are gaining interest as attractive quantum systems due to the well-established techniques for growth and nanofabrication of the host material, as well as its remarkable chemical stability and optoelectronic properties. We investigate the nature of such single-photon emitters in GaN with a systematic analysis of various samples produced under different growth conditions. We explore the effect that intrinsic structural defects (dislocations and stacking faults), doping and crystal orientation in GaN have on the formation of quantum emitters. We investigate the relationship between the position of the emitters (determined via spectroscopy and photoluminescence measurements) and the location of threading dislocations (characterised both via atomic force microscopy and cathodoluminescence). We find that quantum emitters do not correlate with stacking faults or dislocations; instead, they are more likely to originate from point defects or impurities whose density is modulated by the local extended defect density.

The direction of the orbital angular momentum of the $B$-phase of superfluid $^3$He can be controlled by engineering the anisotropy of the silica aerogel framework within which it is imbibed. In this work, we report our discovery of an unusual and abrupt `orbital-flop' transition of the superfluid angular momentum between orientations perpendicular and parallel to the anisotropy axis. The transition has no hysteresis, warming or cooling, as expected for a continuous thermodynamic transition, and is not the result of a competition between strain and magnetic field. This demonstrates the spontaneous reorientation of the order parameter of an unconventional BCS condensate.

Measurements of temperature-dependent resistance and magnetization under hydrostatic pressures up to 2.13 GPa are reported for single-crystalline, superconducting BaBi$_3$. A temperature - pressure phase diagram is determined and the results suggest three different superconducting phases ${\alpha}$, $\beta$, and $\gamma$ in the studied pressure range. We further show that occurrence of the three superconducting phases is intuitively linked to phase transitions at higher temperature which are likely first order in nature. $T_p$, which separates phase ${\alpha}$ from $\beta$ and $\gamma$, is associated with an abrupt resistance change as pressure is increased from 0.27 GPa to 0.33 GPa. Above 0.33 GPa, an "S-shape" anomaly in the temperature-dependent resistance curve, $T_\text S$, is observed and associated with the transition between the $\beta$ and $\gamma$ phases. Further increasing of pressure above 1.05 GPa suppresses this transition and BaBi$_3$ stays in $\gamma$ phase over the whole investigated temperature range. These high-temperature anomalies are likely related to structural degrees of freedom. With the ${\alpha}$ phase being the ambient-pressure tetragonal structure ($P4/mmm$), our first-principle calculations suggest the $\beta$ phase to be cubic structure ($Pm-3m$) and the $\gamma$ phase to be a distorted tetragonal structure where the Bi atoms are moved out of the face-centered position. Finally, an analysis of the evolution of the superconducting upper critical field with pressure further confirms these transitions in the superconducting state and suggests a possible change of band structure or a Lifshitz transition near 1.54 GPa in $\gamma$ phase. Given the large atomic numbers of both Ba and Bi, our results establish BaBi$_3$ as a good candidate for the study of the interplay of structure with superconductivity in the presence of strong spin-orbit coupling.

The pressure dependence of the order parameter in superfluid $^3$He is amazingly simple. In the Ginzburg-Landau regime, i.e. close to $T_c$, the square of the order parameter can be accurately measured by its proportionality to NMR frequency shifts and is strictly linear in pressure. This behavior is replicated for superfluid $^3$He imbibed in isotropic and anisotropic silica aerogels. The proportionality factor is constrained by the symmetry of the superfluid state and is an important signature of the corresponding superfluid phase. For the purpose of identifying various new superfluid states in the $p$-wave manifold, the order parameter amplitude of $^3$He-A is a useful reference, and this simple pressure dependence greatly facilitates identification.

Quantum technologies require robust and photostable single photon emitters (SPEs) that can be reliably engineered. Hexagonal boron nitride (hBN) has recently emerged as a promising candidate host to bright and optically stable SPEs operating at room temperature. However, the emission wavelength of the fluorescent defects in hBN has, to date, been shown to be uncontrolled. The emitters usually display a large spread of zero phonon line (ZPL) energies spanning over a broad spectral range (hundreds of nanometers), which hinders the potential development of hBN-based devices and applications. We demonstrate bottom-up, chemical vapor deposition growth of large-area, few layer hBN that hosts large quantities of SPEs: 100 per 10x10 \mum2. Remarkably, more than 85 percent of the emitters have a ZPL at (580\pm10)nm, a distribution which is over an order of magnitude narrower than previously reported. Exploiting the high density and uniformity of the emitters, we demonstrate electrical modulation and tuning of the ZPL emission wavelength by up to 15 nm. Our results constitute a definite advancement towards the practical deployment of hBN single photon emitters in scalable quantum photonic and hybrid optoelectronic devices based on 2D materials.

Hexagonal Boron Nitride (hBN) mono and multilayers are promising hosts for room temperature single photon emitters (SPEs). In this work we explore high energy (~ MeV) electron irradiation as a means to generate stable SPEs in hBN. We investigate four types of exfoliated hBN flakes - namely, high purity multilayers, isotopically pure hBN, carbon rich hBN multilayers and monolayered material - and find that electron irradiation increases emitter concentrations dramatically in all samples. Furthermore, the engineered emitters are located throughout hBN flakes (not only at flake edges or grain boundaries), and do not require activation by high temperature annealing of the host material after electron exposure. Our results provide important insights into controlled formation of hBN SPEs and may aid in identification of their crystallographic origin.

To reduce material and processing costs of commercial permanent magnets and to attempt to fill the empty niche of energy products, 10 - 20 MGOe, between low-flux (ferrites, alnico) and high-flux (Nd2Fe14B- and SmCo5-type) magnets, we report synthesis, structure, magnetic properties and modeling of Ta, Cu and Fe substituted CeCo5. Using a self-flux technique, we grew single crystals of I - Ce15.1Ta1.0Co74.4Cu9.5, II - Ce16.3Ta0.6Co68.9Cu14.2, III - Ce15.7Ta0.6Co67.8Cu15.9, IV - Ce16.3Ta0.3Co61.7Cu21.7 and V - Ce14.3Ta1.0Co62.0Fe12.3Cu10.4. X-ray diffraction analysis (XRD) showed that these materials retain a CaCu5 substructure and incorporate small amounts of Ta in the form of \dumb-bells", filling the 2e crystallographic sites within the 1D hexagonal channel with the 1a Ce site, whereas Co, Cu and Fe are statistically distributed among the 2c and 3g crystallographic sites. Scanning electron microscopy, energy dispersive X-ray spectroscopy (SEM-EDS) and scanning transmission electron microscopy (STEM) examinations provided strong evidence of the single-phase nature of the as-grown crystals, even though they readily exhibited significant magnetic coercivitie of ~1.6 - ~1.8 kOe caused by Co-enriched, nano-sized, structural defects and faults that can serve as pinning sites. Formation of the "composite crystal" during the heat treatment creates a 3D array of extended defects within a primarily single grain single crystal, which greatly improves its magnetic characteristics. Possible causes of the formation of the "composite crystal" may be associated with Ta atoms leaving matrix interstices at lower temperatures and/or matrix degradation induced by decreased miscibility at lower temperatures. Fe strongly improves both the Curie temperature and magnetization of the system resulting in (BH)max:~13 MGOe at room temperature.

Stochastic thermodynamics provides a useful set of tools to analyze and constrain the behavior of far from equilibrium systems. In this paper, we report an application of ideas from stochastic thermodynamics to the problem of membrane growth. Non-equilibrium forcing of the membrane can cause it to buckle and undergo a morphological transformation. We show how ideas from stochastic thermodynamics, in particular the recently derived thermodynamic uncertainty relations, can be used to phenomenologically describe and constrain the parameters required to excite morphological changes during a non-equilibrium growth process.

In this paper, we present a coupled experimental/theoretical investigation of pressure effect on the ferromagnetism of LaCrGe3 and LaCrSb3 compounds. The magnetic, electronic, elastic and mechanical properties of LaCrGe3 and LaCrSb3 at ambient condition are studied by first-principles density functional theory calculations. The pressure dependences of the magnetic properties of LaCrGe3 and LaCrSb3 are also investigated. The ferromagnetism in LaCrGe3 is rather fragile with a ferro- to paramagnetic transition at a relatively small pressure (around 7 GPa from our calculations, and 2 GPa in experiments). The key parameter controlling the magnetic properties of LaCrGe3 is found to be the proximity of the Cr DOS to the Fermi surface, a proximity that is strongly correlated to the distance between Cr atoms along the c-axis, suggesting that there would be a simple way to suppress magnetism in systems with one dimensional arrangement of magnetic atoms. By contrast, the ferromagnetism in LaCrSb3 is not fragile. Our calculation results are consistent with our experimental results and demonstrate the feasibility of using first-principles calculations to aid experimental explorations in screening for materials with fragile magnetism.

We performed a systematic search for low-energy structures of binary iron silicide over a wide range of compositions using the crystal structure prediction method based on adaptive genetic algorithm. 36 structures with formation energies within 50 meV/atom (11 of them are within 20 meV) above the convex hull formed by experimentally known stable structures are predicted. Magnetic properties of these low-energy structures are investigated. Some of these structures can be promising candidates for rare-earth-free permanent magnet.

Recent research has indicated that introducing impurities that increase the resistivity of Pt can enhance the efficiency of the spin Hall torque it generates. Here we directly demonstrate the usefulness of this strategy by fabricating prototype 3-terminal in-plane-magnetized magnetic tunnel junctions that utilize the spin Hall torque from a $\rm{Pt}_{85}\rm{Hf}_{15}$ alloy, and measuring the critical currents for switching. We find that $\rm{Pt}_{85}\rm{Hf}_{15}$ reduces the switching current densities compared to pure Pt by approximately a factor of 2 for both quasi-static ramped current biases and nanosecond-scale current pulses, thereby proving the feasibility of this approach to assist in the development of efficient embedded magnetic memory technologies.

Single defect centers in layered hexagonal boron nitride (hBN) are promising candidates as single photon sources for quantum optics and nanophotonics applications. However, until today spectral instability hinders many applications. Here, we perform resonant excitation measurements and observe Fourier-Transform limited (FL) linewidths down to $\approx 50$ MHz. We investigate optical properties of more than 600 quantum emitters (QE) in hBN. The QEs exhibit narrow zero-phonon lines (ZPL) distributed over a spectral range from 580 nm to 800 nm and with dipole-like emission with high polarization contrast. The emission frequencies can be divided into four main regions indicating distinct families or crystallographic structures of the QEs, in accord with ab-initio calculations. Finally, the emitters withstand transfer to a foreign photonic platform - namely a silver mirror, which makes them compatible with photonic devices such as optical resonators and paves the way to quantum photonics applications including quantum commmunications and quantum repeaters.

Artificial atomic systems in solids are becoming increasingly important building blocks in quantum information processing and scalable quantum nanophotonic networks. Yet, synthesis of color centers that act as single photon emitters which are suitable for on-chip applications is still beyond reach. Here, we report a number of plasma and thermal annealing methods for the fabrication of emitters in tape-exfoliated hexagonal boron nitride (hBN) crystals. A two-step process comprised of Ar plasma etching and subsequent annealing in Ar is highly robust, and yields a seven-fold increase in the concentration of emitters in hBN. The initial plasma etching step generates emitters that suffer from blinking and bleaching, whereas the two-step process yields emitters that are photostable at room temperature and have an emission energy distribution that is red-shifted relative to that of pristine hBN. An analysis of emitters fabricated by a range of plasma and annealing treatments, combined with a theoretical investigation of point defects in hBN indicates that single photon emitters characterized by a high degree of photostability and emission wavelengths greater than ~700 nm are associated with defect complexes that contain oxygen. This is further confirmed by generating the emitters by annealing hBN in an oxidative atmosphere. Our findings advance present understanding of the structure of quantum emitter in hBN and enhance the nanofabrication toolkit that is needed to realize integrated quantum nanophotonics based on 2D materials.

Quasi-two dimensional transition metal dichalcogenides (TMD) exhibit dramatic properties that may transform electronic and photonic devices. We report on how the anomalously large magnetoresistance (MR) observed under high magnetic field in MoTe$_2$, a type II Weyl semimetal, can be reversibly controlled under tensile strain. The MR is enhanced by as much as ~ 30 % at low temperatures and high magnetic fields, when uniaxial strain is applied along the $a$-crystallographic direction and reduced by about the same amount when strain is applied along the $b$-direction. We show that the large in-plane electric anisotropy is coupled with the structural transition from the 1T' monoclinic to the Td orthorhombic Weyl phase. A shift of the Td - 1T' phase boundary is achieved by minimal tensile strain. The sensitivity of the MR to tensile strain suggests the possibility of a nontrivial spin-orbital texture of the electron and hole pockets in the vicinity of Weyl points. Our ab initio calculations indeed show a significant orbital mixing on the Fermi surface, which is modified by the tensile strains.

The 1144 iron arsenide (e.g. CaKFe4As4) has recently been discovered and inspired a tide of search for superconductors. Such far, the discovered compounds are confined to iron arsenides (ABFe4As4), where A and B are either alkali metals or alkaline earth elements. In this work, we propose two directions in searching 1144 structures: (i) using tri-valence cations for A; (ii) substituting the transition metal, e.g. replacing Fe by Co. Following the two directions, we employ density functional theory to study stability and electronic structures of 1144 pnictides of various tri-valence cations (La, Y, In, Tl, Sm and Gd), as well as cobalt arsenides. For LaAFe4As4, the 1144 phase can be stabilized in three systems: LaKFe4As4, LaRbFe4As4 and LaCsFe4As4, which show quasi-two-dimensional semi-metal features similar to the iron pnictide superconductors: hole-type Fermi surface at Gama point and electron-type Fermi surface at M point in B.Z. In addition, LaKFe4As4 feature an extra bubble shaped Fermi surface sheets, distinct from the other two peers. Y does not support any 1144 phase within our search. For In and Tl, substitute Fe by Co and two unknown compounds of the 122 phase are stabilized: InCo2As2 and TlCo2As2. The two cobalt arsenides have Fermi surfaces of similar topology as iron arsenides, but the Fermi surfaces are all electron-type, showing potentials to be undiscovered superconductors. Stable 1144 phases are also found in InKCo4As4 and InRbCo4As4. For Sm and Gd, most 1144 and 122 iron arsenides are found unstable.

Quantum emitters in layered hexagonal boron nitride (hBN) have recently attracted a great attention as promising single photon sources. In this work, we demonstrate resonant excitation of a single defect center in hBN, one of the most important prerequisites for employment of optical sources in quantum information application. We observe spectral linewidths of hBN emitter narrower than 1 GHz while the emitter experiences spectral diffusion. Temporal photoluminescence measurements reveals an average spectral diffusion time of around 100 ms. On-resonance photon antibunching measurement is also realized. Our results shed light on the potential use of quantum emitters from hBN in nanophotonics and quantum information.

The dependence of the magnetocrystalline anisotropy energy (MAE) of MCo5 (M = Y, La) on the Coulomb correlations and strength of spin orbit (SO) interaction within the GGA + U scheme is investigated. A range of parameters suitable for the satisfactory description of key magnetic properties is determined. The origin of MAE in these materials is mostly related to the large orbital moment anisotropy of Co atoms on the 2c crystallographic site. Dependence of relativistic effects on Coulomb correlations, applicability of the second order perturbation theory for the description of MAE and effective screening of the SO interaction in these systems are discussed using a generalized virial theorem.

Co3Si was recently reported to exhibit remarkable magnetic properties in the nanoparticle form [Appl. Phys. Lett. 108, 152406 (2016)], yet better understanding of this material is to be promoted. Here we report a study on the crystal structures of Co3Si using adaptive genetic algorithm, and discuss its electronic and magnetic properties from first-principles calculations. Several competing phases of Co3Si have been revealed from our calculations. We show that the hexagonal Co3Si structure reported in experiments has lower energy in non-magnetic state than ferromagnetic state at zero temperature. The ferromagnetic state of the hexagonal structure is dynamically unstable with imaginary phonon modes and transforms to a new orthorhombic structure, which is confirmed by our structure searches to have the lowest energy for both Co3Si and Co3Ge. Magnetic properties of the experimental hexagonal structure and the lowest-energy structures obtained from our structure searches are investigated in detail.

Transport and magnetic studies of PbTaSe$_2$ under pressure suggest existence of two superconducting phases with the low temperature phase boundary at $\sim 0.25$ GPa that is defined by a very sharp, first order, phase transition. The first order phase transition line can be followed via pressure dependent resistivity measurements, and is found to be near 0.12 GPa near room temperature. Transmission electron microscopy and x-ray diffraction at elevated temperatures confirm that this first order phase transition is structural and occurs at ambient pressure near $\sim 425$ K. The new, high temperature / high pressure phase has a similar crystal structure and slightly lower unit cell volume relative to the ambient pressure, room temperature structure. Based on first-principles calculations this structure is suggested to be obtained by shifting the Pb atoms from the $1a$ to $1e$ Wyckoff position without changing the positions of Ta and Se atoms. PbTaSe$_2$ has an exceptionally pressure sensitive, structural phase transition with $\Delta T_s/\Delta P \approx - 1700$ K/GPa near 4 K, this first order transition causes an $\sim 1$ K ($\sim 25 \%$) step - like decrease in $T_c$ as pressure is increased through 0.25 GPa.

Homogeneous highly epitaxial LaSrMnO3 (LSMO) thin films have been grown on Yttria-stabilized-Zirconia (YsZ) / CeO2 buffer layers on technological relevant 4" silicon wafers using a Twente Solid State Technology B.V. (TSST) developed large area Pulsed Laser Deposition (PLD) setup. We study and show the results of the effect of an additional SrRuO3 buffer layer on the growth temperature dependent structural and magnetic properties of LSMO films. With the introduction of a thin SrRuO3 layer on top of the buffer stack, LSMO films show ferromagnetic behaviour for growth temperatures as low as 250C. We suggest that occurrence of epitaxial crystal growth of LSMO at these low growth temperatures can be understood by an improved surface diffusion, which ensures sufficient intermixing of surface species for formation of the correct phase. This intermixing is necessary because the full plume is collected on the 4" wafer resulting in a compositional varying flux of species on the wafer, in contrast to small scale experiments.

The temperature-pressure phase diagram of the ferromagnet LaCrGe$_3$ is determined for the first time from a combination of magnetization, muon-spin-rotation and electrical resistivity measurements. The ferromagnetic phase is suppressed near $2.1$~GPa, but quantum criticality is avoided by the appearance of a magnetic phase, likely modulated, AFM$_Q$. Our density functional theory total energy calculations suggest a near degeneracy of antiferromagnetic states with small magnetic wave vectors $Q$ allowing for the potential of an ordering wave vector evolving from $Q=0$ to finite $Q$, as expected from the most recent theories on ferromagnetic quantum criticality. Our findings show that LaCrGe$_3$ is a very simple example to study this scenario of avoided ferromagnetic quantum criticality and will inspire further study on this material and other itinerant ferromagnets.

Hard X-ray generation for Au nanoparticle dispersion was systematically investigated for different particle diameters ranging from 10 to 100 nm with a narrow size distribution of +/- 2%. Scaling law of X-ray generation is close to a 6-photon process before the onset of saturation for excitation by 45 fs laser pulses with central wavelength of 800 nm. This is consistent with bulk plasmon excitation at wavelength ~ 138 nm. The longitudinal E-field component due to nanoparticle focusing is responsible for the excitation of the longitudinal bulk plasmon. The proposed analysis also explains X-ray emission from water breakdown via an electron solvation mechanism at ~6.2 eV. The most efficient emission of X-rays was observed for 40 +/- 10 nm diameter nanoparticles which also had the strongest UV extinction. X-ray emission was the most efficient when induced by pre-chirped 370 +/- 20 fs laser pulses and exhibited the highest intensity at a negative chirp.

We report measurements of the spin torque efficiencies in perpendicularly-magnetized Pt/Co bilayers where the Pt resistivity $\rho_{Pt}$ is strongly dependent on thickness $t_{Pt}$ . The damping-like spin Hall torque efficiency per unit current density, $\xi^j_{DL}$ , varies significantly with $t_{Pt}$, exhibiting a peak value $\xi^j_{DL}=0.12$ at $t_{Pt} = 2.8 - 3.9$ nm. In contrast, $\xi^j_{DL}/\rho_{Pt}$ increases monotonically with $t_{Pt}$ and saturates for $t_{Pt} > 5$ nm, consistent with an intrinsic spin Hall effect mechanism, in which $\xi^j_{DL}$ is enhanced by an increase in $\rho_{Pt}$ . Assuming the Elliott-Yafet spin scattering mechanism dominates we estimate that the spin diffusion length $\lambda_s = (0.77 \pm 0.08) \times 10^{-15} \Omega m^2 /\rho_{Pt}$.

Sodium orthosilicates Na2MSiO4 (M denotes transition metals) have attracted much attention due to the possibility of exchanging two electrons per formula unit. In this work, we report a group of sodium iron orthosilicates Na2FeSiO4, the crystal structures of which are characterized by a diamond-like Fe-Si network. The Fe-Si network is quite robust against the charge/discharge process, which explains the high structural stability observed in experiment. Using the density functional theory within the GGA+U framework and X-ray diffraction studies, the crystal structures and structural stabilities during the sodium insertion/deinsertion process are systematically investigated. The calculated average deintercalation voltages are in good agreement with the experimental result.

Using density-functional calculations, we show that electron or hole doped graphene can strongly change the mobility of adsorbed atoms H and O. Interestingly, charge doping affects the diffusion of H and O in the opposite way, namely, electron doping increases/reduces while hole doping reduces/increases the diffusion barrier of H/O, respectively. Specifically, on neutral graphene the diffusion barriers of O and H are 0.74 and 1.01 eV, which are, upon a hole doping of $+5.9\times10^{13}$ cm$^{-2}$, 0.90 and 0.77 eV, and upon an electron doping of $-5.9\times10^{13}$ cm$^{-2}$, 0.38 and 1.36 eV, respectively. This means, within the harmonic transition state theory, at room temperature, the diffusion rate of O can be decreased or increased by 470 or 2.2$\times 10^7$ times, and that of H can be increased or decreased by $10^5$ or $7\times 10^7$ times, by that hole or electron doping level. The difference between the H and O cases is interpreted in terms of the difference in geometric and bonding changes upon charge doping.

We consider an important class of self-assembly problems and using the formalism of stochastic thermodynamics, we derive a set of design principles for growing controlled assemblies far from equilibrium. The design principles constrain the set of structures that can be obtained under non-equilibrium conditions. Our central result provides intuition for how equilibrium self-assembly landscapes are modified under finite non-equilibrium drive.