Nonlocal Corrections Research Articles

Numerical surface-corrected nonlocal electrodynamic model for nanophotonic structures

Recent work has shown the significance of a nonlocal dielectric response and surface correction for nanometer-length-scale plasmonic structures. In this paper, we propose a new surface hydrodynamic model which incorporates such nonlocality and surface correction. Our approach, which is based on the hydrodynamic model, uses a numerical approach based on full-wave numerical computation and thus enables calculation of surface plasmon polariton (SPP) fields. The model also introduces a discontinuity in the normal component of the electric displacement at the interface by taking into account the change in the electron distribution at the interface. The method makes use of the Feibelman d parameter approach for the surface correction by equating the corrected Fresnel reflection of a p-polarized incident field across a planar interface. To demonstrate our method, we first examine numerical calculation of SPP propagation at a single interface structure; this work is then followed by a demonstration for a set of more complex thin-film structures. The latter demonstrates that our method is suitable for use in numerical modeling of complex nanophotonic structures.

The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual

We give an exposition of the SYK model with several new results. A non-local correction to the Schwarzian effective action is found. The same action is obtained by integrating out the bulk degrees of freedom in a certain variant of dilaton gravity. We also discuss general properties of out-of-time-order correlators.

DEMNUni: massive neutrinos and the bispectrum of large scale structures

The main effect of massive neutrinos on the large-scale structure consists in a few percent suppression of matter perturbations on all scales below their free-streaming scale. Such effect is of particular importance as it allows to constraint the value of the sum of neutrino masses from measurements of the galaxy power spectrum. In this work, we present the first measurements of the next higher-order correlation function, the bispectrum, from N-body simulations that include massive neutrinos as particles. This is the simplest statistics characterising the non-Gaussian properties of the matter and dark matter halos distributions. We investigate, in the first place, the suppression due to massive neutrinos on the matter bispectrum, comparing our measurements with the simplest perturbation theory predictions, finding the approximation of neutrinos contributing at quadratic order in perturbation theory to provide a good fit to the measurements in the simulations. On the other hand, as expected, a linear approximation for neutrino perturbations would lead to \U0001d4aa(fν) errors on the total matter bispectrum at large scales. We then attempt an extension of previous results on the universality of linear halo bias in neutrino cosmologies, to non-linear and non-local corrections finding consistent results with the power spectrum analysis.

Charge Separation in Donor–C60 Complexes with Real-Time Green Functions: The Importance of Nonlocal Correlations

We use the nonequilibrium Green function (NEGF) method to perform real-time simulations of the ultrafast electron dynamics of photoexcited donor-C60 complexes modeled by a Pariser-Parr-Pople Hamiltonian. The NEGF results are compared to mean-field Hartree-Fock (HF) calculations to disentangle the role of correlations. Initial benchmarking against numerically highly accurate time-dependent density matrix renormalization group calculations verifies the accuracy of NEGF. We then find that charge-transfer (CT) excitons partially decay into charge separated (CS) states if dynamical nonlocal correlation corrections are included. This CS process occurs in ∼10 fs after photoexcitation. In contrast, the probability of exciton recombination is almost 100% in HF simulations. These results are largely unaffected by nuclear vibrations; the latter become however essential whenever level misalignment hinders the CT process. The robust nature of our findings indicates that ultrafast CS driven by correlation-induced decoherence may occur in many organic nanoscale systems, but it will only be correctly predicted by theoretical treatments that include time-nonlocal correlations.

On the local frame in nonlinear higher-spin equations

Properties of the resolution operator dloc∗ in higher-spin equations, that leads to local current interactions at the cubic order and minimally nonlocal higher-order corrections, are formulated in terms of the condition on the class of master fields of higher-spin theory that restricts both the dependence on the spinor Y , Z variables and on the contractions of indices between the constituent fields in bilinear terms. The Green function in the sector of zero-forms is found for the case of constituent fields carrying helicities of opposite signs. It is shown that the local resolution dloc∗ differs from the conventional De Rham resolution dZ∗ by a non-local shift.

Hybrid density functional study of bandgaps for 27 new proposed half-Heusler semiconductors

Recently, 27 new half-Heusler compounds XYZ (X = Co, Rh, Fe, Ru, Ni; Y = Sc, Ti, V; Z = P, As, Sb, Si, Ge, Sn, Al, Ga, In) with 18 valence electrons are proposed and their bandgaps span a wide range of 0.10–1.39 eV, which have a great potential of applications in varied areas. Note that the bandgaps are predicted on the gradient-corrected Perdew-Burke-Ernzerhof functional, which underestimates the magnitude of bandgap. To obtain the accurate bandgaps, we recalculate them based on the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional. Our results show that the nonlocal correction from the HSE06 functional mainly acts on the two lowest conduction bands. The variation in energy separation between these two bands dominates the relative increment of bandgap. More importantly, the band ordering is distinguished in the presence of HSE06 functional, where the dz2 orbital exhibits. When the lattice constant varies, such a band ordering can be inverted, similar to the case of topological insulators. In addition, we find an abnormal behavior of the bandgap related to the Pauling electronegativity difference between the X- and Z-sites, which arises from the delocalization of charge on the Y-site. We expect that our work can provide guidance to the study of bandgap based on the hybrid density functional theory in the half-Heusler semiconductors.

Analogies for simply supported nonlocal Kirchhoff plates of polygonal planform

In the present paper, we consider nonlocal linear elastic Kirchhoff plates, where we restrict to thin, isotropic, and homogeneous plates under the action of static transverse forces, utilizing the differential equation form of the Eringen nonlocal continuum theory. For the case of simply supported plates of polygonal planform, we derive analogies between the solutions of the nonlocal Kirchhoff theory and its local counterpart. First, we extend the Marcus decomposition method for local Kirchhoff plates, where we show that, analogous to the local case considered by Marcus, the moment sum and the nonlocal deflection are both governed by Poisson boundary value problems, which correspond to auxiliary (local) membrane problems. In the present context, it eventually follows that there is a nonvanishing term responsible for a correction of the deflection due to the nonlocal effect, while the moments and shear forces of the local and the nonlocal plate coincide. The nonlocal correction of the deflection turns out to be governed by a membrane-type boundary value problem again. From this fact, it follows immediately that the correction for the deflection due to the nonlocal effect can be derived alternatively from both the local deflection and the local moment sum, which represents a substantial simplification of the nonlocal computations. For the sake of demonstration, we consider examples with closed form solutions. We first consider (as limiting case) infinite plates under the action of single forces, where the singular behavior of Green’s function of the nonlocal Kirchhoff theory can be clarified. Then we discuss the bending of nonlocal plate strips for comparison sake, as well as equilateral triangular plates. To our best knowledge, no results for bending of nonlocal triangular plates have been presented in the literature so far. The present paper has been strongly influenced by a former contribution on analogies between simply supported polygonal Kirchhoff plates rigid in shear and shear-deformable plate solutions. This paper was co-authored together with our teacher, the late Professor Franz Ziegler, to whom we dedicate the present paper. In light of this latter contribution, and extending an idea promoted by Professor Franz Ziegler and his co-workers in the framework of various other fields, we finally show in the Appendix that the deflections of simply supported nonlocal Kirchhoff plates can be considered as deflections of a local “background” Kirchhoff plate under the action of additional fictitious eigenstrain loadings, such as thermal moments.

Analytic approximation for the primordial spectra of single scalar potential models and its use in their reconstruction

We give final shape to a recent formalism for deriving the functional forms of the primordial power spectra of single-scalar potential models and theories which are related to them by conformal transformation. An excellent analytic approximation is derived for the nonlocal correction factors which are crucial to capture the "ringing" that can result from features in the potential. We also present the full algorithm for using our representation, including the nonlocal factors, to reconstruct the inflationary geometry from the power spectra.

OptPBE-vdW density functional theory study of liquid water and pressure-induced structural evolution in ice Ih

The accuracy of several local and non-local van der Waals (vdW) corrected exchange correlation functionals on the description of the effect of pressure on ice has been investigated. In a preliminary survey, the non-local vdW correction used in conjunction with the optPBE functional was shown to provide the best overall agreement on the structural parameters of ice Ih with experiments. More importantly, this combination reproduced correctly the recently observed crystal → crystal transformation in ice Ih at 80 K prior to amorphisation. The predicted transition pressure of 1.9 GPa is somewhat higher, showing that the current generation of vdW functionals are still not sufficiently accurate for the ice system. The existence of an intermediate crystalline state with a shear-hexagonal structure confirms the earlier prediction that the collapse of crystalline structure under compression originates from the softening of phonon modes in ice Ih’s basal plane.

Multitier self-consistent GW+EDMFT

We discuss a parameter-free and computationally efficient ab initio simulation approach for moderately and strongly correlated materials, the multitier self-consistent $GW$+EDMFT method. This scheme treats different degrees of freedom, such as high-energy and low-energy bands, or local and nonlocal interactions, within appropriate levels of approximation, and provides a fully self-consistent description of correlation and screening effects in the solid. The ab initio input is provided by a one-shot $G^0W^0$ calculation, while the strong-correlation effects originating from narrow bands near the Fermi level are captured by a combined $GW$ plus extended dynamical mean-field (EDMFT) treatment. We present the formalism and technical details of our implementation and discuss some general properties of the effective EDMFT impurity action. In particular, we show that the retarded impurity interactions can have non-causal features, while the physical observables, such as the screened interactions of the lattice system, remain causal. We then turn to stretched sodium as a model system to explore the performance of the multitier self-consistent $GW$+EDMFT method in situations with different degrees of correlation. While the results for the physical lattice spacing $a_0$ show that the scheme is not very accurate for electron-gas like systems, because nonlocal corrections beyond $GW$ are important, it does provide physically correct results in the intermediate correlation regime, and a Mott transition around a lattice spacing of $1.5a_0$. Remarkably, even though the Wannier functions in the stretched compound are less localized, and hence the bare interaction parameters are reduced, the self-consistently computed impurity interactions show the physically expected trend of an increasing interaction strength with increasing lattice spacing.

Robustness of the Rabi Splitting under Nonlocal Corrections in Plexcitonics

We explore theoretically how nonlocal corrections in the description of the metal affect the strong coupling between excitons and plasmons in typical examples where nonlocal effects are anticipated to be strong, namely small metallic nanoparticles, thin metallic nanoshells or dimers with narrow separations, either coated with or encapsulating an excitonic layer. Through detailed simulations based on the generalised nonlocal optical response theory, which simultaneously accounts both for modal shifts due to screening and for surface-enhanced Landau damping, we show that, contrary to expectations, the influence of nonlocality is rather limited, as in most occasions the width of the Rabi splitting remains largely unaffected and the two hybrid modes are well distinguishable. We discuss how this behaviour can be understood in view of the popular coupled-harmonic-oscillator model, while we also provide analytic solutions based on Mie theory to describe the hybrid modes in the case of matryoshka-like single nanoparticles. Our analysis provides an answer to a so far open question, that of the influence of nonlocality on strong coupling, and is expected to facilitate the design and study of plexcitonic architectures with ultrafine geometrical details.

Terahertz magnetoplasmon-polaritons with nonlocal corrections for lossy two dimensional electron gas in GaN-based heterostructures

The high electron concentration in GaN-based heterostructures necessitate the consideration of nonlocal corrections in the magnetoconductivity for the study of magnetoplasmon-polaritons (MPPs) in the lossy two dimensional electron gas system with grating couplers. With the complete set of Maxwell equations, the complex dispersion frequency and absorption spectrum are calculated numerically at different magnetic field (Bmax = 10 T) and plasmon wavevectors (kmax = 5 × 107 m−1). Taking the AlGaN/GaN structure as a representative case, we observe the cyclotron resonance and its high order harmonics, as well as the MPP modes. The effective aspect ratio of the grating is determined according to the absorption spectrum. Effects of the nonlocal corrections on the dispersion frequency and absorption spectrum are analyzed in detail. The contributions of LO phonons, electron collisions, THz wave polarizations and retardations are also discussed.

Validation of the MIPAS CO2 volume mixing ratio in the mesosphere and lower thermosphere and comparison with WACCM simulations

AbstractWe present the validation of Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) CO2 daytime concentration in the mesosphere and lower thermosphere by comparing with Atmospheric Chemistry Experiment (ACE) Fourier transform spectrometer and Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) data. MIPAS shows a very good agreement with ACE below 100 km with differences of ∼5%. Above 100 km, MIPAS CO2 is generally lower than ACE with differences growing from ∼5% at 100 km to 20–40% near 110–120 km. Part of this disagreement can be explained by the lack of a nonlocal thermodynamic equilibrium correction in ACE. MIPAS also agrees very well (∼5%) with SABER below 100 km. At 90–105 km, MIPAS is generally smaller than SABER by 10–30% in the polar summers. At 100–120 km, MIPAS and SABER CO2 agree within ∼10% during equinox but, for solstice, MIPAS is larger by 10–25%, except near the polar summer. Whole Atmosphere Community Climate Model (WACCM) CO2 shows the major MIPAS features. At 75–100 km, the agreement is very good (∼5%), with maximum differences of ∼10%. At 95–115 km MIPAS CO2 is larger than WACCM by 20–30% in the winter hemisphere but smaller (20–40%) in the summer. Above 95–100 km WACCM generally overestimates MIPAS CO2 by about 20–80% except in the polar summer where underestimates it by 20–40%. MIPAS CO2 favors a large eddy diffusion below 100 km and suggests that the meridional circulation of the lower thermosphere is stronger than in WACCM. The three instruments and WACCM show a clear increase of CO2 with time, more markedly at 90–100 km.

How nonlocal damping reduces plasmon-enhanced fluorescence in ultranarrow gaps

The nonclassical modification of plasmon-assisted fluorescence enhancement is theoretically explored by placing two-level dipole emitters at the narrow gaps encountered in canonical plasmonic architectures, namely dimers and trimers of different metallic nanoparticles. Through detailed simulations, in comparison with appropriate analytical modelling, it is shown that within classical electrodynamics, and for the reduced separations explored here, fluorescence enhancement factors of the order of $10^{5}$ can be achieved, with a divergent behaviour as the particle touching regime is approached. This remarkable prediction is mainly governed by the dramatic increase in excitation rate triggered by the corresponding field enhancement inside the gaps. Nevertheless, once nonclassical corrections are included, the amplification factors decrease by up to two orders of magnitude and a saturation regime for narrower gaps is reached. These nonclassical limitations are demonstrated by simulations based on the generalised nonlocal optical response theory, which accounts in an efficient way not only for nonlocal screening, but also for the enhanced Landau damping near the metal surface. A simple strategy to introduce nonlocal corrections to the analytic solutions is also proposed. It is therefore shown that the nonlocal optical response of the metal imposes more realistic, finite upper bounds to the enhancement feasible with ultrasmall plasmonic cavities, thus providing a theoretical description closer to state of the art experiments.

Theoretical research on the H2 generation mechanism on Pt6, Pt5Sn5 and Pt3Sn6 clusters by density functional theory

In this paper, the mechanisms of H2 evolution on Pt6, Pt5Sn5, and Pt3Sn6 clusters were respectively investigated by the B3LYP method of density functional theory (DFT). The B3LYP functional with non-local dispersion corrections (B3LYP-D3) method were performed to investigate the adsorption of H and H+ on clusters. The calculation results indicated that the adsorption energy of H on Pt reduced due to the interaction of Sn and Pt, which promoted H desorption from Pt to form H2. Meanwhile, Sn atom of Pt5Sn5 and Pt3Sn6 clusters had strong interaction with H+ due to the existence of Pt, which was benefit for the reduction of H+ on Sn atom. As a consequence, Pt5Sn5 and Pt3Sn6 showed lower potential barrier and higher activities than Pt for H2 evolution. The potential barriers of H2 formation over Pt3Sn6 clusters was only 11.1% of that over Pt cluster.

Local Pauli stabilizers of symmetric hypergraph states

Hypergraph states of many quantum bits share the rich interplay between simple combinatorial description and nontrivial entanglement properties enjoyed by the graph states that they generalize. In this paper, we consider hypergraph states that are also permutationally invariant. We characterize the states in this class that have nontrivial local Pauli stabilizers and give applications to nonlocality and error correction.

Gauging the performance of some density functionals including dispersion and nonlocal corrections for relative energies of water 20-mers

Currently, development of density functional theory approximations and their benchmarking for accurately modeling different types of molecular interactions become a very active field of research. In this report, performance of the dispersion (D3) and nonlocal (NL) corrected density functionals has been compared with generalized energy-based fragmentation approach at the complete basis set limit for predicting the relative energies of 10 low-energy isomers of water nanoclusters (H2O)20 as an illustrative example of hydrogen bonded systems. Considering a variety of exchange-correlation density functionals in combination with D3 and NL corrections we find that the D3 based approximations outperform the functionals incorporating NL correction. It is also shown that the LC-ωPBE-D3 and rPW86PBE-NL functionals have the best trend from the viewpoint of the order of stabilities in water nanoclusters under study.

Quantum corrections to Schwarzschild black hole

Using effective field theory techniques, we compute quantum corrections to spherically symmetric solutions of Einstein’s gravity and focus in particular on the Schwarzschild black hole. Quantum modifications are covariantly encoded in a non-local effective action. We work to quadratic order in curvatures simultaneously taking local and non-local corrections into account. Looking for solutions perturbatively close to that of classical general relativity, we find that an eternal Schwarzschild black hole remains a solution and receives no quantum corrections up to this order in the curvature expansion. In contrast, the field of a massive star receives corrections which are fully determined by the effective field theory.

Photospheric carbon and oxygen abundances of F–G type stars in the Pleiades cluster*

Abstract In order to investigate the carbon-to-oxygen ratio of the young open cluster M 45 (Pleiades), the C and O abundances of 32 selected F–G type dwarfs (in the effective temperature range of Teff ∼ 5800–7600 K and projected rotational velocity range of vesin i ∼ 10–110 km s−1) belonging to this cluster were determined by applying the synthetic spectrum-fitting technique to C i 5380 and O i 6156–8 lines. The non-local thermodynamical equilibrium corrections for these C i and O i lines were found to be practically negligible (less than a few hundredths dex).The resulting C and O abundances (along with the Fe abundance) turned out nearly uniform without any systematic dependence upon Teff or vesin i. We found, however, in spite of almost solar Fe abundance ([Fe/H] ∼ 0), carbon turned out to be slightly subsolar ([C/H] ∼ −0.1) while that of oxygen was slightly supersolar ([O/H] ∼ +0.1). This leads to a conclusion that the [C/O] ratio was moderately subsolar (∼ −0.2) in the primordial gas from which these Pleiades stars were formed ∼ 120–130 Myr ago. Interestingly, similarly young B-type stars are reported to show just the same result ([C/O] ∼ −0.2), while rather aged (∼ 1–10 Gyr) field F–G stars of near-solar metallicity yield almost the solar value ([C/O] ∼ 0) on average. Such a difference in the C/O ratio between two star groups of distinctly different ages may be explained as a consequence of the orbit migration mechanism which Galactic stars may undergo over a long time.

Nanoscale magnetization of a single vortex in d-wave superconductors

A finite-size scaling of the nanoscale magnetization m on size averaging R of a single vortex in d-wave bulk superconductor is developed using quasiclassical Eilenberger equations. Nanoscaling is anchoring around the linear London approximation for bulk superconductors. Comparing the results with those obtained in local nonlinear approach demonstrated the importance of the nonlocal contribution. Temperature dependences of two-point correlation function χ(T,R1,R2)=m(T,R2)/m(0,R2)−m(T,R1)/m(0,R1) with R2 > R1 and one-point function χ(T, R1 → ∞, R2) are calculated. It is found that χ(T, R1, R2), R2 > R1, is a nonmonotonous function of temperature and changes sign at high temperatures. This nonmonotonous temperature dependence can be understood as a result of competition between various effects i) Volovik effect and nonlocal corrections to superconducting electron density dominating in low temperature range, and ii) current-induced suppression of the order parameter dominating at high temperatures. The introduced nonmagnetic disorder greatly suppresses the low temperature nonlocal and nonlinear effects, leaving the order parameter effects to prevail in the whole temperature range. Nonlocal pairing and tunneling effects are investigated at the superconductor - normal metal border by considering a d-wave superconducting dot (d-dot) inside a normal diffusive metal. These effects result in a suppression of the supercurrent in the vortex core and are essential in nanodots with relatively small sizes. At sizes larger than a temperature dependent characteristic length the nanoscale physics transforms into bulk solution.