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Many nonlocal models have adopted Euclidean balls as the nonlocal interaction neighborhoods. When solving them numerically, it is sometimes convenient to adopt polygonal approximations of such balls. A crucial question is, to what extent such approximations affect the nonlocal operators and the corresponding solutions. While recent works have analyzed this issue for a fixed horizon parameter, the question remains open in the case of a small or vanishing horizon parameter, which happens often in many practical applications and has significant impact on the reliability and robustness of nonlocal modeling and simulations. In this work, we are interested in addressing this issue and establishing the convergence of the nonlocal solutions associated with polygonally approximated interaction neighborhoods to the local limit of the original nonlocal solutions. Our finding reveals that the new nonlocal solution does not converge to the correct local limit when the number of sides of polygons is uniformly bounded. On the other hand, if the number of sides tends to infinity, the desired convergence can be established. These results may be used to guide future computational studies of nonlocal models.

Day-and-night radiative sky cooling has emerged as a potential alternative to conventional cooling technologies such as refrigeration-based air conditioning and evaporative wet cooling. Both radiative cooling and evaporative cooling can passively achieve sub-ambient cooling without consuming electricity. Although both cooling techniques are subject to impacts from various weather conditions, the extents of the impacts under the same conditions are not well understood. In this work, we experimentally and theoretically study the thermal performances of a passive radiative cooler and a passive evaporative cooler when exposed to a clear night sky. We show that evaporative cooling is better suited for high-temperature and low-humidity weather conditions, with the measured sub-ambient temperatures of the radiative and evaporative coolers being -13.5{\deg}C and -15.0{\deg}C, respectively, at a low relative humidity of 13% and a high ambient temperature of 26.0{\deg}C. On the other hand, radiative cooling is relatively more resilient than evaporative cooling under high-humidity and/or low-temperature weather conditions, with the measured sub-ambient temperatures of the coolers being -11.5{\deg}C and -10.5{\deg}C, respectively, at a slightly higher relative humidity of 32.0% and a slightly lower ambient temperature of 17.0{\deg}C. Depending on water availability and weather conditions, both evaporative cooling and radiative cooling can be adopted as mutually supplemental cooling technologies., Comment: 26 pages, 8 figures

The piecewise quadratic polynomial collocation is used to approximate the nonlocal model, which generally obtain the {\em nonsymmetric indefinite system} [Chen et al., IMA J. Numer. Anal., (2021)]. In this case, the discrete maximum principle is not satisfied, which might be trickier for the stability analysis of the high-order numerical schemes [D'Elia et al., Acta Numer., (2020); Leng et al., SIAM J. Numer. Anal., (2021)]. Here, we present the modified (shifted-symmetric) piecewise quadratic polynomial collocation for solving the linear nonlocal diffusion model, which has the {\em symmetric positive definite system} and satisfies the discrete maximum principle. Using Faulhaber's formula and Riemann zeta function, the perturbation error for symmetric positive definite system and nonsymmetric indefinite systems are given. Then the detailed proof of the convergence analysis for the nonlocal models with the general horizon parameter $\delta=\mathcal{O}\left(h^\beta\right)$, $\beta\geq0$ are provided. More concretely, the global error is $\mathcal{O}\left(h^{\min\left\{2,1+\beta\right\}}\right)$ if $\delta$ is not set as a grid point, but it shall recover $\mathcal{O}\left(h^{\max\left\{2,4-2\beta\right\}}\right)$ when $\delta$ is set as a grid point. We also prove that the shifted-symmetric scheme is asymptotically compatible, which has the global error $\mathcal{O}\left(h^{\min\left\{2,2\beta\right\}}\right)$ as $\delta,h\rightarrow 0$. The numerical experiments (including two-dimensional case) are performed to verify the convergence., Comment: 23 pages

Numerical solution of nonlocal constrained value problems with integrable kernels are considered. These nonlocal problems arise in nonlocal mechanics and nonlocal diffusion. The structure of the true solution to the problem is analyzed first. The analysis leads naturally to a new kind of discontinuous Galerkin method that efficiently solve the problem numerically. This method is shown to be asymptotically compatible. Moreover, it has optimal convergence rate for one dimensional case under very weak assumptions, and almost optimal convergence rate for two dimensional case under mild assumptions.

Following the emergence of many novel two-dimensional (2-D) materials beyond graphene, interest has grown in exploring implications for fundamental physics and practical applications, ranging from electronics, photonics, phononics, to thermal management and energy storage. In this Colloquium, we first summarize and compare the phonon properties, such as phonon dispersion and relaxation time, of pristine 2-D materials with single layer graphene to understand the role of crystal structure and dimension on thermal conductivity. We then compare the phonon properties, contrasting idealized 2-D crystals, realistic 2-D crystals, and 3-D crystals, and synthesizing this to develop a physical picture of how the sample size of 2-D materials affects their thermal conductivity. The effects of geometry, such as number of layers, and nanoribbon width, together with the presence of defects, mechanical strain, and substrate interactions, on the thermal properties of 2-D materials are discussed. Intercalation affects both the group velocities and phonon relaxation times of layered crystals and thus tunes the thermal conductivity along both the through-plane and basal-plane directions. We conclude with a discussion of the challenges in theoretical and experimental studies of thermal transport in 2-D materials. The rich and special phonon physics in 2-D materials make them promising candidates for exploring novel phenomena such as topological phonon effects and applications such as phononic quantum devices., Comment: This article has been accepted by Reviews of Modern Physics

Detecting coherent phonons pose different challenges compared to coherent photons due to the much stronger interaction between phonons and matter. This is especially true for high frequency heat carrying phonons, which are intrinsic lattice vibrations experiencing many decoherence events with the environment, and are thus generally assumed to be incoherent. Two photon interference techniques, especially coherent population trapping (CPT) and electromagnetically induced transparency (EIT), have led to extremely sensitive detection, spectroscopy and metrology. Here, we propose the use of two photon interference in a three level system to sense coherent phonons. Unlike prior works which have treated phonon coupling as damping, we account for coherent phonon coupling using a full quantum-mechanical treatment. We observe strong asymmetry in absorption spectrum in CPT and negative dispersion in EIT susceptibility in the presence of coherent phonon coupling which cannot be accounted for if only pure phonon damping is considered. Our proposal has application in sensing heat carrying coherent phonons effects and understanding coherent bosonic multi-pathway interference effects in three coupled oscillator systems.

Generating and detection coherent high-frequency heat-carrying phonons has been a great topic of interest in recent years. While there have been successful attempts in generating and observing coherent phonons, rigorous techniques to characterize and detect these phonon coherence in a crystalline material have been lagging compared to what has been achieved for photons. One main challenge is a lack of detailed understanding of how detection signals for phonons can be related to coherence. The quantum theory of photoelectric detection has greatly advanced the ability to characterize photon coherence in the last century and a similar theory for phonon detection is necessary. Here, we re-examine the optical sideband fluorescence technique that has been used detect high frequency phonons in materials with optically active defects. We apply the quantum theory of photodetection to the sideband technique and propose signatures in sideband photon-counting statistics and second-order correlation measurement of sideband signals that indicates the degree of phonon coherence. Our theory can be implemented in recently performed experiments to bridge the gap of determining phonon coherence to be on par with that of photons., Comment: 3 Figures

We propose a numerical strategy to generate the anisotropic meshes and select the appropriate stabilized parameters simultaneously for two dimensional convection-dominated convection-diffusion equations by stabilized continuous linear finite elements. Since the discretized error in a suitable norm can be bounded by the sum of interpolation error and its variants in different norms, we replace them by some terms which contain the Hessian matrix of the true solution, convective fields, and the geometric properties such as directed edges and the area of the triangle. Based on this observation, the shape, size and equidistribution requirements are used to derive the corresponding metric tensor and the stabilized parameters. It is easily found from our derivation that the optimal stabilized parameter is coupled with the optimal metric tensor on each element. Some numerical results are also provided to validate the stability and efficiency of the proposed numerical strategy., Comment: 24 pages, 4 figures

Piezoelectricity offers precise and robust conversion between electricity and mechanical force. Here we report the first experimental evidence of piezoelectricity in a single layer of molybdenum disulfide (MoS2) crystal as a result of inversion symmetry breaking of the atomic structure, with measured piezoelectric coefficient e11 = 2.9e-10 C/m. Through the angular dependence of electro-mechanical coupling, we uniquely determined the two-dimensional (2D) crystal orientation. We observed that only MoS2 membranes with odd number of layers exhibited piezoelectricity, in sharp contrast to the conventional materials. The piezoelectricity discovered in single molecular membrane promises scaling down of nano-electro-mechanical systems (NEMS) to single atomic unit cell - the ultimate material limit.

Transition metal dichalcogenide (TMDC) monolayer has recently emerged as an important two-dimensional semiconductor with promising potentials for electronic and optoelectronic devices. Unlike semi-metallic graphene, layered TMDC has a sizable band gap. More interestingly, when thinned down to a monolayer, TMDC transforms from an indirect bandgap to a direct bandgap semiconductor, exhibiting a number of intriguing optical phenomena such as valley selective circular dichroism, doping dependent charged excitons, and strong photocurrent responses. However, the fundamental mechanism underlying such a strong light-matter interaction is still under intensive investigation. The observed optical resonance was initially considered to be band-to-band transitions. In contrast, first-principle calculations predicted a much larger quasiparticle band gap size and an optical response that is dominated by excitonic effects. Here, we report experimental evidence of the exciton dominance mechanism by discovering a series of excitonic dark states in single-layer WS2 using two-photon excitation spectroscopy. In combination with GW-BSE theory, we find the excitons are Wannier excitons in nature but possess extraordinarily large binding energy (~0.7 eV), leading to a quasiparticle band gap of 2.7 eV. These strongly bound exciton states are observed stable even at room temperature. We reveal an exciton series in significant deviation from hydrogen models, with a novel inverse energy dependence on the orbital angular momentum. These excitonic energy levels are experimentally found robust against environmental perturbations. The discovery of excitonic dark states and exceptionally large binding energy not only sheds light on the importance of many-electron effects in this two-dimensional gapped system, but also holds exciting potentials for the device application of TMDC monolayers and their heterostructures.

Here we present a Brownian ratchet based on plasmonic interactions. By periodically turning on and off a laser beam that illuminates a periodic array of plasmonic nanostructures with broken spatial symmetry, the random thermal motion of a subwavelength dielectric bead is rectified into one direction. By means of the Molecular Dynamics technique we show a statistical directed drift in particle flow.

Heat flow control is essential for widespread applications of heating, cooling, energy conversion and utilization. Here we demonstrate the first observation of temperature-gated thermal rectification in vanadium dioxide beams, in which an environment temperature actively modulates asymmetric heat flow. In this three terminal device, there are two switchable states, which can be accessed by global heating: Rectifier state and Resistor state. In the Rectifier state, up to 28% thermal rectification is observed. In the Resistor state, the thermal rectification is significantly suppressed (below 4%). This temperature-gated rectifier can have substantial implications ranging from autonomous thermal management of micro/nanoscale devices to thermal energy conversion and storage.

Excitons in MoS2 dominate the absorption and emission properties of the two-dimensional system. Here, we study the microscopic origin of the electroluminescence from monolayer MoS2 fabricated on a heavily p-type doped silicon substrate. By comparing the photoluminescence and electroluminescence of a MoS2 diode, direct-exciton and bound-exciton related recombination processes can be identified. Auger recombination of the exciton-exciton annihilation of bound exciton emission is observed under a high electron-hole pair injection rate at room temperature. We expect the direct exciton-exciton annihilation lifetime to exceed the carrier lifetime, due to the absence of any noticeable direct exciton saturation. We believe that our method of electrical injection opens a new route to understand the microscopic nature of the exciton recombination and facilitate the control of valley and spin excitation in MoS2., Comment: 12 pages, 3 figures

Dynamic dipolar toroidal response is demonstrated by an optical plasmonic metamaterial composed of double disks. This response with a hotspot of localized E-field concentration is a well-behaved toroidal cavity mode that exhibits a large Purcell factor due to its deep-subwavelength mode volume. All-optical Hall effect (photovoltaic) due to this optical toroidal moment is demonstrated numerically, in mimicking the magnetoelectric effect in multiferroic systems. The result shows a promising avenue to explore various optical phenomena associated with this intriguing dynamic toroidal moment., Comment: 21 pages, 6 figures

We theoretically demonstrate coherent control over propagation of surface plasmon polaritons(SPP), at both telecommunication and visible wavelengths, on a metallic surface adjacent to quantum coherence (phaseonium) medium composed of three-level quantum emitters (semiconductor quantum dots, atoms, rare-earth ions, etc.) embedded in a dielectric host. The coherent drive allows us to provide sufficient gain for lossless SPP propagation and also lowers the pumping requirements. In case of lossy propagation, an order of magnitude enhancement in propagation length can be achieved. Optical control over SPP propagation dynamics via an external coherent drive holds promise for quantum control in the field of nanophotonics., Comment: 4 pages, 3 figures

This is a reply to the comment from Patrick Bruno (arXiv:1211.4792) on our paper (Phys. Rev. Lett. 109, 163001 (2012)).

We demonstrate that the toroidal dipolar response can be realized in the optical regime by designing a feasible nanostructured metamaterial, comprising asymmetric double-bar magnetic resonators assembled into a toroid-like configuration. It is confirmed numerically that an optical toroidal dipolar moment dominates over other moments. This response is characterized by a strong confinement of an E-field component at the toroid center, oriented perpendicular to the H-vortex plane. The resonance-enhanced optical toroidal response can provide an experimental avenue for various interesting optical phenomena associated with the elusive toroidal moment., Comment: 17 pages, 6 figures

The toroidal response is numerically investigated in a multifold double-ring metamaterials at the antibonding magnetic-dipole mode (i.e., antiparallel magnetic dipoles in one double-ring fold). This intriguing toroidal resonance in metamaterials is considered as a result of the magnetoelectric effect due to the broken balance of the electric near-field environment. We demonstrate that the toroidal dipole response in metamaterials can improve the quality factor of the resonance spectrum. In viewing of the design flexibility on the double-ring geometry, such toroidal metamaterials will offer advantages in application potentials of toroidal dipolar moment., Comment: 7 pages, 4 figures

We demonstrate both theoretically and experimentally nonparaxial Mathieu and Weber accelerating beams, generalizing the concept of previously found accelerating beams. We show that such beams bend into large angles along circular, elliptical or parabolic trajectories but still retain nondiffracting and self-healing capabilities. The circular nonparaxial accelerating beams can be considered as a special case of the Mathieu accelerating beams, while an Airy beam is only a special case of the Weber beams at the paraxial limit. Not only generalized nonparaxial accelerating beams open up many possibilities of beam engineering for applications, but the fundamental concept developed here can be applied to other linear wave systems in nature, ranging from electromagnetic and elastic waves to matter waves., Comment: Physical Review Letters (in press)

Open quantum systems consisting of coupled bound and continuum states have been studied in a variety of physical systems, particularly within the scope of nuclear, atomic and molecular physics. In the open systems, the effects of the continuum decay channels are accounted for by indirect non-Hermitian couplings among the quasi-bound states. Here we explore anti-Hermitian coupling in a plasmonic system for spatially manipulating light on the nano-scale. We show that by utilizing the anti-Hermitian coupling, plasmonic antennas closely packed within only {\lambda}/15 separations can be individually excited from the far field, which are otherwise indistinguishable from each other., Comment: 13 pages, 3 figures

Spontaneous symmetry breaking can lead to the formation of time crystals, as well as spatial crystals. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped trapping potential with a static magnetic field. The ions spontaneously form a spatial ring crystal due to Coulomb repulsion. This ion crystal can rotate persistently at the lowest quantum energy state in magnetic fields with fractional fluxes. The persistent rotation of trapped ions produces the temporal order, leading to the formation of a space-time crystal. We show that these space-time crystals are robust for direct experimental observation. We also study the effects of finite temperatures on the persistent rotation. The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter., Comment: updated to the version published in PRL

The extraordinary electronic properties of graphene, such as its continuously gate-variable ambipolar field effect and the resulting steep change in resistivity, provided the main thrusts for the rapid advance of graphene electronics. The gate-controllable electronic properties of graphene provide a route to efficiently manipulate the interaction of low-energy photons with massless Dirac fermions, which has recently sparked keen interest in graphene plasmonics. However, the electro-optic tuning capability of unpatterned graphene alone is still not strong enough for practical optoelectronic applications due to its nonresonant Drude-like behaviour. Here, we experimentally demonstrate that substantial gate-induced persistent switching and linear modulation of terahertz waves can be achieved in a two-dimensional artificial material, referred to as a metamaterial, into which an atomically thin, gated two-dimensional graphene layer is integrated. The gate-controllable light-matter interaction in the graphene layer can be greatly enhanced by the strong resonances and the corresponding field enhancement in the metamaterial. Although the thickness of the embedded single-layer graphene is more than 'six' orders of magnitude smaller than the wavelength (< {\lambda}/1,000,000), the one-atom-thick layer, in conjunction with the metamaterial, can modulate both the amplitude of the transmitted wave by up to 90 per cent and its phase by more than 40 degrees at room temperature. More interestingly, the gate-controlled active graphene metamaterials show hysteretic behaviour in the transmission of terahertz waves, especially when fabricated with multilayer graphene, which is indicative of persistent photonic memory effects.

A uniform strategy to derive metric tensors in two spatial dimension for interpolation errors and their gradients in $L^p$ norm is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in corresponding metric space, with the metric tensor being computed based on a posteriori error estimates in different norms. Numerical results show that the corresponding convergence rates are always optimal., Comment: 19 pages, 24 figures

A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being computed based on a posteriori error estimates proposed in \cite{YinXie}. The new metric tensor explores more comprehensive information of anisotropy for the true solution than those existing ones. Numerical results show that this approach can be successfully applied to deal with poisson and steady convection-dominated problems. The superior accuracy and efficiency of the new metric tensor to others is illustrated on various numerical examples of complex two-dimensional simulations., Comment: 18 pages, 18 figures

We report an invisibility carpet cloak device, which is capable of making an object undetectable by visible light. The cloak is designed using quasi conformal mapping and is fabricated in a silicon nitride waveguide on a specially developed nano-porous silicon oxide substrate with a very low refractive index. The spatial index variation is realized by etching holes of various sizes in the nitride layer at deep subwavelength scale creating a local effective medium index. The fabricated device demonstrates wideband invisibility throughout the visible spectrum with low loss. This silicon nitride on low index substrate can also be a general scheme for implementation of transformation optical devices at visible frequency.

In this paper, we give a new type of a posteriori error estimators suitable for moving finite element methods under anisotropic meshes for general second-order elliptic problems. The computation of estimators is simple once corresponding Hessian matrix is recovered. Wonderful efficiency indices are shown in numerical experiments., Comment: 16 pages, 16 figures