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Gratings are widely used for coupling into and out of evanescent and propagating electromagnetic modes, which are otherwise not accessible due to their large in-plane wave vector. A precise description of the optical response requires the knowledge of the grating geometry. Here, we present an investigation of the optical properties of dielectric gratings of sub-micron periodicity fabricated on a multilayer structure, which supports Bloch surface waves, by means of spectroscopic ellipsometry. Taking into account non-idealities, such as the finite spectral bandwidth, in the modeling process is shown to be a necessity for an accurate description of the observed spectra. The grating geometry determined from the analysis of ellipsometry data agrees very well with atomic force microscopy scans. Thus, our ellipsometric model is corroborated. [ABSTRACT FROM AUTHOR]

The Zak phase serves as a reliable index for pinpointing topological phase transitions within one-dimensional chains, typically ascertained through numerical methods in complex situations. Nonetheless, in proximity to the transition threshold, the numerical Zak phase may become ambiguous. This ambiguity arises from the discrete nature of numerical approaches and the nonlinear relationship between the wave function's phase and the wave vector (k). In response, this paper presents an innovative method aimed at accurately determining the winding number, thereby facilitating the identification of topological phase transitions. Our approach hinges on analyzing the evolution of the phase difference between the projections of the Bloch wave function onto two distinct sublattices. We demonstrate the efficacy of this method through three illustrative examples: the Su–Schrieffer–Heeger model, a magnetic vortex chain, and a trimer lattice chain. The results indicate that our proposed numerical lagging-phase examination method achieves superior precision in identifying topological phase transitions, particularly at critical junctures, compared to the conventional numerical Zak phase approach. [ABSTRACT FROM AUTHOR]

A theoretical study of a one‐dimensional photonic crystal (1D‐PhC) [TiO2/MgF2]2/TiO2/GaAs terminated by a dielectric metasurface consisting of periodically arranged TiO2 nanospheres for biosensing is proposed. The p polarized incident beam and the prism couplingtechnique are employed to excite Bloch surface waves considering a low biomolecular concentration sensing medium with refractive index changing from 1.33 to 1.34 RIU. The optical properties of the metasurface layer are calculated within the effective medium approximation. The findings reveal that integrating TiO2 nanosphere metasurfaces as the upper layer of a photonic structure allows simultaneous control of biosensor sensitivity and the reflectance curve's full width at half maximum by judiciously tuning its optical properties, relying on the filling fraction (f) and the size (dns$d_{\text{ns}}$) of the TiO2 nanospheres. Moreover, The results show that the biosensor with the metasurface performs superior to the one without it. [ABSTRACT FROM AUTHOR]

Using Chern character, we construct a natural transformation from the local Hilbert functor to a functor of Artin rings defined from Hochschild homology. This enables us to realize (after slight modification) the infinitesimal Abel-Jacobi map as a morphism between tangent spaces of two functors of Artin rings and also enables us to reconstruct the semi-regularity map together with giving a different proof of a theorem of Bloch stating that the semi-regularity map annihilates certain obstructions to embedded deformations of a closed subvariety which is a locally complete intersection. [ABSTRACT FROM AUTHOR]

The g tensor, which determines the reaction of Kramers-degenerate states to an applied magnetic field, is of increasing importance in the current design of spin qubits. It is affected by details of heterostructure composition, disorder, and electric fields, but it inherits much of its structure from the effect of the spin-orbit interaction working at the crystal-lattice level. Here, we uncover interesting symmetry and topological features of g = gL + gS for important valence and conduction bands in silicon, germanium, and gallium arsenide. For all crystals with high (cubic) symmetry, we show that large departures from the nonrelativistic value g = 2 are guaranteed by symmetry. In particular, considering the spin part gS(k), we prove that the scalar function det(gS(k)) must go to zero on closed surfaces in the Brillouin zone, no matter how weak the spin-orbit coupling is. We also prove that for wave vectors k on these surfaces, the Bloch states junki have maximal spin-orbital entanglement. Using tight-binding calculations, we observe that the surfaces det(g(k)) = 0 exhibit many interesting topological features, exhibiting Lifshitz critical points as understood in Fermi-surface theory. [ABSTRACT FROM AUTHOR]

Multi-mode Glauber coherent states (MMGS) as well as Bloch states with zero quasi-momentum, which are a special case of generalized coherent states (GCS), are frequently used to describe condensed phases of bosonic many-body systems. The difference of two-point correlators of MMGS and GCS vanishes in the thermodynamic limit. Using the established expansion of MMGS in terms of GCS, we derive a Fourier-type relation between the (auto-)correlation functions of the two different time-evolved states. This relation reveals that the (auto-)correlation and thus the dynamical free-energy density for the two cases are still different, even in the thermodynamic limit, due to the lack of the U(1) symmetry of the MMGS. Analytic results for the deep lattice model of interacting bosons for increasing filling factors show multiple sharp structures in the dynamical free energy-density of increasing complexity. These are explained using the evolution of Husimi functions in phase space. [ABSTRACT FROM AUTHOR]

Film/substrate structures are often seen in nature and engineering and their characteristic mechanical behaviors facilitating widespread application prospects. Surface patterns of film/substrate structures significantly affect the propagation of elastic waves. This paper investigates elastic wave propagation in the thin film/substrate periodic structure with sinusoidal surface patterns through the uniaxial tension. Based on the Bloch wave theory and numerical simulation, diverse bandgaps are triggered and the overall frequency range of the bandgaps shifts upward with the increase of the tensile strain, which demonstrates that tensioning the bilayer is a reliable and robust way for manipulating bandgaps. Band properties and bandgap evolution by various geometric and material parameters are discussed systematically, including various surface sinusoidal amplitudes, thickness of the substrate and various density or modulus ratio. The underlying mechanism of the exciting results in reversal design and regulation of structural geometry is revealed and is explained by using the spring-mass model. This work can provide new thought and insight for controlling wave propagation and promoting potential applications of the film/substrate systems and devices. [ABSTRACT FROM AUTHOR]

In this paper we characterize some basic properties of composition operators on the spaces of harmonic Bloch functions. First we provide some equivalent conditions for boundedness and compactness of composition operators. In the sequel we investigate closed range composition operators. These results extends the similar results that were proven for composition operators on the Bloch spaces. [ABSTRACT FROM AUTHOR]

We present and discuss practical techniques for formulating effective models to describe the low-energy electronic properties of bilayer graphene systems. We show that such effective models are constructed from a collection of appropriate single-layer Bloch states of two graphene layers. In general, the obtained effective models allow the construction of a so-called moiré band structure. However, it is not the result of an irreducible representation of a translation symmetry group of the bilayer lattices except for the commensurate bilayer configurations. We also point out that the commensurate bilayer configurations are classified into three categories depending on the divisibility of the difference between two commensurate integer indices by 3. The electronic band structure of three lattice configurations, one for each category, is shown. Especially by combining with a real-space calculation, we validate the working ability of constructed effective models for generic bilayer graphene systems by showing that the effects of interlayer sliding are diminished by twisting. This result is consistent with the invariance of effective models under the interlayer sliding operation. [ABSTRACT FROM AUTHOR]

Topological band theory has conventionally been concerned with the topology of bands around a single gap. Only recently non-Abelian topologies that thrive on involving multiple gaps were studied, unveiling a new horizon in topological physics beyond the conventional paradigm. Here, we report on the first experimental realization of a topological Euler insulator phase with unique meronic characterization in an acoustic metamaterial. We demonstrate that this topological phase has several nontrivial features: First, the system cannot be described by conventional topological band theory, but has a nontrivial Euler class that captures the unconventional geometry of the Bloch bands in the Brillouin zone. Second, we uncover in theory and probe in experiments a meronic configuration of the bulk Bloch states for the first time. Third, using a detailed symmetry analysis, we show that the topological Euler insulator evolves from a non-Abelian topological semimetal phase via. the annihilation of Dirac points in pairs in one of the band gaps. With these nontrivial properties, we establish concretely an unconventional bulk-edge correspondence which is confirmed by directly measuring the edge states via. pump-probe techniques. Our work thus unveils a nontrivial topological Euler insulator phase with a unique meronic pattern and paves the way as a platform for non-Abelian topological phenomena. [ABSTRACT FROM AUTHOR]

We investigate magnon–magnon hybrid states using a non-Hermitian Hamiltonian and the concept of magnon hybridization. By comparing our model with micromagnetic simulations conducted on a synthetic antiferromagnet with strong magnon–magnon coupling, the two-level model reproduces not only the resonance frequencies and linewidths but also the phases and amplitudes of the magnon eigenmode. The coherent coupling between magnons results in both the anticrossing of the energy spectra and the mixing of the linewidths. Specially, it forms a two-level system and makes the eigenmode of the hybrid state as a linear combination of the pure acoustic and optic modes. After that, we map the magnon–magnon hybrid state, including the magnon state of exceptional point, onto a Bloch sphere, which enhances the ability to manipulate hybrid magnons for coherent information processing. [ABSTRACT FROM AUTHOR]

The localized nature of a flat band is understood by the existence of a compact localized eigenstate. However, the localization properties of a partially flat band, ubiquitous in surface modes of topological semimetals, have been unknown. We show that the partially flat band is characterized by a non-normalizable quasi-compact localized state (Q-CLS), which is compactly localized along several directions but extended in at least one direction. The partially flat band develops at momenta where normalizable Bloch wave functions can be obtained from a linear combination of the non-normalizable Q-CLSs. Outside this momentum region, a ghost flat band, unseen from the band structure, is introduced based on a counting argument. Then, we demonstrate that the Wannier function corresponding to the partially flat band exhibits an algebraic decay behavior. Namely, one can have the Wannier obstruction in a band with a vanishing Chern number if it is partially flat. Finally, we develop the construction scheme of a tight-binding model for a topological semimetal by designing a Q-CLS. Compact localized states constitute an auxiliary state representation for a flat-band lattice system with wave functions non-zero only in a finite portion of the lattice. Here, the authors show that in some flat-band systems, these states can be partially "hidden"; surprisingly, these ghost flat bands present an obstruction to be represented as maximally localized Wannier functions. [ABSTRACT FROM AUTHOR]

The development of vibration suppression systems with desired efficiency and low cost is one of the significant challenges in engineering. In this study, a parametric lattice model is considered to analyze the wave mitigation features in the metamaterial based on a tetra-chiral topology of the periodic cell equipped with internal resonators. Bloch wave theorem and finite element method are employed to explore the bandgap of the structure and its wave mitigation features. Since the unit cell geometry can be designed to open and shift bandgaps, particle swarm optimization algorithm is used to find the largest possible gap in the desired frequency range. The optimization method is programmed using MATLAB combined with an in-house finite element solver, considering the parameters' ranges to ensure geometric compatibility. In all studied cases, the optimized geometry leads to superior vibration suppression and larger complete bandgaps. [ABSTRACT FROM AUTHOR]

In this paper, a novel silicon nanoparticle-based sensor has been investigated. Bloch surface wave excitation in a one-dimensional photonic crystal using a silicon nanoparticle on the top defect layer is examined on various parameters. This paper compares the confinement of Bloch surface wave using with and without silicon nanoparticles. The confinement of surface waves is modified by varying the size of the silicon nanoparticle. The structural parameters are optimized for an 850 nm (nm) central wavelength. At the central wavelength of 850 nm, the confinement of surface waves gets modified by varying the size of the silicon nanoparticle. The proposed novel silicon nanoparticle-based sensor was investigated and its efficacy in terms of sensitivity, quality factor, and Figure of merit was evaluated. The sensitivity is demonstrated to be 148.88 Degree/Refractive index unit (RIU), with a quality factor of 10,146.83 nm and a figure of merit (FOM) of 1777.24 per Refractive index unit (RIU− 1) for sensors with a silicon nanoparticle-based multilayer structure. [ABSTRACT FROM AUTHOR]

Recent theoretical investigations have revealed unconventional transport mechanisms within high Brillouin zones of two-dimensional superlattices. Electrons can navigate along channels we call superwires, gently guided without brute force confinement. Such dynamical confinement is caused by weak superlattice deflections, markedly different from the static or energetic confinement observed in traditional wave guides or one-dimensional electron wires. The quantum properties of superwires give rise to elastic dynamical tunneling, linking disjoint regions of the corresponding classical phase space, and enabling the emergence of several parallel channels. This paper provides the underlying theory and mechanisms that facilitate dynamical tunneling assisted by chaos in periodic lattices. Moreover, we show that the mechanism of dynamical tunneling can be effectively conceptualized through the lens of a paraxial approximation. Our results further reveal that superwires predominantly exist within flat bands, emerging from eigenstates that represent linear combinations of conventional degenerate Bloch states. Finally, we quantify tunneling rates across various lattice configurations and demonstrate that tunneling can be suppressed in a controlled fashion, illustrating potential implications in future nanodevices. [ABSTRACT FROM AUTHOR]

Orbital current, defined as the orbital character of Bloch states in solids, can travel with larger coherence length through a broader range of materials than its spin counterpart, facilitating a robust, higher density and energy efficient information transmission. Hence, active control of orbital transport plays a pivotal role in the progress of the evolving field of quantum information technology. Unlike spin angular momentum, orbital angular momentum couples to phonon angular momentum efficiently via orbital-crystal momentum (L-k) coupling, allowing us to control orbital transport through crystal field potential mediated angular momentum transfer. Here, leveraging the orbital dependant efficient L-k coupling, we have experimentally demonstrated the active control of orbital current velocity in Ni/Pt heterostructure. We observe terahertz emission from Ni/Pt heterostructure via long-range ballistic orbital transport, as evidenced by the delay, and chirping in the emitted THz pulse correlating with increased Pt thickness. Additionally, we also have identified a critical energy density required to overcome collisions in orbital transport, enabling a swifter flow of orbital current. Femtosecond light driven active control of the ballistic orbital transport lays the foundation for the development of dynamic optorbitronics for transmitting information over extended distance. The authors observe THz emission from Ni/Pt heterostructure due to long-range ballistic orbital transport. The velocity of orbital current can be optically tuned by laser fluence, opening the avenue for future optorbitronic devices. [ABSTRACT FROM AUTHOR]

Nanomagnetism and spintronics are currently active areas of research, with one of the main goals being the creation of low-energy-consuming magnetic memories based on nanomagnet switching. These types of devices could also be implemented in neuromorphic computing by crafting artificial neurons (ANs) that emulate the characteristics of biological neurons through the implementation of neuron models such as the widely used leaky integrate-and-fire (LIF) with a refractory period. In this study, we have carried out numerical simulations of a 120 nm diameter, 250 nm length ferromagnetic nanowire (NW) with the aim of exploring the design of an artificial neuron based on the creation and destruction of a Bloch-point domain wall. To replicate signal integration, we applied pulsed trains of spin currents to the opposite faces of the ferromagnetic NW. These pulsed currents (previously studied only in the continuous form) are responsible for inducing transitions between the stable single vortex (SV) state and the metastable Bloch point domain wall (BP-DW) state. To ensure the system exhibits leak and refractory properties, the NW was placed in a homogeneous magnetic field of the order of mT in the axial direction. The suggested configuration fulfills the requirements and characteristics of a biological neuron, potentially leading to the future creation of artificial neural networks (ANNs) based on reversible changes in the topology of magnetic NWs. [ABSTRACT FROM AUTHOR]

We investigate the behavior of waves in a periodic medium containing small soft inclusions or cavities of arbitrary shape, such that the homogeneous Dirichlet conditions are satisfied at the boundary. The leading terms of Bloch waves, their dispersion relations, and low frequency cutoff are rigorously derived. Our approach reveals the existence of exceptional wave vectors for which Bloch waves are comprised of clusters of perturbed plane waves that propagate in different directions. We demonstrate that for these exceptional wave vectors, no Bloch waves propagate in any one specific direction. [ABSTRACT FROM AUTHOR]

Nonlinear optics has generated a wide range of applications in the fields of optical communications, biomedicine, and materials science, with nonlinear conversion efficiency serving as a vital metric for its progress. However, the weak nonlinear response of materials, high optical loss, and inhomogeneous distribution of the light field hamper the improvement of the conversion efficiency. We present a composite grating waveguide structure integrated into a Bragg reflector platform. This design achieves high Q in the spectral range by exploiting the unique properties exhibited by the bound states in the Bloch surface wave-enhanced continuum, and efficient second-harmonic generation by close-field amplification with the optical field tightly localized in a nonlinear material. By manipulating the symmetry of the grating, a precise tune over the near field within a designated wavelength range can be achieved. Specifically, we select a photonic crystal configuration supporting surface waves, employing TE polarization conditions and an asymmetry factor of −0.1 between the composite gratings. This configuration resonates at a fundamental wavelength of 783.5 nm, exhibiting an impressive Q-factor of 106. Notably, at an incident light intensity of 1.33 GW/cm2, we achieve a normalized electric field strength of up to 940 at the fundamental frequency and a second-harmonic conversion efficiency of up to 6 × 10−3, significantly amplifying the second-harmonic response. The proposed configuration in this investigation has the potential to be integrated into the field of nonlinear optics for sensing frequency conversion applications. [ABSTRACT FROM AUTHOR]

We study the coupling of a finite number of Bloch Surface Waves (BSWs) propagating in different directions at the surface of a dielectric multilayer. These surface waves arise from a set of diffraction orders associated to a grating on the bottom surface of the substrate that is illuminated by a normally incident beam. Simultaneous excitation of multiple BSWs is possible with a set of diffraction orders having the same radial spatial frequency. Using rigorous electromagnetic theory, we design gratings for simultaneous excitation of two, four and six BSWs propagating in directions separated by π, π/2 and π/3 azimuthal intervals, respectively. [ABSTRACT FROM AUTHOR]

A new method is proposed to predict the topological properties of 1D periodic structures in wave physics, including quantum mechanics. From Bloch waves, a unique complex valued function is constructed, exhibiting poles and zeros. The sequence of poles and zeros of this function is a topological invariant that can be linked to the Berry–Zak phase. Since the characterization of the topological properties is done in the complex plane, it can easily be extended to the case of non‐Hermitian systems. The sequence of poles and zeros allows to predict topological phase transitions. [ABSTRACT FROM AUTHOR]

Purpose: To explore efficient encoding schemes for quantitative magnetization transfer (qMT) imaging with few constraints on model parameters. Theory and Methods: We combine two recently proposed models in a Bloch‐McConnell equation: the dynamics of the free spin pool are confined to the hybrid state, and the dynamics of the semi‐solid spin pool are described by the generalized Bloch model. We numerically optimize the flip angles and durations of a train of radio frequency pulses to enhance the encoding of three qMT parameters while accounting for all eight parameters of the two‐pool model. We sparsely sample each time frame along this spin dynamics with a three‐dimensional radial koosh‐ball trajectory, reconstruct the data with subspace modeling, and fit the qMT model with a neural network for computational efficiency. Results: We extracted qMT parameter maps of the whole brain with an effective resolution of 1.24 mm from a 12.6‐min scan. In lesions of multiple sclerosis subjects, we observe a decreased size of the semi‐solid spin pool and longer relaxation times, consistent with previous reports. Conclusion: The encoding power of the hybrid state, combined with regularized image reconstruction, and the accuracy of the generalized Bloch model provide an excellent basis for efficient quantitative magnetization transfer imaging with few constraints on model parameters. [ABSTRACT FROM AUTHOR]

Background: The characteristics of surface waves (SWs) in periodic structures have been given serious attention in recent years. Higher requirement for computers and time consumption must be arose for the calculations of the dispersion relations of SWs. Method: In this paper, a new reduced-order model technique called surface wave Bloch mode synthesis (SW-BMS) method is proposed to accelerate the computations of SWs in elastic periodic structures. In the SW-BMS method, the unit cell is divided into interior and interface degrees of freedoms, which are described by fixed interface modes and constraint modes, respectively, and subsequent reduction of the interior and interface via truncated mode's expansion. Taking the energy criterion of SW's identification into account, the combination of these modes forms a reduced model for the eigenvalue problem of a periodic structure. Results: The performance of the SW-BMS method is validated by three different scenarios, which are the unit cell of a periodic in-filled trench representing a 1D periodic structure, a periodic pile barrier in homogenous soil to describe a 2D periodic structure and a usually occurs in practical engineering structure of periodic pile barrier in layered soil. The results show that the dispersion relations can be exactly predicted and the time consumption is significantly reduced using the present SW-BMS method. Conclusion: The SW-BMS method can greatly reduce the time consumption in calculating the SW's dispersion relations of a periodic structure without any loss of modes and accuracy, which removes a very big obstacle towards practical applications. [ABSTRACT FROM AUTHOR]

The resonant excitation of Bloch Surface Waves (BSWs) in dielectric one-dimensional photonic crystals is becoming a realistic photonic solution for surface integration in many domains, from spectroscopy to local field management. Bringing BSWs to ultrafast and nonlinear regimes requires a deep knowledge of the effects that the photonic crystal dispersion and the resonant surface wave excitation have on the ultrashort laser pulses. We report on the experimental evidence of spectral and temporal modifications of the radiation leaving a planar one-dimensional photonic crystal after coupling to BSWs. In such a resonant condition, a characteristic long temporal tail is observed in the outgoing pulses. Observations are performed by employing both frequency-resolved optical gating and field cross-correlation techniques. [ABSTRACT FROM AUTHOR]

Herein, we realize quasi-bound states in the continuum (quasi-BICs) in a compound grating waveguide structure with a complex lattice. The first layer of the structure is a grating layer composed of two dielectric ridges with different heights and the same width, while the second layer of the structure is a dielectric waveguide layer supporting the guided mode. As the height difference in two dielectric ridges changes from a non-zero value to zero, the lattice of the structure turns from a complex lattice with the period Λ to a simple lattice with the half of the previous period Λ ′ = Λ / 2. Therefore, the previous excitable odd-order resonant guided modes cannot be excited and become BICs. Assisted by the ultra-high Q factor of the quasi-BIC, we achieve high-performance refractive-index sensing at near-infrared wavelengths. Under the proper design, the optimum sensitivity and figure of merit (FoM) reach 676.8 nm/RIU and 9543 RIU−1, respectively. Compared with the reported refractive-index sensors based on surface plasmon polaritons, localized surface plasmon resonances, and Bloch surface waves, the optimum sensitivity achieved in this work reaches the same order of magnitude, while the optimum FoM achieved in this work is one or two orders of magnitude higher. Our work reveals that quasi-BICs would become a powerful competitive mechanism to achieve high-performance refractive-index sensing. [ABSTRACT FROM AUTHOR]

Three‐dimensional electron diffraction (3D‐ED) is a powerful technique for crystallographic characterization of nanometre‐sized crystals that are too small for X‐ray diffraction. For accurate crystal structure refinement, however, it is important that the Bragg diffracted intensities are treated dynamically. Bloch wave simulations are often used in 3D‐ED, but can be computationally expensive for large unit cell crystals due to the large number of diffracted beams. Proposed here is an alternative method, the 'scattering cluster algorithm' (SCA), that replaces the eigen‐decomposition operation in Bloch waves with a simpler matrix multiplication. The underlying principle of SCA is that the intensity of a given Bragg reflection is largely determined by intensity transfer (i.e. 'scattering') from a cluster of neighbouring diffracted beams. However, the penalty for using matrix multiplication is that the sample must be divided into a series of thin slices and the diffracted beams calculated iteratively, similar to the multislice approach. Therefore, SCA is more suitable for thin specimens. The accuracy and speed of SCA are demonstrated on tri‐isopropyl silane (TIPS) pentacene and rubrene, two exemplar organic materials with large unit cells. [ABSTRACT FROM AUTHOR]

The strong interaction of high‐energy electrons with a crystal results in both dynamical elastic scattering and inelastic events, particularly phonon and plasmon excitation, which have relatively large cross sections. For accurate crystal structure refinement it is therefore important to uncover the impact of inelastic scattering on the Bragg beam intensities. Here a combined Bloch wave–Monte Carlo method is used to simulate phonon and plasmon scattering in crystals. The simulated thermal and plasmon diffuse scattering are consistent with experimental results. The simulations also confirm the empirical observation of a weaker unscattered beam intensity with increasing energy loss in the low‐loss regime, while the Bragg‐diffracted beam intensities do not change significantly. The beam intensities include the diffuse scattered background and have been normalized to adjust for the inelastic scattering cross section. It is speculated that the random azimuthal scattering angle during inelastic events transfers part of the unscattered beam intensity to the inner Bragg reflections. Inelastic scattering should not significantly influence crystal structure refinement, provided there are no artefacts from any background subtraction, since the relative intensity of the diffracted beams (which includes the diffuse scattering) remains approximately constant in the low energy loss regime. [ABSTRACT FROM AUTHOR]

Block-lattice materials featuring periodic planar running-bond tessellation of regular rigid blocks and linear elastic homogeneous isotropic interfaces are considered. The governing equations of the discrete masonry-like Lagrangian model are properly manipulated via the novel enhanced continualization scheme, in such a way as to obtain equivalent integral type non-local continua, whose band structure turns out to be coincident with that of the corresponding discrete models. The formal Taylor series expansion of the integral kernels allows deriving homogeneous generalized micropolar higher-order continuum models, characterized by non-local constitutive and inertial terms. The enhanced continualization exhibits thermodynamic consistency in the definition of the overall non-local constitutive tensors, as well as qualitative agreement and quantitative convergent matching of the complex frequency band structure in the regime of both homogeneous and non-homogeneous Bloch waves. The theoretical findings are effectively validated by studying the dispersion relations and the spatial attenuation properties, as referred to realistic representative cases of masonry-like block-lattice micro-structures. [ABSTRACT FROM AUTHOR]

When studying the geometry of quantum states, it is acknowledged that mixed states can be distinguished by infinitely many metrics. Unfortunately, this freedom causes metric-dependent interpretations of physically significant geometric quantities such as the complexity and volume of quantum states. In this paper, we present an insightful discussion on the differences between the Bures and the Sjöqvist metrics inside a Bloch sphere. First, we begin with a formal comparative analysis between the two metrics by critically discussing three alternative interpretations for each metric. Second, we explicitly illustrate the distinct behaviors of the geodesic paths on each one of the two metric manifolds. Third, we compare the finite distances between an initial state and the final mixed state when calculated with the two metrics. Interestingly, in analogy with what happens when studying the topological aspects of real Euclidean spaces equipped with distinct metric functions (for instance, the usual Euclidean metric and the taxicab metric), we observe that the relative ranking based on the concept of a finite distance between mixed quantum states is not preserved when comparing distances determined with the Bures and the Sjöqvist metrics. Finally, we conclude with a brief discussion on the consequences of this violation of a metric-based relative ranking on the concept of the complexity and volume of mixed quantum states. [ABSTRACT FROM AUTHOR]

Trapping and movement of microparticles using the near field of waveguide modes enables the realization of stable and compact integrated optical platforms for manipulating, sorting, and studying single microobjects. In this work, the possibility of optical manipulation via Bloch surface waves propagating in polymer waveguides on the surface of a one-dimensional photonic crystal and localizing light at the waveguide surface is studied. Numerical simulation of optical forces acting on a spherical particle from the fundamental waveguide mode of the Bloch surface wave is performed. Using two-photon laser lithography, SU-8 polymer waveguides are fabricated on the surface of a one-dimensional photonic crystal. The movement of a polystyrene microparticle along the waveguide when the Bloch surface wave is excited in it is experimentally demonstrated. [ABSTRACT FROM AUTHOR]

Many material properties are governed by dislocations and their interactions. The reconstruction of the three-dimensional structure of a dislocation network so far is mainly achieved by tomographic tilt series with high angular ranges, which is experimentally challenging and additionally puts constraints on possible specimen geometries. Here, we show a way to reveal the three dimensional location of dislocations and simultaneously classify their type from single 4D scanning transmission electron microscopy measurements. The dislocation's strain field causes inter-band scattering between the electron's Bloch waves within the crystal. This scattering in turn results in characteristic interference patterns with sufficient information to identify the dislocations type and depth in beam direction by comparison with multi-beam calculations. We expect the presented measurement principle will lead to fully automated methods for reconstruction of the three dimensional strain fields from such measurements with a wide range of applications in material and physical sciences and engineering. Many material properties are governed by the internal dislocation network within the material. Here, the authors describe a method to determine the three dimensional position and type of dislocations from a measurement along only a single direction within a scanning transmission electron microscope. [ABSTRACT FROM AUTHOR]

We implement an all-optically reconfigurable triangular lattice of exciton–polariton condensates in a III–V semiconductor microcavity. For this, we utilize a spatial light modulator to structure an incident nonresonant excitation laser beam into a corresponding triangular lattice of Gaussian beams that are focused onto the cavity plane. The optical excitation pattern locally stimulates and blueshifts polaritons due to exciton interactions. At a critical pump power, polaritons condense into a macroscopically coherent Bloch state with sharp Bragg peaks. We reconstruct the full band structure of the system through energy tomography techniques as a function of lattice constant, allowing us to resolve polaritonic Bloch bands from the condensate emission. While for sufficiently large lattice constants, one observes the formation of triangular arrays of condensates, for small lattice constant and pump powers above condensation threshold, one observes the formation of honeycomb, instead of triangular, lattice of condensates, with clear evidence of condensation into the S-band. Our results underpin the quality of all-optically engineered polariton lattices to simulate condensed matter systems in the strong coupling regime. [ABSTRACT FROM AUTHOR]

Propagation and attenuation of sound through a layered phononic crystal with viscous constituents is theoretically studied. The Navier–Stokes equation with appropriate boundary conditions is solved and the dispersion relation for sound is obtained for a periodic layered heterogeneous structure where at least one of the constituents is a viscous fluid. Simplified dispersion equations are obtained when the other component of the unit is either elastic solid, viscous fluid, or ideal fluid. The limit of low frequencies when periodic structure homogenizes and the frequencies close to the band edge when propagating Bloch wave becomes a standing wave are considered and enhanced viscous dissipation is calculated. Angular dependence of the attenuation coefficient is analyzed. It is shown that transition from dissipation in the bulk to dissipation in a narrow boundary layer occurs in the region of angles close to normal incidence. Enormously high dissipation is predicted for solid–fluid structure in the region of angles where transmission practically vanishes due to appearance of so-called "transmission zeros," according to El Hassouani, El Boudouti, Djafari-Rouhani, and Aynaou [Phys. Rev. B 78, 174306 (2008)]. For the case when the unit cell contains a narrow layer of high viscosity fluid, the anomaly related to acoustic manifestation of Borrmann effect is explained. [ABSTRACT FROM AUTHOR]

The reflection coefficient of ultra-high-energy electrons (~1 MeV) at their normal incidence on a thin single-crystal film is calculated. It is shown that even at such high particle energies, the quantum-size effect of the Bloch waves formed in the film is noticeably manifested. Narrow Bragg reflection peaks are found to appear at certain electron energies. A formula is given that determines their position and intensity on the reflection curve. A comparison of reflection coefficients at intermediate, high, and ultra-high particle energies is made. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model of a double poro-elastic medium derived by the homogenization of a two-component periodically heterogeneous Biot continuum characterized by strong heterogeneities in the permeability and poroelastic coefficients of mesoscopic structure. A new scaling of the mesoscopic material parameters with respect to the small parameter which is involved in the asymptotic analysis is introduced to capture this high contrast quality of the mesoscopic model. It is shown that such a scaling ansatz of the mesoscopic material parameters can be justified using different micromodels associated with the two mesoscopic components. While the "matrix" is a little permeable stiff phase, the "conductive channels" are made of a very soft fibrous structure equivalently represented by an network of helical springs. The unfolding method of the homogenization is employed to derive the macroscopic model involving the frequency-dependent effective parameters. Semipermeable interfaces between hard dual porosity and soft primary porosity are considered. The wave dispersion of two shear wave modes S 1 , S 2 , and two pressure wave modes P 1 , P 2 , is illustrated in an numerical example and validated, in a part, using the reference dispersion analysis based on the Bloch wave decomposition. • A new type high-contrast double porosity Biot medium is introduced by material parameters related to scale. • The effective medium model is derived by the periodic homogenization for the scaling ansatz. • Frequency-dependent homogenized coefficients induce remarkable wave dispersion. • The scaling relevant in the soft matter is justified by homogenization of fibrous microstructures. • The wave response of the homogenized medium is compared with results of the Bloch wave analysis. [ABSTRACT FROM AUTHOR]

We investigate a one-dimensional discrete binary elastic superlattice bridging continuous models of superlattices that showcase a one-way propagation character, as well as the discrete elastic Su–Schrieffer–Heeger model, which does not exhibit this character. By considering Bloch wave solutions of the superlattice wave equation, we demonstrate conditions supporting elastic eigenmodes that do not satisfy the translational invariance of Bloch waves over the entire Brillouin zone, unless their amplitude vanishes for a certain wave number. These modes are characterized by a pseudo-spin and occur only on one side of the Brillouin zone for a given spin, leading to spin-selective one-way wave propagation. We demonstrate how these features result from the interplay of the translational invariance of Bloch waves, pseudo-spins, and a Fabry–Pérot resonance condition in the superlattice unit cell. [ABSTRACT FROM AUTHOR]

This article proposes a design strategy for acoustic metamaterial lattices which leverages the characteristic multi-stability and kinematic amplification of the internal architecture to realize a re-configurable effective mass distribution, enabling a corresponding frequency band structure of extreme tunability. The approach builds metamaterial lattices from bi-stable elastic elements featuring the typical two-bar inertial amplification mechanism, whose deformation axis is uniquely misaligned with that of its elastic support such that the realized amplification is configuration-specific. Conveniently, a change in the configuration does not simultaneously alter the element dimensions and, therefore, the size/shape of the finite metamaterial structure remains constant. Moreover, as the multi-stability and kinematic amplification are each based on geometry, scaling the resulting metamaterial structure is expected to be straightforward. The dynamic performance of 1D/2D metamaterial architectures exhibiting the proposed design strategy is analytically determined via Bloch wave analysis and supported by numerical demonstration of the corresponding finite structures. [ABSTRACT FROM AUTHOR]

We report on a novel scissor-like electromechanical metamaterial (SEMM) with enhanced and tunable damping properties, stemming from its electromechanical resonant effects. The displacement amplification mechanism of the scissor-like structure in SEMM is exploited to amplify the damping ratio for stronger vibration mitigation through the enhanced electrical dissipation of the amplified voltage of the piezoelectric element. The relative dissipation performance, termed as metadamping, is quantified based on complex band structures, which allow frequencies to be complex valued. Using different shunting circuits, the overall damping performance of SEMM is demonstrated to be higher than a statically equivalent traditional systems, such as acoustic metamaterials and monatomic lattices. The dissipation performance of SEMM is numerically verified via finite structure analysis and found to be in an excellent agreement with Bloch's wave analysis. Furthermore, the electromechanical nature of the piezoelectric material in SEMM provides a convenient way to tune the metadamping by adjusting the piezoelectric shunting circuit. [ABSTRACT FROM AUTHOR]

The emergence of information metamaterials has spurred significant advances in the field of information sciences. However, the current studies are predominantly focused on classical bits as the fundamental information units, and the classical bit can only be located at two poles of Bloch sphere, resulting in limited information capacity. To break such limit, quantum bits (qubits) offer a promising solution since they have superposition states anywhere on the Bloch sphere. Here, a Pancharatnam‐Berry (PB) phase metasurface is used to emulate the qubits. Firstly, it proposes a theoretical concept of analog quantum bit and develops its mathematical and geometrical representations. Subsequently, a meta‐atom is designed as a physical platform to implement the concept of analog qubits. By manipulating the geometric configuration of the proposed meta‐atom, it achieves arbitrary superpositions of polarization states. A PB phase metasurface is experimentally fabricated to validate that the proposed analog qubit can be used to emulate the quantum bit in terms of both mathematical and geometrical representations. This work not only provides a theoretical foundation to go beyond the information limit of classical bits but also develops a feasible physics platform to investigate quantum information metasurfaces, which would complement and revolutionize classical information science. [ABSTRACT FROM AUTHOR]

This article shows that for a large class of discrete periodic Schrödinger operators, most wavefunctions resemble Bloch states. More precisely, we prove quantum ergodicity for a family of periodic Schrödinger operators H on periodic graphs. This means that most eigenfunctions of H on large finite periodic graphs are equidistributed in some sense, hence delocalized. Our results cover the adjacency matrix on Z d , the triangular lattice, the honeycomb lattice, Cartesian products, and periodic Schrödinger operators on Z d . The theorem applies more generally to any periodic Schrödinger operator satisfying an assumption on the Floquet eigenvalues. [ABSTRACT FROM AUTHOR]

InAs/AlSb is a material system that can be used as a low-noise avalanche detector and operates in the short-wave infrared band. The interface parameters determine the wave function overlap (WFO). Maximizing the WFO of InAs/AlSb superlattices improves the quantum efficiency (QE) of infrared avalanche photodetectors (APDs). However, this remains a huge challenge. Here, the 8-band k·p perturbation method based on Bloch wave envelope function approximation was used to calculate the energy level structure of InAs/AlSb superlattices. The results indicate that the WFO is enhanced with increasing InSb interface thickness or when the InSb (or AlAs) interface is far from the intersection of InAs and AlSb. As the AlAs interface thickness increases, the WFO enhances and then reduces. The maximum increase in WFO is 15.7%, 93%, and 156.8%, respectively, with three different models. Based on the stress equilibrium condition, we consider the interface engineering scheme proposed for enhancing WFO with an increase of 16%, 114%, and 159.5%, respectively. Moreover, the absorption wavelength shift is less than ±0.1 μm. Therefore, the interface layer thickness and position can be designed to enhance the WFO without sacrificing other properties, thereby improving the QE of the device. It provides a new idea for the material epitaxy of APDs. [ABSTRACT FROM AUTHOR]

In the context of architected materials, it has been observed that both long-wavelength instabilities leading possibly to localization and short-wavelength instabilities leading to the apparition of a deformation pattern could occur. This work proposes for the first time a comparison of the ability of two families of higher order equivalent media, namely strain-gradient and micromorphic media, to capture both patterning and long-wavelength macroscopic instabilities in those materials. The studied architected material consists in a simple one-dimensional arrangement of non-linear springs, thus allowing for analytical or nearly analytical treatment of the problem, avoiding any uncertainties or imprecisions coming from a numerical method. A numerical solution of the problem is then used to compare the post-buckling prediction of both models. The study concludes that, micromorphic media are the appropriate choice of equivalent continuum models to emply when dealing with the possibility of patterning inside a structured medium, but if long-wavelength global instability is of interest, a strain-gradient type equivalent medium is well suited. [ABSTRACT FROM AUTHOR]

Two kinds of periodic composite pipes with support or dynamic vibration absorber are designed based on the theory of phononic crystals. Axial vibration and band gaps of composite fluid-filled pipe are calculated by using transfer matrix method and Bloch wave theory. The present fluid–structure interaction model and frequency domain calculation method are validated by comparing the velocity of fluid from a FEM model. The results show that the stop bands frequency of velocity responses are in good agreement with band gap. Longer length of a single cell decreases the beginning frequency and width of both two kinds' band gaps. [ABSTRACT FROM AUTHOR]

Proposed is a gas concentration monitoring method that is based on the dispersion of Bloch surface wave. Different from the conventional sensing method using a single parameter such as wavelength or angle, all measured data was fully analyzed from a two-dimensional reflection intensity curve of a Bloch surface wave by mutual reflection intensity, which can reflect changes in either the refractive index or the airflow motion. This method does not require recording specific wavelength or incidence angles and measurement of small wavelengths or angle deviations. Our airflow monitoring device has a detection limit of 1.14 × 10−4RIU and good linearity in an open environment with high noise levels. However, in a closed environment, we achieved stable monitoring of the dry ice sublimation process and prediction. [ABSTRACT FROM AUTHOR]

We report on the use of biochips based on one-dimensional photonic crystals sustaining Bloch surface waves to specifically detect target miRNA that is characteristic of hemorrhagic stroke (miR-16-5p) at low concentration in a buffer solution. The biochips were functionalized with streptavidin and ssDNA oligonucleotides to enable miRNA detection. To discriminate the target miRNA from a non-specific control (miR-101a-3p), we made use of an optical platform developed to work both in label-free and fluorescence detection modes. We demonstrate that the limit of detection provided when operating in the fluorescence mode allows us to specifically detect the target miRNA down to 1 ng mL−1 (140 pM), which matches the recommendations for diagnostic miRNA assays, 5 ng mL−1. The low costs open the way towards the application of these disposable optical biochips based on 1DPC sustaining Bloch surface waves as a promising tool for early disease detection in a liquid biopsy format. [ABSTRACT FROM AUTHOR]

Recently, Kayumov [Lobachevskii J. Math. 38 (2017), pp. 466–468] obtained a sharp estimate for the n-th truncated area functional for normalized functions in the Bloch space for n\le 5 and then, together with Wirths [Lobachevskii J. Math. 40 (2019), pp. 1319–1323], extended the result for n=6. We prove that for the functions with non-negative Taylor coefficients, the same sharp estimate is valid for all n. For arbitrary functions, we obtain an estimate that is asymptotically of the same order but slightly larger (roughly by a factor of 4/e). We also consider related weighted estimates for functionals involving the powers n^t, t>0, and show that the exponent t=1 represents the critical case for the expected sharp estimate. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to show that over a large class of bounded domains Ω⊂C², for 1

The interplay among symmetry of lattices, electronic correlations, and Berry phase of the Bloch states in solids has led to fascinating quantum phases of matter. A prototypical system is the magnetic Weyl candidate SrRuO3, where designing and creating electronic and topological properties on artificial lattice geometry is highly demanded yet remains elusive. Here, we establish an emergent trigonal structure of SrRuO3 by means of heteroepitaxial strain engineering along the [111] crystallographic axis. Distinctive from bulk, the trigonal SrRuO3 exhibits a peculiar XY-type ferromagnetic ground state, with the coexistence of high-mobility holes likely from linear Weyl bands and low-mobility electrons from normal quadratic bands as carriers. The presence of Weyl nodes are further corroborated by capturing intrinsic anomalous Hall effect, acting as momentum-space sources of Berry curvatures. The experimental observations are consistent with our first-principles calculations, shedding light on the detailed band topology of trigonal SrRuO3 with multiple pairs of Weyl nodes near the Fermi level. Our findings signify the essence of magnetism and Berry phase manipulation via lattice design and pave the way towards unveiling nontrivial correlated topological phenomena. [ABSTRACT FROM AUTHOR]

Three-dimensional (3D) electronic band structure is fundamental for understanding a vast diversity of physical phenomena in solid-state systems, including topological phases, interlayer interactions in van der Waals materials, dimensionality-driven phase transitions, etc. Interpretation of ARPES data in terms of 3D electron dispersions is commonly based on the free-electron approximation for the photoemission final states. Our soft-X-ray ARPES data on Ag metal reveals, however, that even at high excitation energies the final states can be a way more complex, incorporating several Bloch waves with different out-of-plane momenta. Such multiband final states manifest themselves as a complex structure and added broadening of the spectral peaks from 3D electron states. We analyse the origins of this phenomenon, and trace it to other materials such as Si and GaN. Our findings are essential for accurate determination of the 3D band structure over a wide range of materials and excitation energies in the ARPES experiment. Angular-resolved photoemission data is commonly used to determine the 3D electronic structure assuming free-electron final states. Strocov et al. show that even at high excitation energies the complexity of final states in various materials can go far beyond the free-electron picture. [ABSTRACT FROM AUTHOR]