A brief review of metamaterials for opening low-frequency band gaps

Metamaterials are an emerging type of man-made material capable of obtaining some extraordinary properties that cannot be realized by naturally occurring materials.Due to tremendous application foregrounds in wave manipulations,metamaterials have gained more and more attraction.Especially,developing research interest of low-frequency vibration attenuation using metamaterials has emerged in the past decades.To better understand the fundamental principle of opening low-frequency(below 100 Hz)band gaps,a general view on the existing literature related to low-frequency band gaps is presented.In this review,some methods for fulfilling low-frequency band gaps are firstly categorized and detailed,and then several strategies for tuning the low-frequency band gaps are summarized.Finally,the potential applications of this type of metamaterial are briefly listed.This review is expected to provide some inspirations for realizing and tuning the low-frequency band gaps by means of summarizing the related literature.

Optimal design for rubber concrete layered periodic foundations based on the analytical approximations of band gaps and mapping relations

The seismic performance of rubber concrete-layered periodic foundations are significantly influenced by their design,in which the band gaps play a paramount role.Aiming at providing better designs for these foundations,this study first proposes and validates the analytical formulas to approximate the bounds of the first few band gaps.In addition,the mapping relations linking the frequencies of different band gaps are presented.Furthermore,an optimal design method for these foundations is developed,which is validated through an engineering example.It is demonstrated that ensuring the superstructure’s resonance zones are completely covered by the corresponding periodic foundation’s band gaps can achieve satisfactory vibration attenuation effects,which is a good strategy for the design of rubber concrete layered periodic foundations.

Ultra-wide band gap and wave attenuation mechanism of a novel star-shaped chiral metamaterial

A novel hollow star-shaped chiral metamaterial(SCM)is proposed by incorporating chiral structural properties into the standard hollow star-shaped metamaterial,exhibiting a wide band gap over 1500 Hz.To broaden the band gap,solid single-phase and two-phase SCMs are designed and simulated,which produce two ultra-wide band gaps(approximately 5116 Hz and 6027 Hz,respectively).The main reason for the formation of the ultra-wide band gap is that the rotational vibration of the concave star of two novel SCMs drains the energy of an elastic wave.The impacts of the concave angle of a single-phase SCM and the resonator radius of a two-phase SCM on the band gaps are studied.Decreasing the concave angle leads to an increase in the width of the widest band gap,and the width of the widest band gap increases as the resonator radius of the two-phase SCM increases.Additionally,the study on elastic wave propagation characteristics involves analyzing frequency dispersion surfaces,wave propagation directions,group velocities,and phase velocities.Ultimately,the analysis focuses on the transmission properties of finite periodic structures.The solid single-phase SCM achieves a maximum vibration attenuation over 800,while the width of the band gap is smaller than that of the two-phase SCM.Both metamaterials exhibit high vibration attenuation capabilities,which can be used in wideband vibration reduction to satisfy the requirement of ultra-wide frequencies.

Behavior of exciton in direct−indirect band gap Al_(x)Ga_(1−x)As crystal lattice quantum wells

Excitons have significant impacts on the properties of semiconductors.They exhibit significantly different properties when a direct semiconductor turns in to an indirect one by doping.Huybrecht variational method is also found to influence the study of exciton ground state energy and ground state binding energy in Al_(x)Ga_(1−x)As semiconductor spherical quantum dots.The Al_(x)Ga_(1−x)As is considered to be a direct semiconductor at AI concentration below 0.45,and an indirect one at the concentration above 0.45.With regards to the former,the ground state binding energy increases and decreases with AI concentration and eigenfrequency,respectively;however,while the ground state energy increases with AI concentration,it is marginally influenced by eigenfrequency.On the other hand,considering the latter,while the ground state binding energy increases with AI concentration,it decreases with eigenfrequency;nevertheless,the ground state energy increases both with AI concentration and eigenfrequency.Hence,for the better practical performance of the semiconductors,the properties of the excitons are suggested to vary by adjusting AI concentration and eigenfrequency.

Langmuir-Schaefer Film Investigation and Density Functional Theory Band Gap Calculations of Calix[n]arene-Para-Aminobenzoic Acid for Drug Nanosensor Application

Calix[n]arenes was utilized to detect PABA,the primary sunscreen component.This study investigates the interaction of calix[4]arene(C4),calix[6]arene(C6),and PABA using the Langmuir method and first-principle density functional theory(DFT).Using the Langmuir-Schaefer(LS)technique,an ultrathin film composed of calix[n]arenes and their complexes with PABA was deposited on various substrates.Based on the Langmuir study,the PABA molecule was bonded to the lower rims of both C4 and C6 with the host-guest ratio of 1:1.All of the LS films formed were then characterized by ultravioletvisible spectroscopy(UV-Vis),Fourier-transform infrared spectroscopy(FTIR)and carbon,hydrogen,nitrogen,sulfur elemental analyzer(CHNS).The band gap reduction obtained in the DFT study denotes the charge transfer interaction with promising reactivity between the calix[n]arenes and PABA.The sensing of PABA by C4 and C6 is successful based on the formation of bonding between them due to the hosts’effective trapping capacity.The outcomes of this study could be applied to drug delivery systems for future pharmaceutical and medical applications.

Formation mechanism of the low-frequency locally resonant band gap in the two-dimensional ternary phononic crystals

The low-frequency band gap and the corresponding vibration modes in two-dimensional ternary locally resonant phononic crystals are restudied successfully with the lumped-mass method. Compared with the work of C. Goffaux and J. Sánchez-Dehesa （Phys. Rev. B 67 14 4301（2003））, it is shown that there exists an error of about 50% in their calculated results of the band structure, and one band is missing in their results. Moreover, the in-plane modes shown in their paper are improper, which results in the wrong conclusion on the mechanism of the ternary locally resonant phononic crystals. Based on the lumped-mass method and better description of the vibration modes according to the band gaps, the locally resonant mechanism in forming the subfrequency gaps is thoroughly analysed. The rule used to judge whether a resonant mode in the phononic crystals can result in a corresponding subfrequency gap is also verified in this ternary case.

Folding beam-type piezoelectric phononic crystal with low-frequency and broad band gap

A folding beam-type piezoelectric phononic crystal model is proposed to isolate vibration. Two piezoelectric bimorphs are joined by two masses as a folding structure to comprise each unit cell of the piezoelectric phononic crystal. Each bimorph is connected independently by a resistive-inductive resonant shunting circuit. The folding structure extends the propagation path of elastic waves, while its structure size remains quite small. Propagation of coupled extension-flexural elastic waves is studied by the classical laminated beam theory and transfer matrix method. The theoretical model is further verified with the finite element method(FEM). The effects of geometrical and circuit parameters on the band gaps are analyzed. With only 4 unit cells, the folding beam-type piezoelectric phononic crystal generates two Bragg band gaps of 369 Hz to1 687 Hz and 2 127 Hz to 4 000 Hz. In addition, between these two Bragg band gaps, a locally resonant band gap is induced by resonant shunting circuits. Appropriate circuit parameters are used to join these two Bragg band gaps by the locally resonant band gap.Thus, a low-frequency and broad band gap of 369 Hz to 4 000 Hz is obtained.

Flexural vibration band gaps in thin plates with two-dimensional binary locally resonant structures

The complete flexural vibration band gaps are studied in the thin plates with two-dimensional binary locally resonant structures, i.e. the composite plate consisting of soft rubber cylindrical inclusions periodically placed in a host material. Numerical simulations show that the low-frequency gaps of flexural wave exist in the thin plates. The width of the first gap decreases monotonically as the matrix density increases, The frequency response of the finite periodic thin plates is simulated by the finite element method, which provides attenuations of over 20dB in the frequency range of the band gaps. The findings will be significant in the application of phononic crystals.

Tuning of band gaps for a two-dimensional piezoelectric phononic crystal with a rectangular lattice

In this paper, the elastic wave propagation in a two-dimensional piezoelectric phononic crystal is studied by considering the mechanic-electric coupling. The generalized eigenvalue equation is obtained by the relation of the mechanic and electric fields as well as the Bloch-Floquet theorem. The band structures of both the in-plane and anti-plane modes are calculated for a rectangular lattice by the planewave expansion method. The effects of the lattice constant ratio and the piezoelectricity with different filling fractions are analyzed. The results show that the largest gap width is not always obtained for a square lattice. In some situations, a rectangular lattice may generate larger gaps. The band gap characteristics are influenced obviously by the piezoelectricity with the larger lattice constant ratios and the filling fractions.

INFLUENCES OF ANISOTROPY ON BAND GAPS OF 2D PHONONIC CRYSTAL

Band gaps of 2D phononic crystal with orthotropic cylindrical fillers embedded in the isotropic host are studied in this paper. Two kinds of periodic structures, namely, the square lattice and the triangle lattice, are considered. For anisotropic phononic crystal, band gaps not only depend on the periodic lattice but also the angle between the symmetry axis of orthotropic material and that of the periodic structure. Rotating these cylindrical fillers makes the angle changing continuously; as a result, pass bands and forbidden bands of the phononic crystal are changed. The plane wave expansion method is used to reduce the band gap problem to an eigenvalue problem. The numerical example is given for YBCO/Epoxy composites. The location and the width of band gaps are estimated for different rotating angles. The influence of anisotropy on band gaps is discussed based on numerical results.

Tunable band gaps in acoustic metamaterials with periodic arrays of resonant shunted piezos

Periodic arrays of resonant shunted piezoelectric patches are employed to control the wave propagation in a two-dimensional （2D） acoustic metamaterial. The performance is characterized by the finite element method. More importantly, we propose an approach to solving the conventional issue of the nonlinear eigenvalue problem, and give a convenient solution to the dispersion properties of 2D metamaterials with periodic arrays of resonant shunts in this article. Based on this modeling method, the dispersion relations of a 2D metamaterial with periodic arrays of resonant shunted piezos are calculated. The results show that the internal resonances of the shunting system split the dispersion curves, thereby forming a locally resonant band gap. However, unlike the conventional locally resonant gap, the vibrations in this locally resonant gap are unable to be completely localized in oscillators consisting of shunting inductors and piezo-patches.

Revisit of the band gaps of rutile SnO2 and TiO2: a first-principles study

From the recent experimentally observed conduction band offset and previously reported band gaps,one may deduce that the valence band offset between rutile SnO2 and TiO2 is around 1 eV,with TiO2 having a higher valence band maximum.This implication sharply contradicts the fact that the two compounds have the same rutile structure and the Γ3^+ VBM state is mostly an oxygen p state with a small amount of cation d character,thus one would expect that SnO2 and TiO2 should have small valence band offset.If the valence band offset between SnO2 and TiO2 is indeed small,one may question the correctness of the previously reported band gaps of SnO2 and TiO2.In this paper,using first-principles calculations with different levels of computational methods and functionals within the density functional theory,we reinvestigate the long-standing band gap problem for SnO2.Our analysis suggests that the fundamental band gap of SnO2 should be similar to that of TiO2,i.e.,around 3.0 eV.This value is significantly smaller than the previously reported value of about 3.6 eV,which can be attributed as the optical band gap of this material.Similar to what has been found in In2O3,the discrepancy between the fundamental and optical gaps of SnO2 can be ascribed to the inversion symmetry of its crystal structure and the resultant dipole-forbidden transitions between its band edges.Our results are consistent with most of the optical and electrical measurements of the band gaps and band offset between SnO2 and TiO2,thus provide new understanding of the band structure and optical properties of SnO2.Experimental tests of our predictions are called for.

Syntheses,Structures and Band Gaps of KLnSiS_4(Ln=Sm,Yb)

Two new quaternary sulfides, KSmSiS4 （1） and KYbSiS4 （2）, have been synthesized by high-temperature solid-state reaction. Single,crystal X-ray diffraction analyses indicate that both compounds crystallize in the space group P21/m, and the crystal data are as follows： a = 6.426（11）, b = 6.582（11）, c = 8.602（15）A, β= 107.90（13）°, Z = 2, V= 346.2（10） A^3, Dc = 3.317 g/cm^3, F（000） = 318,μ（MoKα） = 10.334 mm^-1, the final R = 0.0559 and wR = 0.1370 for 1; and α= 6.3244（10）, b = 6.5552（10）, c = 8.5701（15）A, β= 108.001（13）°, Z = 2, V = 337.91（9） A^3, De= 3.621 g/cm^3, F（000） = 334, μ（MoKα） = 15.737 mm^-1, the final R = 0.0422 and wR = 0.0960 for 2. The KLnSiS4 （Ln = Sm, Yb） structure consists of corrugated ∞^2 [LnSiS4]^- layers which are formed by edge-sharing LnS8 bicapped trigonal prisms and SiS4 tetrahedra. The K^＋ cations are located in the cavities defined by S2 anions between the ∞^2[LnSiS4]^- layers. Band-gap analyses show that compounds 1 and 2 are semiconductors with optical band-gaps of 2.40 and 2.34 eV, respectively.

High temperature magnetic semiconductors: narrow band gaps and two-dimensional systems

Magnetic semiconductors have been demonstrated to work at low temperatures, but not yet at room temperature for spin electronic applications. In contrast to the p-type diluted magnetic semiconductors, n-type diluted magnetic semiconductors are few. Using a combined method of the density function theory and quantum Monte Carlo simulation, we briefly discuss the recent progress to obtain diluted magnetic semiconductors with both p- and n-type carriers by choosing host semiconductors with a narrow band gap. In addition, the recent progress on two-dimensional intrinsic magnetic semiconductors with possible room temperature ferromangetism and quantum anomalous Hall effect are also discussed.

Machine learning of theΓ-point gap and flat bands of twisted bilayer graphene at arbitrary angles

The novel electronic properties of bilayer graphene can be fine-tuned via twisting,which may induce flat bands around the Fermi level with nontrivial topology.In general,the band structure of such twisted bilayer graphene(TBG)can be theoretically obtained by using first-principles calculations,tight-binding method,or continuum model,which are either computationally demanding or parameters dependent.In this work,by using the sure independence screening sparsifying operator method,we propose a physically interpretable three-dimensional(3D)descriptor which can be utilized to readily obtain theΓ-point gap of TBG at arbitrary twist angles and different interlayer spacings.The strong predictive power of the descriptor is demonstrated by a high Pearson coefficient of 99%for both the training and testing data.To go further,we adopt the neural network algorithm to accurately probe the flat bands of TBG at various twist angles,which can accelerate the study of strong correlation physics associated with such a fundamental characteristic,especially for those systems with a larger number of atoms in the unit cell.

Effects of rotating noncircular scatterers on spin-wave band gaps of two-dimensional magnonic crystals

Using the plane-wave expansion method, the spin-wave band structures of two-dimensional magnonic crystals consisting of square arrays of different shape scatterers are calculated numerically, and the effects of rotating rectangle and hexagon scaterers on the gaps are studied, respectively. The results show that the gaps can be substantially opened and tuned by rotating the scatterers. This approach should be helpful in designing magnonic crystals with desired gaps.

Laser-assisted Simulation of Dose Rate Effects of Wide Band Gap Semiconductor Devices

Laser-assisted simulation technique has played a crucial role in the investigation of dose rate effects of silicon-based devices and integrated circuits,due to its exceptional advantages in terms of flexibility,safety,convenience,and precision.In recent years,wide band gap materials,known for their strong bonding and high ionization energy,have gained increasing attention from researchers and hold significant promise for extensive applications in specialized environments.Consequently,there is a growing need for comprehensive research on the dose rate effects of wide band gap materials.In response to this need,the use of laser-assisted simulation technology has emerged as a promising approach,offering an effective means to assess the efficacy of investigating these materials and devices.This paper focused on investigating the feasibility of laser-assisted simulation to study the dose rate effects of wide band gap semiconductor devices.Theoretical conversion factors for laser-assisted simulation of dose rate effects of GaN-based and SiC-based devices were been provided.Moreover,to validate the accuracy of the conversion factors,pulsed laser and dose rate experiments were conducted on GaN-based and SiC-based PIN diodes.The results demonstrate that pulsed laser radiation andγ-ray radiation can produce highly similar photocurrent responses in GaN-based and SiC-based PIN diodes,with correlation coefficients of 0.98 and 0.974,respectively.This finding reaffirms the effectiveness of laser-assisted simulation technology,making it a valuable complement in studying the dose rate effects of wide band gap semiconductor devices.

Numerical analysis of acoustic band gaps in two-dimensional periodic materials

Using the plane-wave expansion (PWE)method , the band gaps of the two-dimension phononic crystals composed of square, triangle and honeycomb arrays aluminum cylinders in the air are calculated numerically. The band structures of three lattices were compared and analyzed. It is concluded that the band-gap of honeycomb lattices is located at lower frequency fields, compared with square and triangle lattices. When the filling fraction is between 0.091 and 0.6046, the honeycomb lattices have larger band gaps and gain an advantage over square and triangle lattices. In addition, the gap map is introduced to illustrate the influences of filling fraction on the number, the relative width and the limit frequency of the band-gap.

Influence of Cu doping in Magnesium Hydroxide Nanoparticles for Bandgap Engineering

Cu doped Mg(OH)_(2) nanoparticles were synthesized with varying concentrations from 0 to 10%by a chemical synthesis technique of coprecipitation.X-rays diffraction (XRD) of the samples confirms that all the samples acquire the hexagonal crystal structure.XRD results indicated the solubility limit of dopant in the host material and the secondary phase of CuO was observed beyond 3%Cu doping in Mg(OH)_(2).The reduction in the size of nanoparticles was observed from 166 to 103 nm for Mg(OH)_(2) and 10% Cu doped Mg(OH)_(2)samples,respectively.The shift in absorption spectra exhibited the systematical enhancement in optical bandgap from 5.25 to 6.085 eV.A good correlation was observed between the bandgap energy and crystallite size of the nanocrystals which confirmed the size induced effect in the nanoparticles.The transformation in the sample morphology was observed from irregular spherical particles to sepals like shapes with increasing the Cu concentration in the host material.The energy dispersive X-Ray (EDX) analysis confirmed the purity of mass percentage composition of the elements present in the samples.

On band gaps of nonlocal acoustic lattice metamaterials:a robust strain gradient model

We have proposed an"exact"strain gradient(SG)continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions.The key enhancement is proposing a wavelength-dependent Taylor expansion to obtain a satisfactory accuracy when the wavelength gets close to the lattice spacing.Such a wavelength-dependent Taylor expansion is applied to the displacement field of the diatomic lattice,resulting in a novel SG model.For various kinds of diatomic lattices,the dispersion diagrams given by the proposed SG model always agree well with those given by the discrete model throughout the first Brillouin zone,manifesting the robustness of the present model.Based on this SG model,we have conducted the following discussions.(Ⅰ)Both mass and stiffness ratios affect the band gap structures of diatomic lattice metamaterials,which is very helpful for the design of metamaterials.(Ⅱ)The increase in the SG order can enhance the model performance if the modified Taylor expansion is adopted.Without doing so,the higher-order continuum model can suffer from a stronger instability issue and does not necessarily have a better accuracy.The proposed SG continuum model with the eighth-order truncation is found to be enough to capture the dispersion behaviors all over the first Brillouin zone.(Ⅲ)The effects of the nonlocal interactions are analyzed.The nonlocal interactions reduce the workable range of the well-known long-wave approximation,causing more local extrema in the dispersive diagrams.The present model can serve as a satisfactory continuum theory when the wavelength gets close to the lattice spacing,i.e.,when the long-wave approximation is no longer valid.For the convenience of band gap designs,we have also provided the design space from which one can easily obtain the proper mass and stiffness ratios corresponding to a requested band gap width.