Fundamental principles for generalized Willis metamaterials

Metamaterials that exhibit a constitutive coupling between their momentum and strain, show promise in wave manipulation for engineering purposes and are called Willis materials. They were discovered using an effective-medium theory, showing that their response is nonlocal in space and time. Recently, we generalized this theory to account for piezoelectricity, and demonstrated that the effective momentum can depend constitutively on the electric field, thereby enlarging the design space for metamaterials. Here, we develop the mathematical restrictions on the effective properties of such generalized Willis materials, owing to passivity, reciprocity, and causality. The establishment of these restrictions is of fundamental significance, as they test the validity of theoretical and experimental results-and applicational importance, since they provide elementary bounds for the maximal response that potential devices may achieve.This research was supported by the Israel Science Foundation, funded by the Israel Academy of Sciences and Humanities (Grant No. 2061/20), the United States - Israel Binational Science Foundation (Grant No. 2014358), and the Ministry of Science and Technology (Grant No. 880011)

Fundamental principles for generalized Willis metamaterials

Metamaterials whose momentum is constitutively coupled with their strain show promise in wave manipulation for engineering purposes and are called Willis materials. They were discovered using an effective medium theory which shows that their response is non-local in space and time. Recently, we generalized this theory to account for piezoelectricity and demonstrated that the effective momentum can depend constitutively on the electric field, thereby enlarging the design space for metamaterials. Here, we develop the mathematical restrictions on the effective properties of such generalized Willis materials, owing to passivity, reciprocity, and causality. Establishing these restrictions is of fundamental significance, as they test the validity of theoretical and experimental results and applicational importance since they provide elementary bounds for the maximal response that potential devices may achieve.Comment: 19 pages, 3 figure

Homogenization of piezoelectric planar Willis materials undergoing antiplane shear

Homogenization theories provide models that simplify the constitutive description of heterogeneous media while retaining their macroscopic features. These theories have shown how the governing fields can be macroscopically coupled, even if they are microscopically independent. A prominent example is the Willis theory which predicted the strain–momentum coupling in elastodynamic metamaterials. Recently, a theory that is based on the Green’s function method predicted analogous electro–momentum coupling in piezoelectric metamaterials. Here, we develop a simpler scheme for fibrous piezoelectric composites undergoing antiplane shear waves. We employ a source-driven approach that delivers a unique set of effective properties for arbitrary frequency–wavevector pairs. We numerically show how the resultant homogenized model recovers exactly the dispersion of free waves in the composite. We also compute the effective properties in the long-wavelength limit and off the dispersion curves, and show that the resultant model satisfy causality, reciprocity and energy conservation. By contrast, we show how equivalent models that neglect the electromomentum coupling violate these physical laws

Enhancement of Fano-resonance response in bilayer graphene single and double barriers induced by bandgap opening

Fano resonances in bilayer graphene arise due to the coupling between extended and discrete electrons states, and represent an exotic phenomenon in graphene akin to Klein and anti-Klein tunneling, atomic collapse and negative refraction to mention a few. The hallmark of these resonances is identifiable in the conductance curves of bilayer graphene barrier structures. Furthermore, the Fano line-shape can be presented in the conductance by reducing the angular range in the computation of the transport properties. In this work, we explore the possible consequences that bandgap opening in the band structure of bilayer graphene can have over Fano resonances. We have used a four-band Hamiltonian to taking into account the mentioned band structure modifications. The hybrid matrix method and the Landauer–Büttiker formalism have been implemented to obtain the transmittance and the conductance, respectively. We find that the signatures of the Fano resonances on the conductance are enhanced by the opening of the bandgap. In fact, the Fano profile is manifested in the conductance without the need of reducing the angular range. This enhancement results from the improvement of the chirality matching between extended and discrete states induced by the bandgap opening. The main characteristics of the impact of the bandgap opening on the transmission and transport properties of single and double barriers are presented. So, the bandgap opening far from hamper the Fano resonance response promotes it and can be used as modulation parameter to prove the exotic phenomenon of Fano resonances in bilayer graphene barrier structures

Theory of non-Hermitian topological whispering gallery

Topological insulators have taken the condensed matter physics scenery by storm and captivated the interest among scientists and materials engineers alike. Surprisingly, this arena which was initially established and profoundly studied in electronic systems and crystals, has sparked a drive among classical physicists to pursue a wave-based analogy for sound, light and vibrations. In the latest efforts combining valley-contrasting topological sound with non-Hermitian ingredients, B. Hu et al. [Nature 597, 655 (2021)] employed thermoacoustic coupling in sonic lattices whose elementary building blocks are coated with electrically biased carbon nanotube films. In this contribution, we take a theoretical and numerical route towards understanding the complex acoustic interplay between geometry and added acoustic gain as inspired by the aforesaid publication. Besides complex bulk and edge states predictions and computations of mode-split resonances using whispering gallery configurations, we also predict an acoustic amplitude saturation in dependence on the activated coated elements. We foresee that our computational advances may assist future efforts in exploring thermoacoustic topological properties.We acknowledge the support from the European Research Council (ERC) through the Starting Grant No. 714577 PHONOMETA. R.P.S. acknowledges support from the CONEX-Plus programme funded by Universidad Carlos III de Madrid and the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 801538. Z.Z., Y.C., and X.L. acknowledge the support from the National Natural Science Foundation of China (Nos. 12074183, 11922407, 11834008, 12225408, and 12104226) and the Fundamental Research Funds for the Central Universities (No. 020414380181)

General form of the Green's function regular at infinity for the homogeneous Sturm-Liouville matrix operator

The standard Fourier transform method is used to analyze the expression of the Green's function regular at infinity for the Sturm-Liouville matrix operator in the important case of position independent parameters. A quadratic eigenvalue and eigenvector problem appears naturally. The classification of the former problem solutions allows to obtain the Green's function in a compact general form. Different physical problems were analyzed and the corresponding Green's function for various elementary excitations in less studied systems was predicted also.R. P.-S. acknowledges CONACyT support. R.P.-A. also acknowledges CONACyT support through grant 208108 and hospitality at ICMM-CSIC, Madrid, Spain. V.R.V. acknowledges the Spanish Ministerio de Economía y Competitividad for support through grant MAT2012-38045-C04-04