Valley anisotropy in elastic metamaterials

Abstract

Valley, as a new degree of freedom, raises the valleytronics in fundamental and applied science. The elastic analogs of valley states have been proposed by mimicking the symmetrical structure of either two-dimensional materials or photonic valley crystals. However, the asymmetrical valley construction remains unfulfilled. Here, we present the valley anisotropy by introducing asymmetrical design into elastic metamaterials. The elastic valley metamaterials are composed of bio-inspired hard spirals and soft materials. The anisotropic topological nature of valley is verified by asymmetrical distribution of the Berry curvature. We show the high tunability of the Berry curvature both in magnitude and sign enabled by our anisotropic valley metamaterials. Finally, we demonstrate the creation of valley topological insulators and show topologically protected propagation of transverse elastic waves relying on operating frequency. The proposed topological properties of elastic valley metamaterials pave the way to better understanding the valley topology and to creating a new type of topological insulators enabled by an additional valley degree of freedom. IntroductionElastic waves, possessing plenty of degree of freedoms (DOFs) including frequency, phase and polarization, have demonstrated tremendous promise in a variety of applications including target detection, information processing and biomedical imaging 1-4 . Recently, topology has been proposed as a new DOF in manipulating waves in both photonic and phononic systems, exhibiting remarkable impact not only on fundamental science such as condensed matter physics, but also on engineering applications such as low loss devices and waveguides 5-9 . In photonics, the photonic spin Hall effect has been achieved by taking advantage of spin DOF, which opens up an avenue of spin-dependent light transport and one-way spin transport 10-13 . In phononics, mechanical patterns and deformation have been employed as a new DOF to enable the elastic topological states 8,9,[14][15][16][17][18][19] .Recently, valley, the degenerate yet inequivalent energy extrema in momentum space, has emerged as a new dimension in manipulating waves in electronics, photonics and phononics 5,6,[20][21][22][23][24] . In graphene and transition metal dichalcogenides, valley-selective circular dichroism and valleyHall effect due to the long lifetime of valley polarization and non-zero Berry curvature have been studied for the promising applications in information carrier and storage 20,21,23,24 . As the concept of valley is introduced into the classic system, the photonic and phononic valley crystals are proposed, showing potential applications such as information processing via valley-dependent transportation 5,6,22 . However, existing designs of valley metamaterials are limited to the inherent spatial inversion symmetry of the physical system, where the typical Berry curvature distribution in the Brillouin zone follows Ω −# = Ω # . The valley metamaterials without spatial inversion symmetry have not yet bee...

Reliable and Tunable Elastic Interface States in Soft Metamaterials

“…Interface states, which possess great advantages in the localization and confinement of waves or energy, have been extensively realized in the electronic, [ 1–4 ] photonic, [ 5–17 ] acoustic systems, [ 18–23 ] and also, the elastic systems, [ 24–31 ] recently. Reflection phase match principle is verified to be a useful methodology in the formation of interface states, which has been successfully demonstrated in both symmetric [ 8,17,22,28 ] and nonsymmetric [ 6,11,12,24 ] acoustic or photonic systems. On the one hand, interface states in 1D mirror symmetric systems [ 8,17,22,28 ] have been theoretically and experimentally well developed, which were accustomed to exploiting deformed geometries to reverse the bulk bands.…”

“…However, on the other hand, broken mirror‐symmetric structures own an advantage in the dynamical manipulation of the interface states, which can be realized simply through modifying or adjusting its asymmetric geometry construction. For instance, interface states in 1D graphene‐embedded photonic crystal heterostructures, [ 6 ] 1D composite photonic structures, [ 11 ] compound metasurface/photonic crystal configurations, [ 12 ] and the elastic metamaterials with spiral inclusions, [ 24 ] all of them have successfully adjusted the emergent position and frequency range of the interface states and provide diverse implementation strategies.…”

Bidirectional Elastic Diode with Frequency-Preserved Nonreciprocity

“…Topological states offer nonreciprocity in linear elastic systems [11][12][13][14][15][16] by beating time reversibility with active control or external field, while it is challenging to realize this mechanism in the broad and low frequencies [17][18][19]. Moreover, this manipulation relies on active control or external field.…”

Topological Transition in Spiral Elastic Valley Metamaterials

“…Topological valley metamaterials have emerged as a remarkable impact not only on condensed matter physics but also on manipulation of waves in electronics, photonics and phononics [1][2][3][4][5][6][7][8][9].…”

“…Several strategies have been proposed to achieve the topological transition. For example, the inherent degree of freedom, such as adjusting the geometric parameters, can be exploited to invert the topological phase of metamaterials [4,6,9,12]. Besides, the external degree of freedom, such as deformation, can also affect the band inversion dynamically [13,14].…”