Acoustic valley edge states in a graphene-like resonator system
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The concept of valley physics, as inspired by the recent development in valleytronic materials, has been extended to acoustic crystals for manipulation of air-borne sound. Many valleytronic materials follow the model of a gapped graphene. Yet the previously demonstrated valley acoustic crystal adopted a mirror-symmetry-breaking mechanism, lacking a direct counterpart in condensed matter systems. In this paper, we investigate a two-dimensional (2D) periodic acoustic resonator system with inversion symmetry breaking, as an analogue of a gapped graphene monolayer. It demonstrates the quantum valley Hall topological phase for sound waves. Similar to a gapped graphene, gapless topological valley edge states can be found at a zigzag domain wall separating different domains with opposite valley Chern numbers, while an armchair domain wall hosts no gapless edge states. Our study offers a route to simulate novel valley phenomena predicted in gapped graphene and other 2D materials with classical acoustic waves.Keywords:
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Zigzag carbon nanotubes possess special structural symmetry and some unique characteristics among three categories of single wall carbon nanotubes (SWCNTs). In this work, a quick method to calculate the first five optical transition energies of semiconducting zigzag and nearly zigzag SWCNTs is presented. Using the proposed method, the transition energy of any semiconducting zigzag and nearly zigzag SWCNT can be predicted directly just by knowing its first chiral index. The predicted results are compared with recent experimental data and found to be accurate over a wide diameter range. The proposed method can help finding the relation between geometric structure and optical properties of zigzag SWCNTs. It is also helpful for the applications of SWCNTs where information of optical transitions of a semiconducting zigzag nanotubes is needed.
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The application of a perpendicular electric field can drive silicene into a gapless state, characterized by two nearly fully spin-polarized Dirac cones owing to both relatively large spin-orbital interactions and inversion symmetry breaking. Here we argue that since inter-valley scattering from non-magnetic impurities is highly suppressed by time reversal symmetry, the physics should be effectively single-Dirac-cone like. Through numerical calculations, we demonstrate that there is no significant backscattering from a single impurity that is non-magnetic and unit-cell uniform, indicating a stable delocalized state. This conjecture is then further confirmed from a scaling of conductance for disordered systems using the same type of impurities.
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The first and fifth Harmonic indices for simple connected molecular graph G have been introduced as and , where . The aim of this paper is computing the Harmonic indices for polyhex zigzag TUZC6[m,n] Nanotube and Nanotori. We calculate the first and the fifth harmonic indices for planar polyhex zigzag nanotube PTUZC6[m,n] and polyhex zigzag nanotube TUZC6[m,n].
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Here, higher-order topological insulators and superconductors protected by inversion symmetry are investigated. These phases are characterized by gapped bulk and surface with gapless modes confined to hinges or corners of the sample. Such surface states can be understood as topological defects that are globally stabilized by inversion. They can be built using a layer construction that embeds a standard topological insulator/superconductor into a higher dimension by symmetrically adding to it copies of itself. Using this procedure, a complete classification of such states in any dimension is obtained and several examples for possible physical realizations are provided.
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The concept of valley physics, as inspired by the recent development in valleytronic materials, has been extended to acoustic crystals for manipulation of air-borne sound. Many valleytronic materials follow the model of a gapped graphene. Yet the previously demonstrated valley acoustic crystal adopted a mirror-symmetry-breaking mechanism, lacking a direct counterpart in condensed matter systems. In this paper, we investigate a two-dimensional (2D) periodic acoustic resonator system with inversion symmetry breaking, as an analogue of a gapped graphene monolayer. It demonstrates the quantum valley Hall topological phase for sound waves. Similar to a gapped graphene, gapless topological valley edge states can be found at a zigzag domain wall separating different domains with opposite valley Chern numbers, while an armchair domain wall hosts no gapless edge states. Our study offers a route to simulate novel valley phenomena predicted in gapped graphene and other 2D materials with classical acoustic waves.
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A paper by Mischaikow and Nanda [14] uses filtered acyclic matchingsto form a Morse filtration for a filtered complex. The Morse filtration is smallerin size, yet has persistent homology equivalent to that of the original. We give anextension of acyclic matchings to the case of zigzag complexes and prove that theMorse zigzag complex similarly obtained has zigzag homology isomorphic to thatof the original. We present an algorithm to compute a Morse zigzag complex for agiven zigzag complex and some numerical examples. Since the Morse zigzag complexis smaller in size, calculations of its zigzag homology tend to complete faster thanthose for the original zigzag complex.DOI : http://dx.doi.org/10.22342/jims.20.1.177.47-75
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We realize an elastic second-order topological insulator hosting both one-dimensional gapped edge states and zero-dimensional in-gap corner modes in the double-sided pillared phononic crystal plates with square lattice. Changing the width of two neighbor pillars breaks the inversion symmetry and induces the band inversion to emulate the quantum spin Hall effect where the gapless edge states are obtained. Further breaking the space-symmetry at interface, the gapless edge states are gapped and inducing the edge topological transitions and then giving rise to the zero-dimensional in-gap corner modes. Our work offers a novel way for elastic wave trapping and robustly guiding.
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Gapless criteria that can efficiently determine whether a crystal is gapless or not are particularly useful for identifying topological semimetals. In this work, we propose a sufficient gapless criterion for three-dimensional noninteracting crystals, based on the simplified expressions for the bulk average value of the static axion field. The brief logic is that two different simplified expressions give the same value in an insulator, and thus the gapless phase can be detected by the mismatch of them. We demonstrate the effectiveness of the gapless criterion in the magnetic systems with space groups 26 and 13, where mirror, glide, and inversion symmetries provide the simplified expressions. In particular, the gapless criterion can identify gapless phases that are missed by the symmetry-representation approach, as illustrated by space group 26. Our proposal serves as a guiding principle for future discovery of topological semimetals.
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