Emulation of π-Electron Systems with Mechanical Waves: Borazine

R.A. Méndez-Sáncheza, A.E. Terán-Juáreza, A.M. Martínez-Argüelloa, E. Flores-Olmedob, G. Báezb, E. Sadurníc, Y. Hernández-Espinosad aInstituto de Ciencias Físicas, Universidad Nacional Autónoma de México, P.O. Box 48-3, 62251 Cuernavaca, Mor. Mexico bDepartamento de Ciencias Básicas, Universidad Autònoma Metropolitana-Azcapotzalco, Av. San Pablo 180, Col. Reynosa Tamaulipas, 02200, Ciudad de México, Mexico cBenemérita Universidad Autónoma de Puebla, Instituto de Física, Apartado Postal J-48, 72570 Puebla, Mexico dUniversidad Nacional Autónoma de México, Instituto de Física, Apartado Postal 20-364, CDMX 01000, Mexico

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Elastic waves have emerged as a paradigm of condensed matter physics since many dynamical effects of the latter can be emulated with these waves. Molecular π-orbitals are of great interest in this area because they play a key role in the electronic transport of 2D materials and aromatic molecules such as benzene and borazine. In this work, we show the design, construction and characterization of an elastic, artificial borazine structure that emulates the π-orbitals of borazine. The elastic structure consists of hexagonal resonators that act as artificial elastic atoms coupled to each other through finite phononic crystals that in turn act as artificial π bonds. When the resonant frequency of an artificial atom falls within the gap of the phononic crystal, the vibrations are trapped in the artificial atom and interact weakly with neighboring artificial atoms through evanescent Bloch waves. Thus, a tight-binding regime for elastic waves emerges. Here, these ideas are applied to emulate the π-orbitals of borazine. The design relies on extensive finite element numerical simulations. The experimental results show an excellent agreement with both, the tight-binding formalism and the numerical results.

DOI:10.12693/APhysPolA.140.532 topics: aromatic molecules, finite groups, atomic orbitals, tight-binding models