Fossati Michele, Scheibner Colin, Fruchart Michel, Vitelli Vincenzo
SISSA, Trieste 34136, Italy.
INFN Sezione di Trieste, Trieste 34127, Italy.
Phys Rev E. 2024 Feb;109(2-1):024608. doi: 10.1103/PhysRevE.109.024608.
Odd elasticity describes active elastic systems whose stress-strain relationship is not compatible with a potential energy. As the requirement of energy conservation is lifted from linear elasticity, new antisymmetric (odd) components appear in the elastic tensor. In this work we study the odd elasticity and non-Hermitian wave dynamics of active surfaces, specifically plates of moderate thickness. These odd moduli can endow the vibrational modes of the plate with a nonzero topological invariant known as the first Chern number. Within continuum elastic theory, we show that the Chern number is related to the presence of unidirectional shearing waves that are hosted at the plate's boundary. We show that the existence of these chiral edge waves hinges on a distinctive two-step mechanism. Unlike electronic Chern insulators where the magnetic field at the same time gaps the spectrum and imparts chirality, here the finite thickness of the sample gaps the shear modes, and the odd elasticity makes them chiral.
奇弹性描述的是应力-应变关系与势能不相容的主动弹性系统。由于线性弹性中能量守恒的要求被解除，弹性张量中出现了新的反对称（奇）分量。在这项工作中，我们研究了主动表面的奇弹性和非厄米波动动力学，特别是中等厚度的板。这些奇模量可以赋予板的振动模式一个非零的拓扑不变量，称为第一陈数。在连续介质弹性理论中，我们表明陈数与板边界处存在的单向剪切波有关。我们表明，这些手性边缘波的存在取决于一种独特的两步机制。与电子陈绝缘体不同，在电子陈绝缘体中磁场同时使能谱带隙并赋予手性，而在这里样品的有限厚度使剪切模式带隙，并且奇弹性使它们具有手性。
