Duality,Hidden Symmetry and Dynamic Isomerism in 2D Hinge Structures

Abstract

Recently, a new type of duality was reported in some deformable mechanical networks which exhibit Kramers-like degeneracy in phononic spectrum at the self-dual point. In this work, we clarify the origin of this duality and propose a design principle of 2D self-dual structures with arbitrary complexity. We find that this duality originates from the (PCI) symmetry of the hinge, which belongs to a more general end-fixed scaling transformation. This symmetry gives the structure an extra degree of freedom without modifying its dynamics. This results in , i.e., dissimilar 2D mechanical structures, either periodic or aperiodic, having identical dynamic modes, based on which we demonstrate a new type of wave-guide without reflection or loss. Moreover, the PCI symmetry allows us to design various 2D periodic isostatic networks with hinge duality. At last, by further studying a 2D non-mechanical magnonic system, we show that the duality and the associated hidden symmetry should exist in a broad range of Hamiltonian systems.

6 pages, 4 figures

References in corpus (6)

• Elasticity and Response in Nearly Isostatic Periodic Lattices
• Quasi-symmetry protected topology in a semi-metal
• Existence of Corner Modes in Elastic Twisted Kagome Lattices
• Hidden antiunitary symmetry behind "accidental" degeneracy and its protection of degeneracy
• Hidden-symmetry-protected Z_2 topological insulator in a cubic lattice
• Self-duality triggered dynamical transition

Cited by in corpus (5)

• Fully-Polarized Topological Isostatic Metamaterials in Three Dimensions
• All hourglass bosonic excitations in the 1651 magnetic space groups and 528 magnetic layer groups
• Symmetry-driven Phononic Metamaterials
• Non-local twist sequences in floppy kagome chains
• Transformable Super-Isostatic Crystals Self-Assembled from Segment Colloidal Rods