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.

arXiv comment6 pages, 4 figures

References in corpus (25)

• The (High Quality) Topological Materials In The World
• Catalogue of Topological Electronic Materials
• Topological Boundary Modes in Isostatic Lattices
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Isostaticity, auxetic response, surface modes, and conformal invariance in twisted kagome lattices
• Elasticity and Response in Nearly Isostatic Periodic Lattices
• Dualities and non-Abelian mechanics
• Minimal conductivity, topological Berry winding and duality in three-band semimetals
• Hidden-Symmetry-Protected Topological Semimetals on a Square Lattice
• Quasi-symmetry protected topology in a semi-metal
• Coherent potential approximation of random nearly isostatic kagome lattice
• Phonon analogue of topological nodal semimetals
• Topological mechanics in quasicrystals
• Self-assembly of three-dimensional open structures using patchy colloidal particles
• Hidden symmetries generate rigid folding mechanisms in periodic origami
• Simple views on symmetries and dualities in the theory of elasticity
• Universal Thermodynamic Signature of Self-dual Quantum Critical Points
• Existence of Corner Modes in Elastic Twisted Kagome Lattices
• Synthetic Kramers pair in phononic elastic plates and helical edge states on a dislocation interface
• Hidden antiunitary symmetry behind "accidental" degeneracy and its protection of degeneracy
• Symmetry of the phonon landscape across the duality boundary of twisted kagomes lattices
• Self-Assembly of Isostatic Self-Dual Colloidal Crystals
• Realizing negative Poisson's ratio in unstressed spring networks
• 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