Topological mechanics of gyroscopic metamaterials

Abstract

Topological mechanical metamaterials are artificial structures whose unusual properties are protected very much like their electronic and optical counterparts. Here, we present an experimental and theoretical study of an active metamaterial-composed of coupled gyroscopes on a lattice-that breaks time-reversal symmetry. The vibrational spectrum displays a sonic gap populated by topologically protected edge modes that propagate in only one direction and are unaffected by disorder. We present a mathematical model that explains how the edge mode chirality can be switched via controlled distortions of the underlying lattice. This effect allows the direction of the edge current to be determined on demand. We demonstrate this functionality in experiment and envision applications of these edge modes to the design of oneway acoustic waveguides.topological mechanics | gyroscopic metamaterial | metamaterial A vast range of mechanical structures, including bridges, covalent glasses, and conventional metamaterials, can be ultimately modeled as networks of masses connected by springs (1-6). Recent studies have revealed that despite its apparent simplicity, this minimal setup is sufficient to construct topologically protected mechanical states (7-11) that mimic the properties of their quantum analogs (12). This follows from the fact that, irrespective of its classic or quantum nature, a periodic material with a gapped spectrum of excitations can display topological behavior as a result of the nontrivial topology of its band structure (13-21).All such mechanical systems, however, are invariant under time reversal because their dynamics are governed by Newton's second law, which, unlike the Schrödinger equation, is second order in time. If time-reversal symmetry is broken, as in recently suggested acoustic structures containing circulating fluids (16), theoretical work (13) has suggested that phononic chiral topological edge states that act as unidirectional waveguides resistant to scattering off impurities could be supported. In this paper, we show that by creating a coupled system of gyroscopes, a "gyroscopic metamaterial," we can produce an effective material with intrinsic time-reversal symmetry breaking. As a result, our gyroscopic metamaterials support topological mechanical modes analogous to quantum Hall systems, which have robust chiral edge states (22)(23)(24). We demonstrate these effects by building a real system of gyroscopes coupled in a honeycomb lattice. Our experiments show long-lived, unidirectional transport along the edge, even in the presence of significant defects. Moreover, our theoretical analysis indicates that direction of edge propagation is controlled both by the gyroscope spin and the geometry of the underlying lattice. As a result, deforming the lattice of gyroscopes allows one to control the edge mode direction, offering unique opportunities for engineering novel materials.Much of the counterintuitive behavior of rapidly spinning objects originates from their large angular momentum, which endows th...

Front Matter

“…Now there seems to be a similar migration of ideas from people who have studied topological insulators in the context of the quantum 2D Hall effect to the study of similar effects in man-made periodic structures where there is some time-symmetry breaking. In the context of elasticity this time-symmetry breaking can be achieved with gyroscopic metamaterials [2] and, most significantly, waves can only travel in one direction around the boundary.…”

Geometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlattice

“…Energy can also be added to extrinsic topological elastic systems to break time reversal symmetry. [20][21][22][23][24][25][26] For example, we have considered the externally-driven periodic spatial modulation of the stiffness of a one-dimensional elastic medium and its directed temporal evolution to break symmetry. 26 The bulk elastic states of this time-dependent super-lattice possess non-conventional topological characteristics leading to non-reciprocity in the direction of propagation of the waves.…”

Topological Edge Floppy Modes in Disordered Fiber Networks

“…Introduction -Recent theoretical advances in applying concepts of topological states of matter to mechanical systems has led to the burgeoning new field of "topological mechanics", where nontrivial topologies of the phonon bands give rise to exotic mechanical and acoustic properties [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”