R. Mahore

O. Gamayun

G. Noetinger

R. Fleury

C. Coulais

B. Apffel

A new metamaterial composed of oscillators driven by external pumping is used to study the unidirectional drift of stable phase dislocations.

A driven metamaterial is created from externally pumped oscillators to study dynamical frustration: a state in which competing dynamical constraints cannot be satisfied at once. It also produces stable phase defects that arise on their own, move in one direction and behave as dark solitons. In two dimensions, these defects synchronise across the material, opening routes to controllable waves and new mechanical logic. 

From spin ice and crumpled paper to cold atoms lattices and metamaterials, geometrical frustration occurs generically whenever local constraints cannot be satisfied all at once. The result is a ground state degeneracy, where many equivalent states, each of which contains unsatisfied constraints, coexist. Here, we introduce dynamical frustration, where the ground state degeneracy makes way to a non-reciprocal self-oscillating state instead. To create dynamical frustration, we construct metamaterials that are driven parametrically in time and modulated in space. The parametric pumping leads to period doubling and in turn to a discrete symmetry-breaking. This symmetry breaking, together with the spatial modulation enforces the existence of topologically protected phase dislocations, which propagate unidirectionally with a spontaneous phase that breaks a continuous symmetry. Tesselating 1d frustrated loops, one obtains a 2d metamaterial where phase dislocations self-organize into globally synchronized non-reciprocal phase defects. We expect dynamical frustration to be broadly applicable at any scale, from cold atoms and superconducting circuits to acoustics and RF circuits -- anywhere where space-time modulation can be pushed beyond linear stability.

Dynamical frustration

Dynamical frustration in space-time metamaterials