Pivoting colloidal assemblies exhibit mechanical metamaterial behaviour.

Biological machines use targeted deformations that can be actuated by Brownian fluctuations. However, although synthetic micromachines can similarly make use of targeted deformations, they are too stiff to be driven by thermal fluctuations and require strong forcing1-3. Furthermore, systems that are able to change their conformation by thermal fluctuations do so uncontrollably4,5 or require external control6. Here we use DNA-based sliding contacts7-9 to create colloidal pivots, rigid anisotropic objects that freely fluctuate around their pivot point and use a hierarchical strategy to assemble these into Brownian metamaterials with targeted deformation modes. We realize the archetypical rotating diamond and rotating triangle, or kagome, geometries and quantitatively show how thermal fluctuations drive their predicted auxetic deformations10-15. Finally, we implement magnetic particles into the colloidal pivots to achieve colloidal metamaterials that can be controlled externally as well as use Brownian fluctuations for precisely controlled shape changes. Together, our work introduces a strategy for creating Brownian mechanical metamaterials with easily actuatable deformation modes.