Designing active topological networks

Mechanical and phononic metamaterials with exotic characteristics, including negative elastic moduli or
negative effective mass density, allow for precise control of mechanical functionality. Materials possessing
spectral bandgaps are particularly interesting due to their ability to host topological edge modes that
enable robust signal transmission even in the presence of defects. Active matter can induce and
carry such topological modes through its inherent breaking of time-reversal symmetry. Here, I will present recent
work by our group that aims at harnessing interactions between activity and topology to realize
autonomously acting metamaterials. Specifically, we show how one can program desired spectral properties
such as bandgaps directly into mechanical networks, and thus control topological excitations when
time-reversal symmetry is broken. Furthermore, we demonstrate how these ideas can be generalized
to design active electronic circuits that can self-select and sustain topological modes and how topology can
be used to construct other precisely controllable current patterns.