Topology of Fluctuation Bands in Chiral Active Crystals

Abstract

While band topology is usually associated with the deterministic dynamics of a system, we show that it can instead reside in its fluctuations. Using a reciprocal lattice driven by nonequilibrium chiral active noise, we find that the displacement spectrum---which quantifies displacement fluctuations---admits bands with nonzero Chern numbers despite a Chern-trivial deterministic mechanics. A two-band valley theory captures the emergence of this topology through a Dirac mass inversion, a Haldane-type mechanism, or a quadratic band touching, depending on the relevant transition. Through the bulk--boundary correspondence, we find boundary-localized fluctuation modes that are distinct from the usual propagating mechanical edge states.

arXiv commentstreamlined some derivations, added analytics for quadratic band touching