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A multicomponent mixture of Janus colloids with distinct catalytic coats and phoretic mobilities is a promising theoretical system to explore the collective behavior arising from nonreciprocal interactions. An active colloid produces (or consumes) chemicals, self-propels, drifts along chemical gradients, and rotates its intrinsic polarity to align with a gradient. As a result the connection from microscopics to continuum theories through coarse-graining couples densities and polarization fields in unique ways. Focusing on a binary mixture, we show that these couplings render the unpatterned reference state unstable to small perturbations through a variety of instabilities including oscillatory ones which arise on crossing an exceptional point or through a Hopf bifurcation. For fast relaxation of the polar fields, they can be eliminated in favor of the density fields to obtain a microscopic realization of the Nonreciprocal Cahn–Hilliard model for two conserved species with two distinct sources of non-reciprocity, one in the interaction coefficient and the other in the interfacial tension. Our work establishes Janus colloids as a versatile model for a bottom-up approach to both scalar and polar active mixtures.

We study theoretically an active colloid whose polar axis of self-propulsion rotates to point parallel (antiparallel) to an imposed chemical gradient. We show that the coupling of this ‘chemotactic’ (‘antichemotactic’) response to phoretic translational motion yields remarkable two-particle dynamics reflecting the non-central and non-reciprocal character of the interaction. A pair of mutually chemotactic colloids trap each other in a final state of fixed separation resulting in a self-propelled active dimer. A second type of bound state is observed when the polar axes undergo periodic cycles leading to phase-locked circular motion around a common centre. A pair of swimmers with mismatched phoretic mobilities execute a dance in which they twirl around one another while moving jointly in a wide circle. For sufficiently small initial separation, the speed of self-propulsion controls the transition from bound to scattering states. Mutually anti-chemotactic swimmers always scatter apart. For the special case in which one of the two colloids has uniform surface activity we succeed in exactly classifying the fixed points underlying the bound states, and identify the bifurcations leading to transitions from one type of bound state to another. The varied dynamical behaviours are accessible by tuning the swimmer design and are summarised in state diagrams.