Modeling chiral active particles. From circular motion to odd interactions

In this paper, we discuss microscopic models for chiral active particles, i.e. rotating active units that exhibit circular or spinning motion. While non-chiral active particles are typically governed by self-propulsion and conservative interactions, the rotating motion of chiral particles generates additional non-conservative forces that cannot be derived from a potential. These manifest as effective transverse forces, acting perpendicular to the line connecting the centers of two interacting particles, and are referred to as odd interactions, because they break the mirror symmetry of the system. Here, we demonstrate that odd interactions arise from a limiting case of a well-established model describing spinning granular objects. In addition, we show that these models for chiral active objects give rise to a novel collective phenomenon that emerges uniquely from transverse forces and, hence, chirality. Specifically, the system undergoes a transition from a homogeneous phase to an inhomogeneous one characterized by regions depleted of particles, referred to as bubbles. This collective behavior, termed bubbles induced by odd (BIO) interactions, is a general emergent phenomenon arising from chirality and odd interactions. In this work, we review theoretical approaches to this problem, including a scaling argument and predictions for spatial velocity correlations that account for the BIO phase. Finally, we outline perspectives and open challenges concerning this collective phenomenon.