Finite wave number instability interrupts motility-induced phase separation

Motility-induced phase separation (MIPS) is one of the intriguing findings in active colloidal systems, which has been widely studied in the content of active Brownian particles (ABPs) model. However, ABPs fails describing the effect of the intrinsic curvature and chirality properties of many active units, such as some bacteria, and self-propelled particles with asymmetric shape. Therefore, self-propulsion torque is introduced in the circle-ABPs (cABPs) model. In this work, we formulate a continuum theory for cABPs, and the fluctuation dispersion relation reveals two types of instabilities, i.e. at low torque intensity, type I instability refers to the zero wave number starting unstable mode inducing the MIPS; for large enough torque, type II instability refers to the finite wave number starting unstable modes, which results in the dynamical clustering state and interrupts the conventional MIPS. Besides, by measuring the self intermediate scattering function, we qualitatively verifies the dispersion relation derived and identify the dynamic properties of the dynamical clustering state. The main conclusion of this work is that the finite-wave number instability results in a dynamical clustering state and interrupts MIPS.