  Since the chiral-induced spin selectivity (CISS) was first observed
experimentally, its microscopic mechanism has been continuously explored by the
scientific community. Among these investigations, the non-equilibrium effects
and the unknown origins of spin-orbit coupling (SOC) have been the central
issues discussed in recent years. Here, we have achieved a persistent spin
current in different circular single-helix molecule driven by a magnetic field,
which is inherently linked to the equilibrium state associated with chirality.
Due to its measurement method being different from the transport currents
observed in previous experiments, the origin of its spin-orbit coupling can be
explored by modifying the substrate with different light and heavy metal
elements. Our results demonstrate that a persistent spin current can be
observed regardless of whether the SOC originates from the chiral molecule or
the substrate. Furthermore, by tuning the direction of the magnetic field, we
can achieve a phase transition between trivial and non-trivial chiral
persistent spin currents. Our work provides a new perspective and platform for
exploring the nature of CISS and controlling the effects of CISS.

Mesoscale and Nanoscale Physics