  We uncover a remarkable quantum scattering phenomenon in two-dimensional
Dirac material systems where the manifestations of both classically integrable
and chaotic dynamics emerge simultaneously and are electrically controllable.
The distinct relativistic quantum fingerprints associated with different
electron spin states are due to a physical mechanism analogous to chiroptical
effect in the presence of degeneracy breaking. The phenomenon mimics a chimera
state in classical complex dynamical systems but here in a relativistic quantum
setting - henceforth the term "Dirac quantum chimera," associated with which
are physical phenomena with potentially significant applications such as
enhancement of spin polarization, unusual coexisting quasibound states for
distinct spin configurations, and spin selective caustics. Experimental
observations of these phenomena are possible through, e.g., optical
realizations of ballistic Dirac fermion systems.
