  We theoretically study the nature of parametrically driven dissipative Kerr
soliton (PD-DKS) in a doubly resonant degenerate micro-optical parametric
oscillator (DR-D{\mu}OPO) with the cooperation of \c{hi}(2) and \c{hi}(3)
nonlinearities. Lifting the assumption of close-to-zero group velocity mismatch
(GVM) that requires extensive dispersion engineering, we show that there is a
threshold GVM above which single PD-DKS in DR-D{\mu}OPO can be generated
deterministically. We find that the exact PD-DKS generation dynamics can be
divided into two distinctive regimes depending on the phase matching condition.
In both regimes, the perturbative effective third-order nonlinearity resulting
from the cascaded quadratic process is responsible for the soliton annihilation
and the deterministic single PD-DKS generation. We also develop the
experimental design guidelines for accessing such deterministic single PD-DKS
state. The working principle can be applied to different material platforms as
a competitive ultrashort pulse and broadband frequency comb source architecture
at the mid-infrared spectral range.
