  High-precision isotopic measurements of meteorites revealed that they are
classified into non-carbonaceous (NC) and carbonaceous (CC) meteorites. One
plausible scenario for achieving this grouping is the early formation of
Jupiter because massive planets can create gaps that suppress the mixing of
dust across the gap in protoplanetary disks. However, the efficiency of this
suppression by the gaps depends on dust size and the strength of turbulent
diffusion, allowing some fraction of the dust particles to leak across the
Jovian gap. In this study, we investigate how isotopic ratios of NC and CC
meteorites are varied by the dust leaking across the Jovian gap in the solar
nebula. To do this, we constructed a model to simulate the evolution of the
dust size distribution and the $^{54}$Cr-isotopic anomaly $\varepsilon^{54}$Cr
in isotopically heterogeneous disks with Jupiter. Assuming that the parent
bodies of NC and CC meteorites are formed in two dust-concentrated locations
inside and outside Jupiter's orbit, referred to as the NC reservoir and CC
reservoir, we derive the temporal variation of $\varepsilon^{54}$Cr at the NC
and CC reservoir. Our results indicate that substantial contamination of CC
materials occurs at the NC reservoir in the fiducial run. Nevertheless, the
values of $\varepsilon^{54}$Cr at the NC reservoir and the CC reservoir in the
run are still consistent with those of NC and CC meteorites formed around 2
Myrs after the formation of calcium-aluminum-rich inclusions. Moreover, this
dust leakage causes a positive correlation between the $\varepsilon^{54}$Cr
value of NC meteorites and the accretion ages of their parent bodies.
