  We consider the effect of a local interatomic repulsion on synthetic
heterostructures where a discrete synthetic dimension is created by Raman
processes on top of $SU(N)$-symmetric two-dimensional lattice systems. At a
filling of one fermion per site, increasing the interaction strength, the
system is driven towards a Mott state which is adiabatically connected to a
band insulator. The chiral currents associated with the synthetic magnetic
field increase all the way to the Mott transition, where they reach the maximum
value, and they remain finite in the whole insulating state. The transition
towards the Mott-band insulator is associated with the opening of a gap within
the low-energy quasiparticle peak, while a mean-field picture is recovered deep
in the insulating state.
