  A mesoscopic conducting ring pierced by magnetic flux is known to support the
persistent electron current. Here we propose possibility of the persistent
current in the ring made of the perfect crystalline insulator. We consider a
ring-shaped lattice of one-dimensional "atoms" with a single energy level. We
express the Bloch states in the lattice as a linear combination of atomic
orbitals. The discrete energy level splits into the energy band which serves as
a simple model of the valence band. We show that the insulating ring (with the
valence band fully filled by electrons) supports a nonzero persistent current,
because each atomic orbital overlaps with its own tail when making one loop
around the ring. In the tight-binding limit only the neighboring orbitals
overlap. In that limit the persistent current at full filling becomes zero
which is a standard result.
