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

Possible persistent current in a ring made of the perfect crystalline insulator