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

TL;DR

This paper proposes that a perfect crystalline insulator ring can support a persistent current due to atomic orbital overlaps, challenging the conventional understanding that insulators do not support such currents.

Contribution

It introduces a theoretical model showing that insulator rings can sustain persistent currents because of orbital overlaps, even at full valence band filling.

Findings

Persistent current can exist in insulating rings due to atomic orbital overlaps.

In the tight-binding limit, the persistent current at full filling becomes zero.

The model demonstrates a nonzero current in ideal crystalline insulators.

Abstract

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.