Manipulation of circular currents in a coupled ring system: effects of connectivity and non-uniform disorder

Considering a quantum network, here we propose two kinds of circular charge currents. These are referred as: net current in the full system and the current confined within a particular segment of the network. The network is composed of two rings, where one of the rings is subjected to a magnetic flux. Depending on the connectivity among the rings a new kind of states, insensitive to the magnetic flux, is generated along with the current carrying states. Because of this, a pronounced oscillation in net current with filling factor appears which suggests a possible switching action. Appearance of these vanishing current carrying states gradually decreases with increasing the degree of connectivity between the rings. As long as the rings are coupled by using more than a single bond, a circular current of other kind appears in the flux free ring which induces a strong magnetic field. The strength of this induced magnetic field can be regulated selectively by tuning the magnetic flux in the other ring. This phenomenon can be utilized for spin switching and other spintronic applications. Finally, we examine the role of non-uniform disorder on these currents, and find several atypical signatures. Our study can be generalized to any higher loop system for investigating magneto-transport properties.