Flux induced semiconducting behavior of a quantum network

We show that a diamond shaped periodic network, recently proposed as a model of a spin filter (A. Aharony {\em et al.} \cite{aharon08}) is capable of behaving as a p-type or an n-type semiconductor depending on a suitable choice of the on-site potentials of the atoms occupying the vertices of the lattice, and the strength of the magnetic flux threading each plaquette of the network. A detailed study of the density of states of an infinite network is made together with the conductance of finite sized system to establish the idea.