Networks of quantum wire junctions: A system with quantized integer Hall resistance without vanishing longitudinal resistivity

Abstract

We consider a honeycomb network built of quantum wires, with each node of the network having a Y junction of three wires with a ring through which flux can be inserted. The junctions are the basic circuit elements for the network, and they are characterized by $3\ifmmode\times\else\texttimes\fi{}3$ conductance tensors. The low energy stable fixed point tensor conductances result from quantum effects, and are determined by the strength of the interactions in each wire and the magnetic flux through the ring. We consider the limit where there is decoherence in the wires between any two nodes, and study the array as a network of classical three-lead circuit elements whose characteristic conductance tensors are determined by the quantum fixed point. We show that this network has some remarkable transport properties in a range of interaction parameters: It has a Hall resistance quantized at ${R}_{xy}=h/{e}^{2}$, although the longitudinal resistivity is nonvanishing. We show that these results are robust against disorder, in this case nonhomogeneous interaction parameters $g$ for the different wires in the network.