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

TL;DR

This paper investigates a honeycomb quantum wire network with Y-junctions, revealing a regime where the Hall resistance is quantized at h/e^2 while the longitudinal resistivity remains finite, demonstrating robust quantum transport properties.

Contribution

It introduces a classical network model derived from quantum fixed points showing quantized Hall resistance without zero longitudinal resistivity.

Findings

Hall resistance quantized at Rxy=h/e^2

Longitudinal resistivity remains non-zero

Robust against disorder in interaction parameters

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 x 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 3-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 Rxy=h/e^2, although the longitudinal resistivity is non-vanishing. We show that these results are robust against disorder, in this case non-homogeneous interaction parameters g for the different wires in the network.