Hall Resistivity and Dephasing in the Quantum Hall Insulator

The longstanding problem of the Hall resistivity rho(x,y) in the Hall insulator phase is addressed using four-lead Chalker-Coddington networks. Electron interaction effects are introduced via a finite dephasing length. In the quantum coherent regime, we find that rho(x,y) scales with the longitudinal resistivity rho(x,x), and they both diverge exponentially with dephasing length. In the Ohmic limit, (dephasing length shorter than Hall puddles’ size), rho(x,y) remains quantized and independent of rho(x,x). This suggests a new experimental probe for dephasing processes.