Hall resistivity and dephasing in the quantum Hall insulator

The long-standing problem of the Hall resistivity rho(xy) in the Hall insul ator phase is addressed using four-lead Chalker-Coddington networks. Electr on interaction effects are introduced via a finite dephasing length. In the quantum coherent regime, we find that rho(xy) scales with the longitudinal resistivity rho(xx), and they both diverge exponentially with the dephasin g length. In the Ohmic limit (where the dephasing length is shorter than th e Hall puddle size), rho(xy). remains quantized and independent of rho(xx). This suggests a new experimental probe for dephasing processes. [S0031-900 7(99)08338-3].