Hall resistivity and dephasing in the quantum Hall insulator

The long-standing problem of the Hall resistivity rho(xy) 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(xy) scales with the longitudinal resistivity rho(xx), and they both diverge exponentially with the dephasing length. In the Ohmic limit (where the dephasing length is shorter than the Hall puddle size), rho(xy). remains quantized and independent of rho(xx). This suggests a new experimental probe for dephasing processes. [S0031-9007(99)08338-3].