Quantization of the diagonal resistance: Density gradients and the empirical resistance rule in a 2D system

TL;DR

This paper demonstrates that the quantization of diagonal resistance in quantum Hall states can be explained by electron density gradients, challenging the traditional view that it reflects diagonal resistivity.

Contribution

It reveals that R_xx quantization is governed by density gradients and R_xy, providing a new understanding of the empirical resistivity rule in 2D systems.

Findings

R_xx quantization aligns with differences in R_xy at quantum Hall edges.

Density gradients (~1%/cm) explain R_xx features quantitatively.

R_xx is unrelated to the diagonal resistivity rho_xx.

Abstract

We have observed quantization of the diagonal resistance, R_xx, at the edges of several quantum Hall states. Each quantized R_xx value is close to the difference between the two adjacent Hall plateaus in the off-diagonal resistance, R_xy. Peaks in R_xx occur at different positions in positive and negative magnetic fields. Practically all R_xx features can be explained quantitatively by a ~1%/cm electron density gradient. Therefore, R_xx is determined by R_xy and unrelated to the diagonal resistivity rho_xx. Our findings throw an unexpected light on the empirical resistivity rule for 2D systems.