Experimental Studies of Scaling Behavior of a Quantum Hall System with a Tunable Landau Level Mixing

TL;DR

This study investigates how Landau level mixing affects the scaling behavior of quantum Hall systems, revealing that certain critical exponents remain universal despite changes in degeneracy.

Contribution

It provides experimental evidence that the scaling exponents in quantum Hall systems are universal and unaffected by Landau level mixing for a fixed disorder profile.

Findings

The localization exponent $oldsymbol{\gamma}$ is universal across filling factors.

The scaling exponent $oldsymbol{\kappa}$ remains constant despite Landau level mixing.

Landau level mixing does not alter the critical scaling behavior for a fixed disorder profile.

Abstract

Temperature dependence of the longitudinal and Hall resistance is studied in the regime of localization-delocalization transition. We carry out measurements of a scaling exponent $\kappa$ in the Landau level mixing region at several filling factors. The localization exponent $\gamma$ is extracted using an approach based on the variable range hopping theory. The values of $\gamma$ and $\kappa$ are found to be universal, independent of filling factor in our sample. We can conclude that although Landau level mixing can change the degeneracy of a quantum Hall state, the value of the scaling exponent remains the same for a given sample that contains a fixed disorder profile.