Universal Scaling of Strong-Field Localization in an Integer Quantum Hall Liquid

TL;DR

This study investigates how disorder and magnetic fields influence electron localization in quantum Hall systems, revealing that potential range and Landau level mixing are crucial for universal behavior.

Contribution

It provides a comprehensive finite-size scaling analysis of localization in disordered quantum Hall systems, emphasizing the effects of disorder potential range and Landau level coupling.

Findings

Pure delta-function disorder leads to non-universal localization exponents.

Finite potential range and Landau level mixing can restore universality.

Large system sizes improve the accuracy of critical exponent estimation.

Abstract

We study the Landau level localization and scaling properties of a disordered two-dimensional electron gas in the presence of a strong external magnetic field. The impurities are treated as random distributed scattering centers with parameterized potentials. Using a transfer matrix for a finite-width strip geometry, we calculate the localization length as a function of system size and electron energy. The finite-size localization length is determined by calculating the Lyapunov exponents of the transfer matrix. A detailed finite-size scaling analysis is used to study the critical behavior near the center of the Landau bands. The influence of varying the impurity concentration, the scattering potential range and its nature, and the Landau level index on the scaling behavior and on the critical exponent is systematically investigated. Particular emphasis is put on studying the effects of finite range of the disorder potential and Landau level coupling on the quantum localization behavior. Our numerical results, which are carried out on systems much larger than those studied before, indicate that pure $\delta$-function disorder in the absence of any Landau level coupling gives rise to non-universal localization properties with the critical exponents in the lowest two Landau levels being substantially different. Inclusion of a finite potential range and/or Landau level mixing may be essential in producing universality in the localization.