Spectral weight transfer in a disorder-broadened Landau level

TL;DR

This paper investigates how disorder affects the spectral distribution of Landau levels in quantum Hall systems, revealing that new localized states predominantly emerge within the critical delocalized region, explaining observed experimental phenomena.

Contribution

It demonstrates that localized states in disordered Landau levels appear mainly within the critical region, providing a spectral ordering explanation for experimental observations without interactions.

Findings

Localized states appear mainly inside the critical region.

Spectral ordering explains observed quantum Hall phenomena.

Results align with measurements of compressibility and conductance.

Abstract

In the absence of disorder, the degeneracy of a Landau level (LL) is $N=BA/\phi_0$, where $B$ is the magnetic field, $A$ is the area of the sample and $\phi_0=h/e$ is the magnetic flux quantum. With disorder, localized states appear at the top and bottom of the broadened LL, while states in the center of the LL (the critical region) remain delocalized. This well-known phenomenology is sufficient to explain most aspects of the Integer Quantum Hall Effect (IQHE) [1]. One unnoticed issue is where the new states appear as the magnetic field is increased. Here we demonstrate that they appear predominantly inside the critical region. This leads to a certain ``spectral ordering'' of the localized states that explains the stripes observed in measurements of the local inverse compressibility [2-3], of two-terminal conductance [4], and of Hall and longitudinal resistances [5] without invoking interactions as done in previous work [6-8].