Quasiclassical approach to the weak levitation of extended states in the quantum Hall effect

TL;DR

This paper uses a quasiclassical approach to analyze the weak levitation of extended states in the quantum Hall effect, showing it remains weak at low magnetic fields and suggesting a different mechanism for strong levitation at even lower fields.

Contribution

The paper extends previous work by calculating the weak levitation effect at lower magnetic fields using a quasiclassical method.

Findings

Weak levitation remains small down to the lowest valid magnetic field.

Near the minimum magnetic field, weak levitation is further suppressed.

Strong levitation at lower fields likely has a different origin.

Abstract

The two-dimensional motion of a charged particle in a random potential and a transverse magnetic field is believed to be delocalized only at discrete energies $E_N$. In strong fields there is a small positive deviation of $E_N$ from the center of the $N$th Landau level, which is referred to as the ``weak levitation'' of the extended state. I calculate the size of the weak levitation effect for the case of a smooth random potential re-deriving earlier results of Haldane and Yang [PRL 78, 298 (1997)] and extending their approach to lower magnetic fields. I find that as the magnetic field decreases, this effect remains weak down to the lowest field $B_{min}$ where such a quasiclassical approach is still justified. Moreover, in the immediate vicinity of $B_{min}$ the weak levitation becomes additionally suppressed. This indicates that the ``strong levitation'' expected at yet even lower magnetic fields must be of a completely different origin.