Short--range impurity in the vicinity of a saddle point and the levitation of the 2D delocalized states in a magnetic field

TL;DR

This paper investigates how short-range impurities near saddle points affect electron transmission in strong magnetic fields, revealing an average decrease in transmission and an upward levitation of delocalized states, with the shift increasing as magnetic field decreases.

Contribution

It introduces a model for impurity effects on electron states near saddle points, showing how impurities cause levitation of delocalized states in magnetic fields, a novel insight into quantum Hall physics.

Findings

Impurities reduce average transmission through saddle points.

Delocalized states shift upward in energy due to impurities.

The energy shift scales as B^{-4} with magnetic field.

Abstract

The effect of a short--range impurity on the transmission through a saddle--point potential for an electron, moving in a strong magnetic field, is studied. It is demonstrated that for a random position of an impurity and random sign of its potential the impurity--induced mixing of the Landau levels diminishes {\em on average} the transmission coefficient. This results in an upward shift (levitation) of the energy position of the delocalized state in a smooth potential. The magnitude of the shift is estimated. It increases with decreasing magnetic field $B$ as $B^{-4}$.