Weakly chiral networks and 2D delocalized states in a weak magnetic field

TL;DR

This paper introduces weakly chiral network models to analyze 2D electron localization in weak magnetic fields, revealing a phase diagram consistent with the levitation scenario and confirming the robustness of delocalization transitions.

Contribution

The study develops novel weakly chiral network models separating magnetic field effects, linking percolation theory with quantum Hall transition behavior in weak fields.

Findings

Phase diagram aligns with levitation scenario.

Quantum Hall transition points match percolation predictions.

Time reversal symmetry does not affect delocalization lines.

Abstract

We study the localization properties of two-dimensional electrons in a weak perpendicular magnetic field. For this purpose we construct weakly chiral network models on the square and triangular lattices, by separating in space the regions with phase action of magnetic field, where it affects interference in course of disorder scattering, and the regions with orbital action of magnetic field, where it bends electron trajectories. In our models, the disorder mixes counter-propagating channels on the links, while scattering at the nodes describes the bending of electron trajectories. By introducing a strong spread in the scattering strengths on the links, we eliminate the interference and reduce the electron propagation over a network to a percolation problem. In this limit we establish the form of the disorder vs. magnetic field phase diagram, which is in agreement with levitation scenario: energy separating the Anderson and quantum Hall insulating phases floats up to infinity upon decreasing magnetic field. From numerical study we conclude that the positions of the weak-field quantum Hall transitions on the phase diagram are very close to our percolation results. We checked that, in accord with the Pruisken's theory, presence or absence of time reversal symmetry has no effect on the line of delocalization transitions.