Visibility diagrams and experimental stripe structure in the quantum Hall effect

TL;DR

This paper investigates visibility diagrams in the quantum Hall effect, linking their structure to experimental observations and revealing new properties related to modular symmetries and stripe formations.

Contribution

It provides a physical interpretation of visibility diagrams that explains experimental features and uncovers new subgroup-related properties in the quantum Hall context.

Findings

Visibility diagrams can describe the architecture of quantum Hall states.

Stripe structures in the diagrams match experimental quantum Hall fluctuations.

New properties of diagrams are linked to subgroups of the modular group.

Abstract

We analyze various properties of the visibility diagrams that can be used in the context of modular symmetries and confront them to some recent experimental developments in the Quantum Hall Effect. We show that a suitable physical interpretation of the visibility diagrams which permits one to describe successfully the observed architecture of the Quantum Hall states gives rise naturally to a stripe structure reproducing some of the experimental features that have been observed in the study of the quantum fluctuations of the Hall conductance. Furthermore, we exhibit new properties of the visibility diagrams stemming from the structure of subgroups of the full modular group.