Hierarchical Wigner Crystal at the Edge of Quantum Hall Bar

TL;DR

This paper reveals that quasiholes near the edge of an incompressible Quantum Hall state form a complex hierarchical Wigner structure influenced by electrostatic constraints, deviating from a regular lattice.

Contribution

It introduces the concept of a hierarchical Wigner crystal structure of quasiholes at the Quantum Hall edge, highlighting their complex dislocation patterns.

Findings

Quasiholes form a Wigner structure near the edge.

Density of quasiholes is set by electrostatics and varies with distance.

The arrangement is a complex hierarchy, not a regular lattice.

Abstract

We show that quasiholes persist near the edge of incompressible Quantum Hall state forming a Wigner structure. The average density of quasiholes is fixed by electrostatics and decreases slowly with increasing distance from the edge. As we see from elementary reasoning, their specific arrangement can not be a regular Wigner lattice and shows a complex hierarchical structure of dislocations.