Wigner Crystalline Edges in nu < 1 Quantum Dots

TL;DR

This paper studies edge reconstruction in quantum dots under quantum Hall conditions for filling factors less than one, revealing the formation of Wigner crystalline edges through a novel partial diagonalization approach.

Contribution

It introduces a partial diagonalization method and the concept of projected necklace states to analyze edge structures in quantum dots at nu<1, showing high overlap with ground states.

Findings

PN states have up to 99% overlap with ground states.

PN states are energetically favorable over previous models.

Edge reconstruction involves Wigner crystalline structures.

Abstract

We investigate the edge reconstruction phenomenon believed to occur in quantum dots in the quantum Hall regime when the filling fraction is nu < 1. Our approach involves the examination of large dots (< 40 electrons) using a partial diagonalization technique in which the occupancies of the deep interior orbitals are frozen. To interpret the results of this calculation, we evaluate the overlap between the diagonalized ground state and a set of trial wavefunctions which we call projected necklace (PN) states. A PN state is simply the angular momentum projection of a maximum density droplet surrounded by a ring of localized electrons. Our calculations reveal that PN states have up to 99% overlap with the diagonalized ground states, and are lower in energy than the states identified in Chamon and Wen's study of the edge reconstruction.