Wigner crystalline edges in ν≲1 quantum dots

We investigate the edge reconstruction phenomenon believed to occur in quantum dots in the quantum Hall regime when the filling fraction is $\nu \lesssim 1.$ 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 wave functions 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.