Pfaffian and fragmented states atν=52in quantum Hall droplets

Abstract

When a gas of electrons is confined to two dimensions, application of a strong magnetic field may lead to startling phenomena such as emergence of electron pairing. According to a theory this manifests itself as appearance of the fractional quantum Hall effect with a quantized conductivity at an unusual half-integer ν = 5 2Landau level filling. Here we show that similar electron pairing may occur in quantum dots where the gas of electrons is trapped by external electric potentials into small quantum Hall droplets. However, we also find theoretical and experimental evidence that, depending on the shape of the external potential, the paired electron state can break down, which leads to a fragmentation of charge and spin densities into incompressible domains. The fragmentation of the quantum Hall states could be an issue in the proposed experiments that aim to probe for non-abelian quasi-particle characteristics of the ν = 5 2 quantum Hall state.

Effects of thickness in quantum dots in strong magnetic fields

“…In Ref. 10, the overlap of the corresponding states with the Pfaffian state was investigated and was found to peak high slightly below d = 2l for eight electrons. Interestingly, this ground state angular momentum is unstable when d ∈ [0.5l, 2.2l] indicating that, despite the high overlap, electron pairing is not energetically favorable in the lowest Landau level even if the thickness is optimized.…”

Semi‐local density functional for the exchange‐correlation energy of electrons in two dimensions

“…8 in Ref. [36]). Remarkably, the relative errors of the present functional and the LDA are only ∼0.1 % (note that in Ref.…”

“…Remarkably, the relative errors of the present functional and the LDA are only ∼0.1 % (note that in Ref. [36] a different DFT code was used producing a slightly larger error in the LDA). This test confirms that the present functional is valid also in relatively large 2D systems.…”

Formation of spin droplet atν=52in an asymmetric quantum dot under quantum Hall conditions

“…To calculate exchangecorrelation energy E xc , we use the local spin density approximation (LSDA) with a parametrization provided by Attaccalite et al 34 . The SDFT scheme together with LSDA leads to good numerical accuracy and produce reliable results in comparision with quantum Monte Carlo calculations in quantum dot systems 16,20,35 . In the SDFT calculations, we utilise the OCTOPUS 36,37 code package (published under the General Public License) built on the real space grid discretization method which allows realistic modeling of two dimensional systems.…”

“…Once the spin polarised electrons in the second lowest LL is localised to the centre of the QD emanating from exchange-correlation effects, they are called SD, which is a many-body phenomenon of interacting electrons 16,19,20 . Rasanen et al 16 show that theoretical evidence of SD formation in large (N 30) QDs at the filling factor range 2 < ν < 3 by using numerical many electron methods.…”