Theoretical investigation of edge reconstruction in theν=52and73fractional quantum Hall states

Abstract

The edge physics of the ν = 5/2 fractional quantum Hall state is of relevance to several recent experiments that use it as a probe to gain insight into the nature of the bulk state. We perform calculations in a semi-realistic setup with positive background charge at a distance d, by exact diagonalization both in the full Hilbert space (neglecting Landau level mixing) and in the restricted Pfaffian basis of edge excitations. Our principal finding is that the 5/2 edge is unstable to a reconstruction except for very small d. In addition, the interactions between the electrons in the second Landau level and the lowest Landau level enhance the tendency toward edge reconstruction. We identify the bosonic and fermionic modes of edge excitations and obtain their dispersions by back-calculating from the energy spectra as well as directly from appropriate trial wave functions. We find that the edge reconstruction is driven by an instability in the fermionic sector for setback distances close to the critical ones. We also study the edge of the ν = 7/3 state and find that edge reconstruction occurs here more readily than for the ν = 1/3 state. Our study indicates that the ν = 5/2 and 7/3 edge states are reconstructed for all experimental systems investigated so far and thus must be taken into account when analyzing experimental results. We also consider an effective field theory to gain insight into how edge reconstruction might influence various observable quantities.

Identification of the fractional quantum Hall edge modes by density oscillations

“…As an application, this criterion helps us to identify the properties of the lowest reconstructed edge state in the MR edge spectrum as softening the positive background confinement. The data manifests that the first reconstructed edge mode is fermionic which is consistent to the results by composite fermion diagonalization 47,55 and rencent theoretic discussion of the striped FQH 5/2 states. 56 Another application is the RR state for which the structure of the edge spectrum contains parafermionic edge mode.…”

“…Based on the data for 10-18 electrons, we find the edge reconstruction occurs at d c ∼ 0.4l B which is quantitatively agree with the previous study. 30,47,48 The lowest metastable state, or the first reconstructed state in the spectrum locates at ∆M ′ = N/2−1. Therefore, in order to study the edge reconstruction for Nelectrons at ν = 5/2 on disk with a smooth edge, the smallest number of orbitals we need is N orb = 2N − 2 + ∆M ′ = 5 2 N − 3.…”

Probing theν=52quantum Hall state with electronic Mach-Zehnder interferometry

“…Overall, none of the above-mentioned models seems to fit in the constraints set by the experiments, assuming the effect of edge reconstruction is less important. Edge reconstruction is likely in a pure ν = 5/2 liquid, 21,22 but is expected to be suppressed in real samples with disorder, as is evidenced by the recent experiment 23 showing relatively weak signals associated with edge reconstruction and that such signals disappear at long distances 20 .…”

Striped quantum Hall state in a half-filled Landau level

“…This intermediate state was identified to be a striped phase [31]. More recently, Zhang et al found that as the edge confining potential is weakened, the Pf state is destabilized by softening of the (neutral) fermionic edge mode [32]. This suggests the difference between the resultant striped and Pf states lie in their low-energy neutral modes.…”