Theoretical investigation of edge reconstruction in the $\nu$=5/2 and 7/3 fractional quantum Hall states

Abstract

The edge physics of the $\nu =5/2$ 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 $\nu =7/3$ state and find that edge reconstruction occurs here more readily than for the $\nu =1/3$ state. Our study indicates that the $\nu =5/2$ 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.

19 pages, 15 figures

References in corpus (11)

• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Fractional Quantum Hall States and Jack Polynomials
• Observation of neutral modes in the fractional quantum Hall regime
• Fractional quantum Hall effect at $\nu =5/2$: Ground states, non-Abelian quasiholes, and edge modes in a microscopic model
• Experimental probe of topological orders and edge excitations in the second Landau level
• Edge Excitations and Non-Abelian Statistics in the Moore-Read State: A Numerical Study in the Presence of Coulomb Interaction and Edge Confinement
• Testing the topological nature of the fractional quantum Hall edge
• Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton
• Electron operator at the edge of the 1/3 fractional quantum Hall liquid

Cited by in corpus (6)

• Experimental constraints and a possible quantum Hall state at $\nu =5/2$
• Phase diagram and edge states of the $\nu =5/2$ fractional quantum Hall state with Landau level mixing and finite well thickness
• Probing the $\nu =\frac{5}{2}$ quantum Hall state with electronic Mach-Zehnder interferometry
• Entanglement spectrum edge reconstruction and correlation hole of the FQH liquids
• Edge Reconstruction and Emergent Neutral Modes in Integer and Fractional Quantum Hall Phases
• Universality Lost: Relation between quantizations of the Hall conductance and the edge exponents in fractional quantum Hall effect