Successive electron-vortex binding in quantum Hall bilayers at $\nu=\frac{1}{4}+\frac{3}{4}$

TL;DR

This paper explores how electrons in quantum Hall bilayers at filling fractions 1/4 and 3/4 bind with vortices, revealing a transition from interlayer pairing to composite fermion formation as interlayer separation increases.

Contribution

It demonstrates the successive binding of vortices to electrons in quantum Hall bilayers and constructs trial wavefunctions that match exact diagonalization results across different interlayer distances.

Findings

Vortex attachment increases with interlayer separation.

Trial wavefunctions show good overlap with exact ground states.

Different excitations are well described by specific trial states.

Abstract

Electrons in a quantum Hall fluid can bind with an integer number of vortices to form composite fermions and composite bosons. We show that the quantum Hall bilayer at filling $\nu=\frac{1}{4}+\frac{3}{4}$ with interlayer separation $d$ can be well-described in terms of these composite particles. At small $d$ the system can be understood as interlayer paired electrons and holes, whereas at large $d$ the system is best understood in terms of composite fermions with four vortices attached to each electron. By computing the overlaps of trial wavefunctions with the ground state from exact diagonalization, we find that as $d$ increases, the number of vortices that attach to each electron increases. We also construct trial states for two types of excitation, the Goldstone mode and a meron excitation. These two trial states have good overlaps with the lowest excited states in the exact diagonalization spectrum for small and intermediate $d$ respectively.