Quantum coherence and Skyrmions in a bilayer quantum Hall system

Abstract

We analyze quantum coherence in a bilayer quantum Hall system. We use a bosonic Chern-Simons gauge theory with the lowest Landau-level projection taken into account. Although the kinetic energy term is quenched in the Hamiltonian, the dynamics arises since the X and Y components of the guiding center X=(X,Y) do not commute. In the case of the bilayer system the dynamics is governed by the ${\mathrm{W}}_{\mathrm{\infty }}$×SU(2) algebra. We emphasize that the fractional quantum Hall state is a condensed but not a coherent phase of composite bosons. It follows from this ground-state property and the ${\mathrm{W}}_{\mathrm{\infty }}$ algebra that the fractional quantum Hall system is incompressible. In a certain bilayer quantum Hall system the ground state is a coherent state of the SU(2) component of the composite boson field, which is the ${\mathrm{CP}}^1$ field. Skyrmions are topological excitations in this coherent mode. A systematic method is presented to calculate the current and static correlation functions. It is argued that Skyrmion excitations are detectable by measuring the Hall current distribution. We construct the Landau-Ginzburg theory of the coherent mode. The coherent mode is a superfluid mode in the vanishing limit of the tunneling interaction.