$\nu =1/2$ Bilayer Tunnelling

TL;DR

This paper investigates electron tunneling between two $ u=1/2$ quantum Hall layers using Chern-Simons gauge theory, finding no gap in the density of states and suggesting possible roles of disorder or the limitations of perturbation theory.

Contribution

It applies Chern-Simons gauge field formalism to analyze bilayer tunneling at $ u=1/2$, contrasting theoretical predictions with experimental results.

Findings

No gap in the physical electron density of states was observed.

Perturbation theory about the Fermi liquid ground state may be inadequate.

Disorder within the interplanar barrier could influence tunneling behavior.

Abstract

Tunneling of electrons between two $\nu = 1/2$ quantum Hall parallel planes is studied. In order to calculate the physical electron Green's function, the Chern-Simons gauge field formalism is used, both in a perturbative many-body calculation and in a semiclassical calculation. In contrast to recent experiments, no gap in the physical electron density of states is found. A conjecture is made that either perturbation theory about the mean field Fermi liquid ground state is inadequate, or that disorder within the interplanar barrier plays a role.