$\nu =1/2$ Bilayer Tunnelling

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.