Broken Symmetry Ground States in \nu=2 Bilayer Quantum Hall Systems

We report on a study of a bilayer two-dimensional electron gas at Landau level filling factor $\nu =2$. The system exhibits both magnetic and spontaneous interlayer phase coherence broken symmetries. We propose a 3-parameter Slater determinant variational wavefunction which describes the ground state over the full range of bias potential (${\mathrm{\Delta }}_V$) Zeeman coupling (${\mathrm{\Delta }}_z$) and interlayer tunneling amplitude (${\mathrm{\Delta }}_t$) strengths. Broken symmetry states occur inside a volume in this three-dimensional phase diagram near the ${\mathrm{\Delta }}_z^2={\mathrm{\Delta }}_V^2+{\mathrm{\Delta }}_t^2$ surface. We have obtained analytic results for the intersections of the phase diagram with the ${\mathrm{\Delta }}_t=0$, ${\mathrm{\Delta }}_z=0$, and ${\mathrm{\Delta }}_V=0$, planes and show that the differential capacitance of the bilayer system is singular at the phase boundary.