Broken-symmetry ground states inν=2bilayer quantum Hall systems

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