Global Phase Diagram of nu = 2 Bilayers Quantum Hall Systems in Tilted Magnetic Field

We consider a bilayer quantum Hall system at total filling fraction nu = 2 in tilted magnetic field allowing for change imbalance as well as tunnelling between the two layers. Using an "unrestricted Hartree Fock," previously discussed by Burkov and MacDonald (Phys Rev B vol. 66, 115323 2002), we examine the two temperature global phase diagrams that would be accessed experimentally by changing the in-place field and the bias voltage between the layers while keeping the tunneling between the two layers fixed. In accordance with previous work, we find symmetric and ferromagnetic phases as well as a first order transition between two canted phases with a spontaneously broken U(1) symmetry.