Spontaneous Fermi surface symmetry breaking in bilayer systems

We perform a comprehensive numerical study of d-wave Fermi surface deformations (dFSD) on a square lattice, the so-called d-wave Pomeranchuk instability, including bilayer coupling. Since the order parameter corresponding to the dFSD has Ising symmetry, there are two stacking patterns between the layers, (+, +) and (+, -). This additional degree of freedom gives rise to a rich variety of phase diagrams. The phase diagrams are classified by means of the energy scale Lambda(z), which is defined as the bilayer splitting at the saddle points of the in-plane band dispersion. As long as Lambda(z) not equal 0, a major stacking pattern is usually (+, -), and (+, +) stacking is stabilized as a dominant pattern only when the temperature scale of the dFSD instability becomes much smaller than Lambda(z). For Lambda(z) = 0, the phase diagram depends on the precise form of the bilayer dispersion. We also analyze the effect of a magnetic field on the bilayer model in connection with a possible dFSD instability in the bilayered ruthenate Sr(3)Ru(2)O(7).