Spontaneous Fermi surface symmetry breaking in bilayered systems

TL;DR

This paper investigates the phase diagrams and stacking patterns of d-wave Fermi surface deformations in bilayer systems, revealing how bilayer coupling and magnetic fields influence the symmetry-breaking phases.

Contribution

It provides a comprehensive numerical analysis of dFSD in bilayer systems, classifying phase diagrams based on bilayer splitting and exploring effects of magnetic fields.

Findings

Major stacking pattern is (+,-) when bilayer splitting is non-zero.

(+,+) stacking is favored at low temperatures when Lambda_z is large.

Magnetic fields can influence the stability of dFSD phases.

Abstract

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 layeres, (+,+) 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} ne 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 bilyared ruthenate Sr_3Ru_2O_7.