Phase diagram of the edge pair-density wave

Construct the complete phase diagram of the finite-amplitude edge pair-density wave in the square-lattice extended Hubbard model by determining throughout parameter space where the finite-wavevector instability is energetically favored over translation-invariant edge states.

Background

The supplementary analysis maps the occurrence of finite-momentum zero-energy Andreev bound-state crossings across a broad region of the mixed-symmetry $s+d+ip_x$ phase. However, the presence of a candidate scattering wavevector does not by itself establish a finite-amplitude pair-density-wave instability; the edge pairing stiffness must also become negative, and the resulting self-consistent state must be energetically favorable.

The authors analyze this distinction along a limited interaction cut and explicitly state that determining the full region of stable edge pair-density-wave order requires self-consistent solutions and free-energy comparisons throughout the parameter space.