Fig. 5: Phase diagram of pairing symmetries under various dominant LC pathways.

a A polar plot showing how the dominant pairing instability depends on the LC pattern, as parametrized by \({\widehat{J}}^{\,\,\ell }=\sin \theta \cos \phi {\widehat{J}}_{(a)}^{\,\,\ell }+\sin \theta \sin \phi {\widehat{J}}_{(b)}^{\,\,\ell }+\cos \theta {\widehat{J}}_{(c)}^{\,\,\ell }\). The variables \({\widehat{J}}_{(a)}^{\,\,\ell },{\widehat{J}}_{(b)}^{\,\,\ell },{\widehat{J}}_{(c)}^{\,\,\ell }\) refer to the current patterns of Fig. 3a, b, c, respectively. The plot is periodic in ϕ. \(\theta \in [\frac{\pi }{2},\pi ]\) is not shown because \({\widehat{J}}^{\,\,\ell }\) and \(-{\widehat{J}}^{\,\,\ell }\) both give the same interaction. When θ (radial variable) is small, the currents flow predominantly between V-Sb, driving s^± pairing. b The phase diagram as a function of ϵ_z, which is the tuning parameter for the Γ-point pocket, for \({\widehat{J}}_{(a)}\) (dashed lines) and \({\widehat{J}}_{(c)}\) (solid lines) exchange. Since \({\widehat{J}}_{(a)}\) is a current pattern flowing only between V-V, the Γ-pocket plays essentially no role, so its removal (vertical dotted line) does not affect the leading pairing eigenvalue. In contrast, because \({\widehat{J}}_{(c)}\) flows only between V-Sb, which strongly couples the Γ-pocket and outer Fermi surface, the removal of the Γ-pocket destroys the s^± superconductivity; only weak interactions between the M-points on the outer Fermi surface remain, yielding d + id pairing. c A schematic phase diagram illustrating the quantitative result of (b), wherein the removal of the Γ pocket at the Lifshitz transition destroys the s^± state. a and b were calculated using the RPA LC propagator from Eq. (4).