Density Wave order and Topological superconductivity in Pd₂ZrGa

Pd-based Heusler alloys demonstrate intriguing transport properties, including superconductivity and density wave order, due to the presence of a van Hove Singularity at the L point. Through first-principle calculations, we investigate the properties of Pd₂ZrGa, exploring both its primitive L2₁ (FCC) and conventional cubic Heusler structures. The divergent behavior seen in the Pd-d and Zr-d states at the Fermi level, coupled with the notable enhancement in the Ga p states, suggests that this occurrence is a consequence of lattice instability rather than magnetic instability. The phonon dispersion relation for Pd₂ZrGa exhibited an imaginary frequency for both the primitive and conventional cells, indicating lattice instability. We estimated the Fermi surface nesting function using a double delta integration over the full Brillouin zone, revealing the presence of small parallel surfaces at the M and R points, suggesting a weak nesting behaviour. The frequency dependence of the mode-resolved and total α²F(ω) indicates that low-energy phonon is involved in electron scattering, resulting in an estimated λ value of 1.37 and T_c value of 4.3 K and log(ω_D) = 62 signifies strong coupling and phonon-mediated superconductivity. Further, Dirac point at the Fermi level and four additional points within ±4 meV points toward exotic electronic properties in Pd₂ZrGa.