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Predicted superconductivity of Ni2VAl and pressure dependence of superconductivity in Ni2NbX (X = Al, Ga and Sn) and Ni2VAl

A first-principles study of the electronic and superconducting properties of the Ni$_2$VAl Heusler compound is presented. The electron-phonon coupling constant of $λ_{ep}$ = 0.68 is obtained, which leads to a superconducting transition temperature of T$_c$ = $\sim$4 $K$ (assuming a Coulomb pseudopotential $μ^*$ = 0.13), which is a relatively high transition temperature for Ni based Heusler alloys. The electronic density of states reveals a significant hybridization between Ni-$eg$ and V-$t_{2g}$ states around the Fermi level. The Fermi surface, consisting of two electron pockets around the X-points of the Brillouin zone, exhibits nesting and leads to a Kohn anomaly of the phonon dispersion relation for the transverse acoustic mode TA2 along the (1,1,0) direction, which is furthermore found to soften with pressure. As a consequence, T$_c$ and $λ_{ep}$ vary non-monotonically under pressure. The calculations are compared to similar calculations performed for the Ni$_2$NbX (X = Al, Ga and Sn) Heusler alloys, which experimentally have been identified as superconductors. The experimental trend in T$_c$ is well reproduced, and reasonable quantitative agreement is obtained. The calculated T$_c$ of Ni$_2$VAl is larger than either calculated and observed T$_c$s of any of the Nb compounds. The Fermi surfaces of Ni$_2$NbAl and Ni$_2$NbGa consist of only a single electron pocket around the X point, however under compression second electron pocket similar to that of Ni2VAl emerges only in Ni2NbAl and the Tc increases non monotonically in all the compounds. Fermi surface nesting and associated Kohn anomalies are a common feature of all four compounds, albeit weakest in Ni$_2$VAl.