Importance of nonlocal electron correlation in the BaNiS2 semimetal from quantum oscillations studies

By means of Shubnikov--de Haas and de Haas--van Alphen oscillations, and ab initio calculations, we have studied the Fermi surface of high-quality ${\mathrm{BaNiS}}₂$ single crystals, with mean free path $l\ensuremath{\sim}400\phantom{\rule{4.pt}{0ex}}\text{\AA{}}$. The angle and temperature dependence of quantum oscillations indicates a quasi-two-dimensional Fermi surface, made of an electronlike tube centered at $\mathrm{\ensuremath{\Gamma}}$, and of four holelike cones, generated by Dirac bands, weakly dispersive in the out-of-plane direction. Ab initio electronic structure calculations, in the density functional theory framework, show that the inclusion of screened exchange is necessary to account for the experimental Fermi pockets. Therefore, the choice of the functional becomes crucial. A modified HSE hybrid functional with 7% of exact exchange outperforms both GGA and $\mathrm{GGA}+U$ density functionals, signaling the importance of nonlocal screened-exchange interactions in ${\mathrm{BaNiS}}₂$, and, more generally, in $3d$ compensated semimetals.