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We investigate the lead-free halide double perovskites (HDPs) Cs$ _2BB'X_6$($B$=Ag, Na; $B'$=In, Bi; $X$=Cl, Br) via first-principles calculations. Wefind that both the geometric and electric structures of the HDPs obtained bythe Heyd-Scuseria-Ernzerhof (HSE) hybrid functional are much better than thoseof the Perdew-Burke-Ernzerhof (PBE) functional. Importantly, we find that theelectronic structures of DHPs are very sensitive to their geometries,especially the $B$-$X$ bond lengths. As a consequence, the electronicstructures calculated by the HSE functional using the PBE optimized geometriesmay still significantly underestimate the band gaps, whereas the calculationson the HSE optimized geometries provide much more satisfactory results. Thesensitivity of the band gaps of the DHPs to their geometries opens a promisingpath for the band structure engineering via doping and alloying. This worktherefore provides an useful guideline for further improvement of HDPsmaterials.

Importance of exact exchange to the geometric and electronic structures of Cs$_2$$B$$B'$$X_6$ double perovskites