Chemical trends in halide perovskite electronic properties

The halide perovskites ABX$_3$ with $B=$Pb or Sn, $X$=I, and $A$=Cs or methylammionium (MA), have recently attracted attention as solar cell materials. We discuss the basic bonding, stability and electronic band structure of these materials for different chemical substitutions using first-principles calculations. An important feature of the Pb and Sn based halides is that these element's $s$-electrons strongly hybridize with the halogen $p$-orbitals leading to a valence band maximum with strong Sn or Pb-$s$ character and small effective mass. The conduction band minimum is Sn or Pb $p$-like. We present trends in the electronic band structure with the halogen $X=$I, Br, Cl and the $B$ cation Pb, Sn, Ge, Si. The gap is remarkably insensitive because of the opposing trends of the increased spin-orbit coupling for heavier elements (reducing the gap) and the decreased valence band width for heaver elements due to the larger B-X distance, which increases the gap. The stability of the perovskite structure {\sl vs.} competing structures is influenced by the tolerance factor $t=R_{AC}/\sqrt{2}R_{BC}$. The smaller this factor, the least stable is the perovskite structure. CsSiI$_3$ is found to be a topological insulator. Its stability with respect to CsI and SiI$_n$ is discussed.