  In this paper we analyze the band-structure of two-dimensional (2D) halide
perovskites by considering structures related to the simpler case of the
series, (BA)$_2$PbI$_4$, in which PbI$_4$ layers are intercalated with
butylammonium (BA=CH$_3$(CH$_2$)$_3$NH$_3$) organic ligands. We use
density-functional-theory (DFT) based calculations and tight-binding (TB)
models aiming to discover a simple description of the bands in the vicinity of
the valence-band maximum and the conduction-band minimum. We find that the
atomic orbitals of the butylammonium chains have negligible contribution to the
Bloch states which form the conduction and valence bands in near the Fermi
energy. Our calculations reveal a rather universal, i.e., independent of the
intercalating BA, rigid-band picture characteristic of the layered perovskite
``matrix''. Besides demonstrating the above conclusion, the main goal of this
paper is to find accurate TB models which capture the essential features of the
DFT bands near the Fermi energy. First, we ignore electron hopping along the
$c$-axis and the octahedral distortions and this increased symmetry halves the
Bravais-lattice unit-cell size and the Brillouin zone unfolds to a 45$^{\circ}$
rotated square and this allows some analytical handling of the 2D
TB-Hamiltonian. The Pb $6s$ and I $5s$ orbitals are far away from the Fermi
level and, thus, we integrate them out to obtain an effective model which only
includes hybridized Pb $6p$ and I $5p$ states. Our TB-based treatment a)
provides a good quantitative description of the DFT band-structure, b) helps us
conceptualize the complex electronic structure in the family of these materials
in a simple way and c) yields the one-body part to be combined with
appropriately screened electron interaction to describe many-body effects, such
as excitonic bound-states.
