Band gap engineering $via$ electrostatic chemical strain in cation ordered LaSrAlO$_4$

In this work, we employ density functional theory to examine a novel design route that employs A-site cation ordering to engineer the band gaps of (A,A$^\prime$)BO$_4$ Ruddlesden-Popper (RP) oxides. Using LaSrAlO$_4$ as a model material, we show that the band gap is highly sensitive to the A-site cation ordering ranging from 3-4.5 eV. When the [AlO$_2$]$^{-1}$ layers are interleaved between two chemically equivalent [LaO]$^{1+}$ or [SrO]$^{0+}$ layers, we obtain the smallest band gap with a reduction of $\sim$1 eV determined from the Heyd, Scuseria, and Ernzerhof (HSE) hybrid exchange-correlation functional. We relate the observed band gap reduction to the local bond distortions arising from electrostatic chemical strain induced changes to the O 2$p$ and La 5$d$ states in the valence and conduction bands, respectively.