Jahn-Teller distortion on strained La${}_3$Ni${}_2$O${}_7$ thin films

We present a systematic study of the electronic structure of strained La${}_3$Ni${}_2$O${}_7$ thin films. We show that biaxial compressive strain mainly elongates the outer apical Ni-O bond while leaving the inner apical Ni-O bond nearly unchanged. As a result, the Jahn-Teller splitting ${\mathrm{\Delta }}_{JT}$ is strongly enhanced, whereas the interlayer $d_{z^2}$ hopping $t_{\perp }^z$ changes only weakly. Since superconductivity is widely believed to emerge only below a critical in-plane lattice constant, our results identify the strain-enhanced ${\mathrm{\Delta }}_{JT}$ as the relevant microscopic tuning parameter. Consistently, the calculated Fermi surfaces and Hall response for LaAlO${}_3$ and SrLaAlO${}_4$ substrates agree with ARPES and Hall measurements. Our results identify Jahn-Teller distortion as a key tuning parameter in strained La${}_3$Ni${}_2$O${}_7$ and support its central role in optimizing superconductivity in bilayer nickelates.