A charge density wave-like instability in a doped spin-orbit-assisted weak Mott insulator

Layered perovskite iridates realize a rare class of Mott insulators that are predicted to be strongly spin-orbit coupled analogues of the parent state of cuprate high-temperature superconductors. Recent discoveries of pseudogap, magnetic multipolar ordered and possible $d$-wave superconducting phases in doped Sr$_2$IrO$_4$ have reinforced this analogy among the single layer variants. However, unlike the bilayer cuprates, no electronic instabilities have been reported in the doped bilayer iridate Sr$_3$Ir$_2$O$_7$. Here we show that Sr$_3$Ir$_2$O$_7$ realizes a weak Mott state with no cuprate analogue by using ultrafast time-resolved optical reflectivity to uncover an intimate connection between its insulating gap and antiferromagnetism. However, we detect a subtle charge density wave-like Fermi surface instability in metallic electron doped Sr$_3$Ir$_2$O$_7$ at temperatures ($T_{DW}$) close to 200 K via the coherent oscillations of its collective modes, which is reminiscent of that observed in cuprates. The absence of any signatures of a new spatial periodicity below $T_{DW}$ from diffraction, scanning tunneling and photoemission based probes suggests an unconventional and possibly short-ranged nature of this density wave order.