Motivated by experiments on the carrier-doped bilayer iridate (${\mathrm{Sr}}_{1-x}{\mathrm{La}}_x{)}_3{\mathrm{Ir}}_2{\mathrm{O}}_7$, we study the dynamics of a single doped electron in a bilayer magnet in the presence of spin-orbit coupling, taking into account the spatially staggered rotation of ${\mathrm{IrO}}_6$ octahedra. We employ an effective single-orbital bilayer $t-J$ model, concentrating on the quantum paramagnetic phase near the magnetic quantum critical point. We determine the carrier dispersion using a combination of self-consistent Born and bond-operator techniques. Extrapolating to finite small carrier density we find that, for experimentally relevant parameters, the combination of octahedral rotation and spin-orbit coupling induces a band folding which results in a Fermi surface of small double electron pockets, in striking agreement with experimental observations. We also determine the influence of spin-orbit coupling on the location of the quantum critical point in the undoped case, and discuss aspects of the global phase diagram of doped bilayer Mott insulators.

• Received 28 March 2018
• Revised 11 July 2018

DOI:https://doi.org/10.1103/PhysRevB.98.115102