Topological Magnon Bands and Unconventional Superconductivity in Pyrochlore Iridate Thin Films

We theoretically study the magnetic properties of pyrochlore iridate bilayer and trilayer thin films grown along the $[111]$ direction using a strong coupling approach. We find the ground state magnetic configurations on a mean field level and carry out a spin-wave analysis about them. In the trilayer case the ground state is found to be the all-in-all-out (AIAO) state, whereas the bilayer has a deformed AIAO state. For all parameters of the spin-orbit coupled Hamiltonian we study, the lowest magnon band in the trilayer case has a nonzero Chern number. In the bilayer case we also find a parameter range with nonzero Chern numbers. We calculate the magnon Hall response for both geometries, finding a striking sign change as function of temperature. Using a slave-boson mean-field theory we study the doping of the trilayer system and discover an unconventional time-reversal symmetry broken $d+id$ superconducting state. Our study complements prior work in the weak coupling limit and suggests that the $[111]$ grown thin film pyrochlore iridates are a promising candidate for topological properties and unconventional orders.