Microscopic model for the Sr$_{n+1}$Ir$_{n}$O$_{3n+1}$ Ruddlesden-Popper series of materials

The Sr$_{n+1}$Ir$_{n}$O$_{3n+1}$ family of materials displays an insulator to metal transition as the number of layers (n) increases. The presence of large spin-orbit coupling is believed to be a significant ingredient for the novel J$_{eff}= 1/2$ state found in Sr$_{2}$IrO$_{4}$. We offer a microscopic tight-binding Hamiltonian with spin-orbit coupling and Hubbard interactions, and compare our results with experimentally observed phases.