Constraints on the two-dimensional pseudo-spin 1/2 Mott insulator description of Sr$_2$IrO$_4$

Sr$_{2}$IrO$_{4}$ has often been described via a simple, one-band pseudo-spin
1/2 model, subject to electron-electron interactions, on a square lattice,
fostering analogies with cuprate superconductors, believed to be well described
by a similar model. In this work we argue - based on a detailed study of the
low-energy electronic structure by circularly polarized spin and angle-resolved
photoemission spectroscopy combined with dynamical mean-field theory
calculations - that a pseudo-spin 1/2 model fails to capture the full
complexity of the system. We show instead that a realistic multi-band Hubbard
Hamiltonian, accounting for the full correlated $t_{2g}$ manifold, provides a
detailed description of the interplay between spin-orbital entanglement and
electron-electron interactions, and yields quantitative agreement with
experiments. Our analysis establishes that the $j_{3/2}$ states make up a
substantial percentage of the low energy spectral weight, i.e. approximately
74% as determined from the integration of the $j$-resolved spectral function in
the $0$ to $-1.64$ eV energy range. The results in our work are not only of
relevance to iridium based materials, but more generally to the study of
multi-orbital materials with closely spaced energy scales.

Authors

Berend Zwartsenberg, Ryan P. Day, Elia Razzoli, Matteo Michiardi, Mengxing Na, Guoren Zhang, Jonathan D. Denlinger, Ivana Vobornik, Chiara Bigi, Bumjoon Kim, Ilya S. Elfimov, Eva Pavarini, Andrea Damascelli