Abstract
Analogs of the high-T$_c$ cuprates have been long sought after in transition metal oxides. Due to the strong spin-orbit coupling (SOC), the $5d$ perovskite iridates Sr$_2$IrO$_4$ exhibit a low-energy electronic structure remarkably similar to the cuprates. Whether a superconducting state exists as in the cuprates requires understanding the correlated spin-orbit entangled electronic states. Recent experiments discovered hidden order in the parent and electron doped iridates, some with striking analogies to the cuprates, including Fermi surface pockets, Fermi arcs, and pseudogap. Here, we study the correlation and disorder effects in a five-orbital model derived from the band theory. We find that the experimental observations are consistent with a $d$-wave spin-orbit density wave order that breaks the symmetry of a joint two-fold spin-orbital rotation followed by a lattice translation. There is a Berry phase and a plaquette spin flux due to spin procession as electrons hop between Ir atoms, akin to the intersite SOC in quantum spin Hall insulators. The associated staggered circulating $J_\text{eff}=1/2$ spin current can be probed by advanced techniques of spin-current detection in spintronics. This electronic order can emerge spontaneously from the intersite Coulomb interactions between the spatially extended iridium $5d$ orbitals, turning the metallic state into an electron doped quasi-2D Dirac semimetal with important implications on the possible superconducting state suggested by recent experiments.
Highlights
Analogs of the high-Tc cuprates have been long sought after in transition metal oxides
We find that the experimental observations are consistent with a d-wave spin-orbit density wave order that breaks the symmetry of a joint twofold spin-orbital rotation followed by a lattice translation
In high-quality undoped Sr2IrO4 samples, the most recent angle-resolved photoemission (ARPES) experiment [21] was able to resolve the broad spectra in the canted AFM insulator near the high-symmetry point X 1⁄4 ðπ; 0Þ and ð0; πÞ observed in earlier experiments [1,22,23,24,25] and reveal a degeneracy splitting of the quasiparticle (QP)
Summary
Surface doping [28,29,30]. ARPES measurements showed that the collapse of the AFM insulating gap gives rise to a paramagnetic (PM) metallic state with Fermi surface (FS) pockets for bulk electron doping at x 1⁄4 0.1 [21] and to Fermi arcs [28] with d-wave-like pseudogaps around X [21,29] under surface doping, in striking analogy to the high-Tc cuprates. Our focus is the hidden electronic order in the low-energy QP properties observed by ARPES and STM in undoped and electron-doped iridates To this end, we study the effects of correlation, SOC, and structure distortion on the spin-orbit entangled electronic states. Variations in the staggered IrO6 octahedral rotation and those in the s-wave SOC for the Jeff 1⁄4 1=2 QP [19] about the average value This necessarily generates a local distribution of the d-PSCO with “smeared out” band splittings that contribute to the broad spectrum near X observed in all ARPES measurement [1,21,22,23,24,25].
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