Bilayer splitting and wave functions symmetry in ${\text{Sr}}_3{\text{Ir}}_2{\text{O}}_7$

The influence of dimensionality on the electronic properties of layered perovskite materials remains an outstanding issue. We address it here for ${\text{Sr}}_3{\text{Ir}}_2{\text{O}}_7$, the bilayer compound of the iridate ${\text{Sr}}_{n+1}{\text{Ir}}_n{\text{O}}_{3n+1}$ series. By angle-resolved photoemission spectroscopy we show that in this material the interlayer coupling is large and that the intercell coupling is, conversely, negligible. From a detailed mapping of the bilayer splitting, and from the intensity modulation of the bonding and antibonding bands with photon energy, we establish differences and similarities with the prominent case of the bilayer superconducting cuprates.

Figure 1

(a) ARPES constant energy cut taken at $E=-180$ meV, near the top of the $J_{\mathrm{eff}}=3/2$ states. The square indicates the surface BZ, determined by the in-plane rotation of the ${\text{IrO}}_6$ octahedra and the G-type antiferromagnetic ordering. The characteristic contours of the distinct $J_{\mathrm{eff}}$ bands are indicated by arrows. (b) and (c) show the band dispersion along the two high-symmetry directions through $\Gamma$. Note in (b) the intensity modulation due to the folding potential generated by the structural distortion. The dashed curves outline the dispersion along the same directions for the monolayer compound ${\text{Sr}}_2{\text{IrO}}_4$, as reported in Ref. [2]. The relevant dimensions are $\overline{\Gamma \mathrm{M}}=0.78{\AA }^{-1}$ and $\overline{\Gamma X}=0.55{\AA }^{-1}$.

Figure 2

(a) The crystal structure of ${\text{Sr}}_3{\text{Ir}}_2{\text{O}}_7$, where the ${\text{IrO}}_6$ octahedra are colored and the large spheres indicate Sr atoms; $a$ and $c$ are the lattice constants parallel and normal to the Ir-O layers, respectively, and $d$ is the bilayer spacing. (b) and (c) show stacks of spectra measured for varying photon energy at $\Gamma$ and $M$, where the intensity is normalized to the lowest binding energy peak, at $-0.23$ and $-0.09$ eV, respectively. The slight irregularity in the measured intensity around $k_z=6{\AA }^{-1}$ is due to the Sr 3$d$ doublet generated by second order radiation from the monochromator. The $k_z$ values are calculated assuming an inner potential $V_0=10$ eV. Note that due to the lack of a measurable $k_z$ periodicity a precise extraction of $V_0$ is not possible. However, it can be approximately set to 10 eV through analysis of the photoemission intensity modulation (see text).

Figure 3

(a) The spectra of Fig. 2 are shown as an image plot and with no intensity normalization. The dashed line is a sine wave of period $10\pi /c$. The intervals defined above the panel indicate the approximate ranges where the intensity of either the bonding (B) or antibonding (AB) branch of the $J_{\mathrm{eff}}=3/2$ states is dominant. (b) Energy distribution curve measured at $\Gamma$ and $h\nu =96$ eV, in the second BZ. (c)–(e) Band dispersion along a $\Gamma M\Gamma$ line at $k_y=\pi /a$, measured at $h\nu =85$, 96, and 113 eV, respectively, corresponding to the arrows in (a); the corresponding constant energy cuts at $E=-90$ meV are shown in (f)–(h). In reference to the intervals in (a), (c), (f): B; (d), (g): $\mathrm{B}+\mathrm{AB}$; (e), (h): AB. (i) Pictorial representations of the initial state bonding wave functions for Bi-2212 and for ${\text{Sr}}_3{\text{Ir}}_2{\text{O}}_7$.

Figure 4

(a) Band dispersion along a $\Gamma XM\Gamma$ path in the second BZ. (b) The peak energies extracted from the experimental data are superposed to the calculated bands of a TB model. The calculation follows Ref. [26], but neglects for simplicity the in-plane octahedra rotation. Colors represent the projected weights of each band on a fourfold bilayer basis set. Intermediate colors indicate mixed character.