Spectroscopic indications of polaronic behavior of the strong spin-orbit insulator Sr${}_3$Ir${}_2$O${}_7$

We investigate the bilayer Ruddlesden-Popper iridate Sr${}_3$Ir${}_2$O${}_7$ by temperature-dependent angle-resolved photoemission. At low temperatures, we find a fully gapped correlated insulator, characterized by a small charge gap and narrow bandwidths. The low-energy spectral features show a pronounced temperature-dependent broadening and non-quasiparticle-like Gaussian line shapes. Together, these spectral features provide experimental evidence for a polaronic ground state. We observe similar behavior for the single-layer cousin Sr${}_2$IrO${}_4$, indicating that strong electron-boson coupling dominates the low-energy excitations of this exotic family of $5d$ compounds.

Figure 1

Low-energy electronic structure of Sr${}_3$Ir${}_2$O${}_7$, measured with a photon energy of 40 eV at 50 K along the (a) $\Gamma$-$X$, (b) $\Gamma$-$M$, and (c) $M$-$X$ high-symmetry directions of the Brillouin zone (see insets). (d) Second-derivative image plots clearly show rapid dispersion of multiple bands along $X$-$\Gamma$-$M$. Temperature-dependent resistivity and valence band photoemission are compared for the bilayer (green) and single-layer (blue) compounds in (e) and (f), respectively. A magnified view of the near-$E_F$ valence band emission is shown inset in (f).

Figure 2

(a) Constant energy contours measured across the full Brillouin zone of Sr${}_3$Ir${}_2$O${}_7$ at 50 K ($h\nu =70$ eV) and normalized to the same total intensity for each energy. (b) Comparison of low-temperature (50 K) and high-temperature (330 K) maps at the Fermi level and 0.1 and 0.2 eV binding energy, normalized to the highest intensity at that binding energy to maximize contrast.

Figure 3

(a) Temperature dependence of EDCs (black dots) at the $X$ point. The spectra were all measured on a single sample, from bottom to top with increasing time, at a photon energy of 31 eV. Fits to two Gaussian peaks and a polynomial background are also shown (solid lines). The resulting extracted width $\Gamma \left(T\right)$ of the lowest-energy peak is shown in (b), and for equivalent measurements at the $\Gamma$-point in (c). These full data sets were fit by a linear slope (black lines) and by a model function to describe Franck-Condon broadening (green-dashed lines), as discussed in the main text.

Figure 4

(a) EDC at the $X$ point (black, $h\nu =40$ eV), with the low-energy side of the peak fit by Gaussian (red dot-dashed) and Lorentzian (green dashed) line shapes. An independent boson model calculation [${\omega }_0=0.016$ eV, $g=6$, $T=50$ K, with the (zero-temperature) quasiparticle pole 30 meV below the chemical potential] is also shown, in excellent agreement with the measured ARPES data at low binding energies. The inset shows the width of Gaussian fits to the low binding energy half of the peak in the spectral function of equivalent calculations as a function of temperature. (b) EDCs close to the $X$ point. Red closed circles show the peak position of Gaussian fits, $E_B$. Blue open circles show $E_B+1.76\Gamma$, where $\Gamma$ is the width of the Gaussian fits. (c),(d) Equivalent measurements (performed at 125 K to prevent charging) and fits for Sr2IrO${}_4$. In (d), blue open circles are shown at $E_B+1.5\Gamma$.