Spectroscopic Evidence for Electron-Boson Coupling in Electron-Doped ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$

The pseudogap, $d$-wave superconductivity and electron-boson coupling are three intertwined key ingredients in the phase diagram of the cuprates. ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ is a $5d$-electron counterpart of the cuprates in which both the pseudogap and a $d$-wave instability have been observed. Here, we report spectroscopic evidence for the presence of the third key player in electron-doped ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$: electron-boson coupling. A kink in nodal dispersion is observed with an energy scale of $\sim 50\mathrm{meV}$. The strength of the kink changes with doping, but the energy scale remains the same. These results provide the first noncuprate platform for exploring the relationship between the pseudogap, $d$-wave instability, and electron-boson coupling in doped Mott insulators.

Figure 1

Identification of the nodal kink in electron-doped ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. (a) Photoelectron intensity plot as a function of energy and momentum measured along the $(0,0)\text{−}(\pi ,\pi )$ nodal direction at 30 K. The white-dashed line labels the reconstructed Brillouin zone boundary at ($\pi /2$, $\pi /2$). The black arrow marks the dispersion kink in the main band (MB). The energy feature in the folded band (FB, possibly associated with the octahedral rotation) is harder to identify due to its weak spectral intensity. (b) MDC-derived dispersion of the MB. The black straight line is the empirical bare band connecting the two energy points in the dispersion at $E_F$ and $-150\mathrm{meV}$. The dashed line is a guide for the eye. (c) Effective real part of electron self-energy. The black arrow marks the peak position at $\sim 50\mathrm{meV}$. Another possible weak feature locates at $\sim 90\mathrm{meV}$, which might be affected by its proximity to the FB. (d),(e) Full-width-at-half-maximum (FWHM) of the EDC (d) and MDC (e) peaks. Black arrows label the drop in the peak width and dashed lines are a guide to the eye. The error bars represent the uncertainties in the determination of the peak width. Because of the doping limit in conventional chemical substitution, in situ potassium deposition was performed on a metallic ${({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x)}_2{\mathrm{IrO}}_4$ sample ($x\sim 0.04$) to reach a higher electron doping level [14, 21]. The estimated electron concentration $n^{\prime }$ is $\sim 0.12$ (see Fig. 4 and Supplemental Material for details [26]).

Figure 2

Doping dependence of the electron band along the nodal direction. (a)–(c) Photoelectron intensity plots of the nodal dispersion as a function of doping at 30 K. Continuous electron doping is achieved via in situ potassium deposition on a [${({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x)}_2{\mathrm{IrO}}_4$, $x\sim 0.04$] sample. The black arrows indicate the kink position. The location of the momentum cut is shown in the inset of (a). (d) Fermi surface mapping of a [${({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x)}_2{\mathrm{IrO}}_4$, $x\sim 0.04$] sample without potassium doping. (e) Same as (d), but for a [${({\mathrm{Sr}}_{1-x}{\mathrm{La}}_x)}_2{\mathrm{IrO}}_4$, $x\sim 0.04$] sample with potassium surface doping.

Figure 3

Doping dependence of the nodal dispersion kink. (a)–(c) MDC-derived nodal dispersion extracted from the MB in Figs. 2, respectively. The black arrow marks the kink and the dashed lines are a guide to the eye. (d)–(f) Effective real parts of the electron self-energy obtained from the data in panels (a)–(c), respectively. The peak position as a function of doping is summarized in Fig. 4 as sample 1 (blue circles).

Figure 4

Summary of the kink energy and band renormalization as a function of electron doping. In order to avoid excessive cycles of in situ potassium deposition, two samples were used to study the high and low doping regimes, respectively. Blue (green) circles represent the energy of the dispersion kink measured on sample 1 (sample 2). Empty squares indicate the renormalization factor ${\lambda }^{\prime }$ as defined in the main text. The estimated electron concentration $n^{\prime }$ is obtained by calculating the area of the underlying Fermi surface following the procedure used in [14]; this procedure underestimates electron concentration in the low doping regime, where the antinodal pseudogap exists [14] (also see Supplemental Material, Fig. S7 [26]). The error bars for the kink energy (renormalization factor ${\lambda }^{\prime }$) are from the uncertainties in the determination of the kink position (dispersion velocities).