Orbital-dependent polaron formation in the relativistic Mott insulator ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$

We use optical spectroscopy to investigate the electron-phonon interaction in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$, a well-known $5d$ transition metal oxide with spin-orbit entangled states. The temperature evolution in the optical spectra is well described by the Fröhlich polaron model, indicating a large electron-phonon interaction. We further find that electrons in different orbitals selectively couple with different phonon modes. While $J_{\mathrm{eff}}$ = 3/2 holes do not seem to couple with any phonons, $J_{\mathrm{eff}}$  = 1/2 and $3z^2-r^2$ electrons mainly couple with in-plane and out-of-plane Ir-O bending modes, respectively. The symmetries of the orbitals and phonons are consistent with our observations.

Figure 1

(a) $T$-dependent σ${}_1$(ω) of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. The black dashed line indicates the contribution of broad $p$-$d$ transitions. Five sharp electronic transitions are indicated by α, β, γ, $A$, and $B$, in order of increasing energy. (b) Schematic diagram of the optical transition and spectral weights in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. The solid (dashed) line represents the spectral weights in a noninteracting (interacting) system. (c) Second derivatives of σ${}_1$(ω), $d^2$σ${}_1$(ω)/$d$ω${}^2$. The black arrows indicate the dips in $d^2$σ${}_1$(ω)/$d$ω${}^2$, corresponding to the peak energies in ${\sigma }_1$(ω).

Figure 2

Δ$E_{\mathrm{peak}}$($T)$ for (a) peaks α, β, and γ, and (b) peaks $A$ and $B$. (c) Δ$E_{\alpha }$($T)$/2, Δ$E_{\beta }$($T)$, and Δ$E_{\gamma }$($T)$, which represent Σ′($T)$ of $J_{\mathrm{eff}}$ = 1/2 electrons. The black thick line is the best fitting result with the Fröhlich polaron model. (d) Δ$E_A$($T)$−Δ$E_{\alpha }$($T)$/2 and Δ$E_B$($T)$, which represent Σ′($T)$ of 3$z^2-r^2$ electrons. The black thick line is the best fitting result with the polaron model, while the red thin line is the fitting line with 54 meV phonon energy for comparison.

Figure 3

(a) − Im(1/ε) of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ taken at 25 K. The six sharp peaks correspond to LO phonon modes. Each phonon mode is illustrated in the inset. Schematics of the formation of polarons in the cases of (b) 3$z^2-r^2$ electrons and (c) $J_{\mathrm{eff}}$ = 1/2 electrons.