Correlation of Fe-Based Superconductivity and Electron-Phonon Coupling in an $\mathrm{FeAs}/\text{Oxide}$ Heterostructure

Interfacial phonons between iron-based superconductors (FeSCs) and perovskite substrates have received considerable attention due to the possibility of enhancing preexisting superconductivity. Using scanning tunneling spectroscopy, we studied the correlation between superconductivity and $e\text{−}\text{ph}$ interaction with interfacial phonons in an iron-based superconductor ${\mathrm{Sr}}_2{\mathrm{VO}}_3\mathrm{FeAs}$ ($T_c\approx 33\mathrm{K}$) made of alternating FeSC and oxide layers. The quasiparticle interference measurement over regions with systematically different average superconducting gaps due to the $e\text{−}\text{ph}$ coupling locally modulated by O vacancies in the ${\mathrm{VO}}_2$ layer, and supporting self-consistent momentum-dependent Eliashberg calculations provide a unique real-space evidence of the forward-scattering interfacial phonon contribution to the total superconducting pairing.

Figure 1

(a) Topograph of the SrO-terminated surface of ${\mathrm{Sr}}_2{\mathrm{VO}}_3\mathrm{FeAs}$ showing quasi-$C_2$-symmetric surface reconstructions. The lower right inset shows the magnetic susceptibility vs temperature, showing bulk superconductivity near 33 K. (b) Superconducting gap ($\mathrm{\Delta }$) map taken over the same area shown in the topograph of (a). (c) Averaged spectra (inset) taken at 4.6 and 140 K and their difference showing the superconducting gap near the Fermi level marked with arrows. (d) Temperature dependence of spatially averaged tunneling spectra. The error bars in (c) and (d) correspond to 0.5 times the standard deviation taken over 256 different locations.

Figure 2

(a) Quasiparticle interference maps $dI/dV(\mathit{q},V)$, shown at various representative energies. The crosses mark $\mathit{q}=[\pm \frac{1}{4}(2\pi /a_0),0]$. (b) The band structure (two-iron unit cell) of ${\mathrm{Sr}}_2{\mathrm{VO}}_3\mathrm{FeAs}$ near the Fermi level, based on ARPES measurements and this work. The isotropic paraboloid (orange) is the Fe $d_{xz}/d_{yz}$ band (denoted $\alpha$ band) at the $\mathrm{\Gamma }$ point seen in Figs. S1(b),S1(c) [22]. (c) A cross section of the three-dimensional quasiparticle interference $dI/dV(\mathit{q},V)$ along two different crystallographic orientations ($\pi$, $\pi$) and ($\pi$, 0). (d),(e) A cross section of the simulated spectral function (SF) (d) and QPI (e) with $\mathrm{\lambda }\equiv g_{\text{ph}}^2/{\mathrm{\Omega }}_{\text{ph}}^2=0.69$ [22]. The curves marked ${\alpha }^{\prime }$ and ${\alpha }^{\prime \prime }$ are the replicas of the $\alpha$ band with apparent energy shifts by $\sim {\mathrm{\Omega }}_{\text{ph}}$. (f) The phonon dispersion in ${\mathrm{Sr}}_2{\mathrm{VO}}_3\mathrm{FeAs}$, where the fat band thickness indicates the Coulomb coupling strength of each mode to the Fe layer electrons. The black boxes represent the symmetric breathing phonon mode most strongly coupled with the itinerant Fe electrons, whose atomic displacement snapshot is shown in (g) [22].

Figure 3

(a),(b) Experimental $dI/dV(|\mathit{q}|,V)$ evaluated over two intertwined areas determined by superconducting gap higher (${\mathrm{\Delta }}^{+}$) (a) and lower (${\mathrm{\Delta }}^{-}$) (b) than the median gap value. The insets show corresponding masks applied to the original gap map ($300\mathrm{nm}\times 300\mathrm{nm}$). (c),(d) Images corresponding to (a),(b) for the simulated QPI intensity with parameters ${\lambda }^{+}=0.75$ and ${\lambda }^{-}=0.63$. The red and blue solid (dashed) curves in (a)–(d) indicate the EDC maxima of original (replica) bands. (e) The contour plots of both (a) and (b) with the background showing the unmasked original $dI/dV(|\mathit{q}|,V)$. (f) The contour plots of both (c) and (d) with the background showing their sum. The black dashed lines in (e) and (f) indicate the EDC maxima of the backgrounds. As shown in (e),(f) and their insets, the increase of the replica band intensity $Z_R$, the band shifts of the filled and the empty state $\alpha$ band segments toward the Fermi level (yellow arrows) and the down-shift of the filled-state replica band segment (yellow arrows) are visible as the superconducting gap is increased (orange arrows).

Figure 4

(a) $dI/dV$ map at $-18\mathrm{meV}$ showing the $C_2$ defects corresponding to O vacancies in the ${\mathrm{VO}}_2$ layer above the topmost FeAs plane. (b) The $dI/dV$ map in (a) overlaid on the gap map in Fig. 1. (c) Gap histograms taken over all field of view and over $C_2$ defects only, with their fitted Gaussian curves shown. The right inset shows $dI/dV$ spectra taken over the six points on (red) and away from (black) a $C_2$ defect shown in the left inset. (d),(e) Crystal structures without and with a $C_2$ defect induced by an O vacancy in ${\mathrm{VO}}_2$ layer. Arrows indicate the proportionally exaggerated ionic displacements for the symmetric breathing phonon mode. The O vacancies at $A_2$ and $B_2$ sites are invisible to our tunneling measurement but they should exist and affect the superconductivity in the same way as the visible O vacancies on $A_1$ and $B_1$ sites seen in (a).