Unified trend of superconducting transition temperature versus Hall coefficient for ultrathin FeSe films prepared on different oxide substrates

High transition temperature ($T_{\mathrm{c}}$) superconductivity in FeSe/$\mathrm{SrTi}{\mathrm{O}}_3$ has been widely discussed on the possible mechanisms in conjunction with the various effects of interface between FeSe and $\mathrm{SrTi}{\mathrm{O}}_3$ substrate. By employing an electric-double-layer transistor configuration, which enables both the electrostatic carrier doping and electrochemical thickness tuning, we investigated the interfacial effect on the high-$T_{\mathrm{c}}$ phase at around 40 K in FeSe films deposited on $\mathrm{SrTi}{\mathrm{O}}_3$, MgO, and $\mathrm{KTa}{\mathrm{O}}_3$ substrates. The systematic study on thickness dependence of transport properties under a certain gate voltage reveals the universal trend of the onset $T_{\mathrm{c}}$ against the Hall coefficient in all the FeSe films, irrespective of the substrate materials in which the different contribution of interfacial effect is expected. The independence of the highest $T_{\mathrm{c}}$ on substrate materials evidences that the high-$T_{\mathrm{c}}$ superconductivity at around 40 K does not primarily originate from a specific interface combination but from a charge carrier filling at specific electronic band structure.

Figure 1

(a) Schematics of layer geometry of FeSe-EDLT on oxide substrate and (b) corresponding conduction band minimum (CBM, solid red line) at the M point and valence band maximum (VBM, solid blue line) at the Γ point. The length scales $d,d_{\mathrm{bulk}},d_{\mathrm{EDL}}$, and $d_{\mathrm{CT}}$ indicate thicknesses of total FeSe film, bulky middle layer, electron-rich layers from EDL, and from substrate, respectively. (c) Optical micrograph of FeSe-EDLT with Hall bar geometry. S and D stand for source and drain electrodes.

Figure 2

Normalized sheet resistance with respect to $T=100\mathrm{K}$ (denoted $R/R^{100\mathrm{K}}$) as a function of temperature for FeSe on (a) $\mathrm{SrTi}{\mathrm{O}}_3$, (b) MgO, and (c) $\mathrm{KTa}{\mathrm{O}}_3$ substrates. The arrow in Fig. 2 indicates the $T_{\mathrm{c}}^{\mathrm{on}}$ at which extrapolated lines from the normal state and the superconducting transition region intersect. The corresponding Hall resistance $R_{\mathrm{Hall}}$ measured at $T=50\mathrm{K}$ are shown for FeSe on (d) $\mathrm{SrTi}{\mathrm{O}}_3$, (e) MgO, and (f) $\mathrm{KTa}{\mathrm{O}}_3$ substrates. Color code reflects film thickness.

Figure 3

Thickness dependence of (a) $T_{\mathrm{c}}^{\mathrm{on}}$ and (b) $R_{\mathrm{H}}$ at $T=50\mathrm{K}$ for the FeSe-EDLT on $\mathrm{SrTi}{\mathrm{O}}_3$ (green), MgO (red), and $\mathrm{KTa}{\mathrm{O}}_3$ (purple) substrates. (c) (Top) Schematic image of electronic band structure of FeSe film at different thickness regions. (Bottom) A sketch of thickness dependence of $R_{\mathrm{H}}$ for FeSe-EDLT in this study.

Figure 4

$T_{\mathrm{c}}^{\mathrm{on}}$ as a function of $R_{\mathrm{H}}$ at $T=50\mathrm{K}$ for FeSe-EDLT on $\mathrm{SrTi}{\mathrm{O}}_3$ (filled green circles), MgO (filled red triangles), and $\mathrm{KTa}{\mathrm{O}}_3$ (filled purple squares). The data for another FeSe-EDLT on $\mathrm{KTa}{\mathrm{O}}_3$ during etching before the discharging experiments presented in Fig. 5 is also plotted (open purples squares).

Figure 5

(a) $R/R^{100\mathrm{K}}-T$ curves for discharging experiments for 1.0-nm-thick FeSe on $\mathrm{KTa}{\mathrm{O}}_3$. (b) The corresponding Hall resistance measured at $T=50\mathrm{K}$. (c), (d) The same data set for 2.9-nm-thick FeSe on MgO. Color code reflects the degree of discharging. (e) $T_{\mathrm{c}}^{\mathrm{on}}-R_{\mathrm{H}}$ curve for discharging experiments on 2.9-nm-thick FeSe/MgO (open red triangles) and 1.0-nm-thick FeSe/$\mathrm{KTa}{\mathrm{O}}_3$ (open purple squares). Arrows indicate the direction of removing $V_{\mathrm{G}}$. For comparison, the data for 10-nm-thick FeSe EDL transistor [24] (filled gray squares) are also plotted.