Spatial inhomogeneity of the superconducting gap and order parameter in FeSe${}_{0.4}$Te${}_{0.6}$

We have performed a low-temperature scanning tunneling microscopy and spectroscopy study of the iron chalcogenide superconductor ${\mathrm{FeSe}}_{0.4}{\mathrm{Te}}_{0.6}$ with $T_{\mathrm{C}}\approx 14$ K. Spatially resolved measurements of the superconducting gap reveal substantial inhomogeneity on a nanometer length scale. Analysis of the structure of the gap seen in tunneling spectra by comparison with calculated spectra for different superconducting order parameters ($s$-wave, $d$-wave, and anisotropic $s$-wave) yields the best agreement for an order parameter with anisotropic $s$-wave symmetry with an anisotropy of $\sim$40%. The temperature dependence of the superconducting gap observed in places with large and small gap size indicates that it is indeed the superconducting transition temperature which is inhomogeneous. The temperature dependence of the gap size has been found to differ from the one predicted by BCS theory. An analysis of the local gap size in relation to the local chemical composition shows almost no correlation with the local concentration of Se/Te atoms at the surface.

Figure 1

(a) Atomically resolved topography of ${\mathrm{FeSe}}_{0.4}{\mathrm{Te}}_{0.6}$ ($80\times 80$ nm${}^2$), taken at $2.1$ K ($V=90$ mV, $I=0.2$ nA). Inset in (a) shows a magnified image of the atomic lattice, which contains $\mathrm{Se}$ and $\mathrm{Te}$ atoms. (b) Temperature-dependent spectra (4096 single spectra) averaged over an area of size $20\times 20$ nm${}^2$ (stabilization condition: $V=40$ mV, $I=0.5$ nA).

Figure 2

(a) Gap map of ${\mathrm{FeSe}}_{0.4}{\mathrm{Te}}_{0.6}$ taken in an area of $20\times 20$ nm${}^2$ obtained from a spectroscopic map taken with a tunneling set point of $V=40$ mV and $I=0.5$ nA before switching off the feedback loop. Over this area we have acquired temperature-dependent spectroscopic maps with $64\times 64$ points. (b) Histogram of the gap distribution. (c) Raw spectra along the line cut shown in (a). (d) Autocorrelation of the gap map taken over a large field of view ($38\times 38$ nm${}^2$). (e) Radial line cut around the center of the autocorrelation shown in (d) obtained by averaging azimuthally (blue); the solid red line represents a fit of an exponential decay to the radial line cut.

Figure 3

The black symbols represent a spectrum extracted from a spatial average of the map shown in Fig. 2a at $2.1$ K. The spectrum has been symmetrized and normalized as discussed in the text. Blue, red, and green solid lines are fitted curves using Eq. (1) with $s$-wave [$\Delta \left(\theta \right)={\Delta }_0$], anisotropic $s$-wave (${\Delta }_0+{\Delta }_1\cos 4\theta$), and $d$-wave (${\Delta }_0\cos 2\theta$) gap functions, respectively.

Figure 4

(a) and (b) Averaged spectra acquired at different temperatures over two different areas of size $\sim$$3\times 3$ nm${}^2$ each in regions with large [position 1 in Fig. 2a] and small [position 5 in Fig. 2a] local gap size. (c) and (d) Symmetrized and normalized spectra taken at different temperatures in regions of (a) large and (b) small gap size with fits (solid lines) according to Eq. (1) for an anisotropic $s$-wave order parameter and accounting for thermal broadening. Spectra are normalized by spectra taken at 16 K.

Figure 5

(a) Gap size ${\Delta }_0$ as a function of $T$ for different gap regions [marked in Fig. 2 (a)], showing local differences in the temperature at which the gap is completely closed. Solid lines are fits of a $\sqrt{1-T/T_{\mathrm{C}}}$ behavior for the temperature dependence of the gap size. The dashed light blue line is the temperature dependence of the superconducting gap as it would be expected from BCS theory for an $s$-wave gap [assuming the same $T_{\mathrm{C}}$ and ${\Delta }_0\left(0\right)$ as obtained from the fit of the dark blue line for region 1]. (b) Tunneling spectra from a spectroscopic map averaged for different ranges of relative topographic heights and normalized at $V=-10$ mV (marked by the green arrow). Inset: The same spectra as in the main graph normalized at the energy of the coherence peak (marked by the blue arrow).