We have performed a low temperature scanning tunneling microscopy and spectroscopy study of the iron chalcogenide superconductor FeSe_{0.4}Te_{0.6} with T_{C}~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 ~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 is substantially larger than would be expected from BCS theory. An analysis of the local gap size in relation with the local chemical composition shows almost no correlation with the local concentration of Se-/Te-atoms at the surface.
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