Signature of BCS-BEC Crossover in an Iron-Based Superconductor FeSe$_{\mathrm{0.5}}$Te$_{\mathrm{0.5}}$.

Microscopic mechanism of superconductivity in high-T$_{\mathrm{C}}$ superconductors has been one of the burning questions of condensed matter physics at the moment. Here, we present the scanning tunneling microscopy/spectroscopy (STM/STS) studies of an iron-based superconductor, FeSe$_{\mathrm{0.5}}$Te$_{\mathrm{0.5}}$ [1]. The value of superconducting order parameter $\Delta $, has been extracted from differential conductance (dI/dV) spectra with the help of extended Bardeen Cooper Schieffer (BCS) phenomenology for anisotropic s-wave pairing. The tunneling spectra are quite inhomogeneous with the values of $\Delta $ extended from $\sim $0.6 to $\sim $4.5 meV and have two distinct peaks in the histogram around 1 and 3 meV. The corresponding values of pairing strength, 2$\Delta $/k$_{\mathrm{B}}$T$_{\mathrm{C}}$ for the peaks are $\sim $1.5 and $\sim $5.0, respectively, which indicates the coexistence of weak and strong coupling mechanism. We also measured the gap to Fermi energy ratio ($\Delta $/E$_{\mathrm{f}}$ ) of the material and found two different regions of coupling inferring to the composite superconductivity in the realm of BCS-BEC (Bose Einstein Condensate) crossover. [1] Kunwar S., et.al. J Supercond Nov Magn, 30, 3183 (2017).