Superconducting gaps in FeSe studied by soft point-contact Andreev reflection spectroscopy

FeSe single crystals have been studied by soft point-contact Andreev reflection spectroscopy. Superconducting gap features in the differential resistance $dV/dI\left(V\right)$ of point contacts such as a characteristic Andreev reflection double-minimum structure have been measured versus temperature and magnetic field. Analyzing $dV/dI$ within the extended two-gap Blonder-Tinkham-Klapwijk model allows one to extract both the temperature and magnetic field dependence of the superconducting gaps. The temperature dependence of both gaps is close to the standard BCS behavior. Remarkably, the magnitude of the double-minimum structure gradually vanishes in magnetic field, while the minima position only slightly shifts with field, indicating a weak decrease of the superconducting gaps. Analyzing the $dV/dI\left(V\right)$ spectra for 25 point contacts results in the averaged gap values $\langle {\mathrm{\Delta }}_L\rangle =1.8\pm 0.4\mathrm{meV}$ and $\langle {\mathrm{\Delta }}_S\rangle =1.0\pm 0.2$ meV and reduced values $2\langle {\mathrm{\Delta }}_L\rangle /k_B{T}_c=4.2\pm 0.9$ and $2\langle {\mathrm{\Delta }}_S\rangle /k_B{T}_c=2.3\pm 0.5$ for the large ($L$) and small ($S$) gap, respectively. Additionally, the small gap contribution was found to be within tens of percent, decreasing with both temperature and magnetic field. No signatures in the $dV/dI$ spectra were observed, testifying to a gapless superconductivity or the presence of even smaller gaps.

Figure 1

Upper panel: Examples of raw $dV/dI$ curves measured at 3 K for three “soft” PCs created by a tiny drop of silver paint on a cleaved FeSe surface. The small picture shows an image of the FeSe single crystal (triangle shape) with a drop of silver paint and a Cu wire with a diameter of 0.08 mm. Bottom panel: Antisymmetric part $dV/d{I}^{\text{as}}(\%)=100[dV/dI(V>0)-dV/dI(\mathrm{V}<0)]/2dV/dI(V=0)$ of $dV/dI$ calculated for the PCs from the upper panel. The inset shows the behavior of thermopower in single FeSe crystals according to Kasahara et al. [2] and FeSe polycrystals reported by Song et al. [17] and Bhaskar et al. [18].

Figure 2

(a) Temperature and (b) magnetic field evolution of the $dV/dI$ spectra of a soft FeSe PC with a normal state resistance of 1.45 $\mathrm{\Omega }$. The left insets on both panels show $dV/dI$ at a larger bias taken at low temperature and (a) above the critical temperature or (b) at maximal magnetic field. The right inset in (a) shows the fit of the symmetrized $dV/dI$ at 3 K normalized to the normal state (see text and Table 1, No. 552) by the two-gap Blonder-Tinkham-Klapwijk model, while the right inset in (b) shows the fit of the same $dV/dI$ by the anisotropic model $\mathrm{\Delta }={\mathrm{\Delta }}_0(1+\alpha cos4\mathrm{\Theta })$ (see text).

Figure 3

Temperature and magnetic field dependencies of the fitting parameters for the PC from Fig. 2 in a two-gap approximation: Solid and open triangles are the large and small gaps ${\mathrm{\Delta }}_L$ and ${\mathrm{\Delta }}_S$, respectively, ${\mathrm{\Gamma }}_L$ is the broadening parameter (squares), $Z$ is the barrier parameter (diamonds), and $V_{\text{min}}$ is the minimum position in $dV/dI$ (crosses). Solid lines are BCS-like curves.