Data measured at (a) 3.65, 3.7 and 3.75 K and (b) 2.6, 2.65 and 2.7 K in the in-plane magnetic field of 9 T, where α is the angle between the field and the Fe-Se-Fe bond direction. Fourfold oscillations are observed and the amplitude is ~0.12 mJ mol⁻¹ K⁻² (T=2.6 K). The fourfold oscillations were repeatable in two separate samples. The maximum of C/T is located at about zero degrees (H||Fe-Se-Fe), whereas the sign of the oscillations is reversed when the temperature is increased to 3.7 K. The red lines are theoretical simulations (see Supplementary Methods) using the d(x²−y²) order parameter Δ_k=Δ₀ (cos k_x−cos k_y). The actual functional dependence is not important: any reasonable model that yields the gap nodes located at the same directions4647 would produce a very similar angular dependence. (c) The temperature dependence of the difference of C/T at 0° and 45°, a crossover is clearly seen at ~2.9 K. The random error bars (after the averaging of 300 data points) of specific heat are ±0.04 mJ mol⁻¹ K⁻². (d) Possible locations of nodes or gap minima suggested by our data are shown by the red and blue balls on the folded electron Fermi pockets, and by red segments on the hole Fermi surfaces. The ellipticity of the electron pockets is exaggerated in this drawing.

(a) The temperature dependence of resistivity in a wide temperature region for the FeSe_0.45Te_0.55 sample. It shows a sharp resistive transition at T_c,mid ≈ 14.5 K. (b) Zero-field-cooling (ZFC) and field-cooling (FC) magnetization measured in the field of 10 Oe. The magnetization in the low-temperature region is flat and the Meissner screening volume is almost 100%. (c, d) Resistivity in magnetic fields (c) H||ab and (d) H||c. The curves from the right to left correspond to magnetic fields of 0, 0.2, 0.5, and from 1 to 9 T with increments of 1 T. The random error bars of resistivity and magnetization are ±0.0005 mΩ cm and ±0.0008 e.m.u. mol⁻¹, respectively. (e) The upper critical fields H_c2(T) for in-plane and out-of-plane field orientations, with error bars of ±0.05 T. The black line shows H||ab, whereas the red line refers to H||c.

(a) The angle dependence of the gap on the electron pocket around M(π,π), based on the extended s-wave gap function Δ_e (φ)=Δ₀ [1−r sin 2φ] with Δ₀=1.3 meV. The minima are located at 45° (Fe–Fe or ΓM direction), if 1>r>0. For the negative r, maxima are located at −45°. For |r|>1, instead of minima, sign-changing nodes appear. (b, c) The FSs of FeSe_xTe_1−x, as calculated from first principles. Note the strong warping of the outer electron pocket (now shown in the center of the picture for a better view). The shading represents the function , which controls the electronic transport in the ab-plane (b), and the same for (c axis transport) (c).