Unconventional Superconductivity in the ${\mathrm{BiS}}_2$-Based Layered Superconductor ${\mathrm{NdO}}_{0.71}{\mathrm{F}}_{0.29}{\mathrm{BiS}}_2$

We investigate the superconducting-gap anisotropy in one of the recently discovered ${\mathrm{BiS}}_2$-based superconductors, ${\mathrm{NdO}}_{0.71}{\mathrm{F}}_{0.29}{\mathrm{BiS}}_2$ ($T_c\sim 5\mathrm{K}$), using laser-based angle-resolved photoemission spectroscopy. Whereas the previously discovered high-$T_c$ superconductors such as copper oxides and iron-based superconductors, which are believed to have unconventional superconducting mechanisms, have $3d$ electrons in their conduction bands, the conduction band of ${\mathrm{BiS}}_2$-based superconductors mainly consists of Bi $6p$ electrons, and, hence, the conventional superconducting mechanism might be expected. Contrary to this expectation, we observe a strongly anisotropic superconducting gap. This result strongly suggests that the pairing mechanism for ${\mathrm{NdO}}_{0.71}{\mathrm{F}}_{0.29}{\mathrm{BiS}}_2$ is an unconventional one and we attribute the observed anisotropy to competitive or cooperative multiple paring interactions.

Figure 1

FS and $E\text{−}k$ maps of ${\mathrm{NdO}}_{0.71}{\mathrm{F}}_{0.29}{\mathrm{BiS}}_2$. FS maps measured using (a) He $\mathrm{I}\alpha$ at 10 K and (c) a VUV laser at 8 K. The integration energy window of each FS map is $\pm 5\mathrm{meV}$ from $E_F$. Red, blue, and green symbols indicate the positions of $k_F$. The solid square in (a) corresponds to the region displayed in (c). The definition of the FS angle $\varphi$ is shown in (c), and the open circle in (c) indicates the $k_F$ for the temperature-dependent EDC shown in Fig. 2. (b) $E\text{−}k$ map along cut 1 in (a) measured using He $\mathrm{I}\alpha$ at 10 K. (d) Enlarged plot for the region indicated by the solid square displayed in (c). (e) $E\text{−}k$ map along cut 2 in (c) measured using the VUV laser at 8 K.

Figure 2

Temperature-and FS-angle-dependent symmetrized EDCs at $k_F$ measured using $c$-polarized light. (a) Temperature-dependent EDC symmetrized with respect to $E_F$ at $k_F$ indicated by the open circle in Fig. 1. (b) Temperature dependence of the SC gap size deduced from the fitting. The solid line indicates the SC gap size from the BCS theory for $\mathrm{\Delta }(0)=810\mu \mathrm{eV}$ and $T_c=5\mathrm{K}$. (c)–(e) Symmetrized EDCs at $k_F$ (c) in the degenerate region, and clearly separated region of (d) outer FS and (e) inner FS. The EDCs were measured at 1.5 and 8 K ($T_c\sim 5\mathrm{K}$) for various FS angles $\varphi$, as shown in each panel. Gray symbols indicate the EDCs above $T_c$, and solid lines indicate the fitting functions using a BCS spectral function. EDCs before symmetrization are shown in Fig. S2 of Supplemental Material [28].

Figure 3

SC gap anisotropy of ${\mathrm{NdO}}_{0.71}{\mathrm{F}}_{0.29}{\mathrm{BiS}}_2$. (a),(b) The $k_F$ positions at which the SC gap was measured plotted on the FS map image for the outer and inner FSs, respectively. Color scale corresponds to each SC gap size derived from the fitting. Solid symbols are derived from the EDCs shown in Fig. 2; open symbols are plotted after symmetrization, taking into account the tetragonal crystal symmetry. (c),(d) SC gap sizes derived from the fitting plotted as a function of FS angle for the outer and inner FSs, respectively. Error bar denotes the standard deviation of the $E_F$ position (see Supplemental Material and Fig. S6 therein [28]). Solid lines are fitting functions using a model gap function of $\mathrm{\Delta }(\varphi )=|{\mathrm{\Delta }}_0[1+{\mathrm{\Delta }}_2\cos (2\varphi )+{\mathrm{\Delta }}_4\cos (4\varphi )+{\mathrm{\Delta }}_6\cos (6\varphi )+{\mathrm{\Delta }}_8\cos (8\varphi )]|$. (e),(f) Enlarged plots for the regions indicated by solid squares in (c) and (d), respectively.

Figure 4

Schematic illustration of multiple pairing interactions. Positive and negative SC gaps $\mathrm{\Delta }$ correspond to those originated from attractive and repulsive interactions, respectively. (a) Competition of $q$-independent conventional electron-phonon coupling and $q$-dependent repulsive spin fluctuations. (b) Cooperation of $q$-independent electron-phonon coupling and $q$-dependent attractive charge fluctuations. (c) Competition of $q$-dependent attractive charge fluctuations and $q$-dependent repulsive spin fluctuations. The attractive charge fluctuations are assumed to be peaked at $q=(0,0)$, whereas the repulsive spin fluctuations are assumed to be peaked at $q=(\pi ,\pi )$.