Observation of anomalous temperature dependence of spectrum on small Fermi surfaces in a ${\mathrm{BiS}}_2$-based superconductor

We have performed an angle-resolved photoemission spectroscopy study of the ${\mathrm{BiS}}_2$-based superconductor $\mathrm{Nd}(O,F){\mathrm{BiS}}_2$. Two small electronlike Fermi surfaces around $X(\pi ,0)$ are observed, which enclose $2.4\%$ and $1.1\%$ of the Brillouin zone area, respectively, corresponding to an electron doping of $7\%$ per Bi site. The Fermi surface topology is far from the nesting scenario proposed in most of the theoretical models for the ${\mathrm{BiS}}_2$-based superconductors. The conduction bands show significant anisotropic splitting along $XM$ and $\Gamma X$, which is attributed to the cooperative effects of large spin-orbit coupling and interlayer coupling. The low-energy spectrum exhibits a weakly dispersing broad hump near the bottom of the conduction bands. This hump is drastically suppressed with increasing temperature, while the spectral weight at the Fermi level is essentially unaffected. These anomalous spectral features indicate that the electrons could be strongly coupled with the lattice in the low-temperature normal state of this superconductor.

Figure 1

(a) ARPES intensity plot along the high-symmetry lines $\Gamma -M-X-\Gamma$ taken at 30 K. $\Gamma -X$ is along the nearest Bi-Bi direction. (b) Corresponding two-dimensional curvature intensity plot. LDA bands without SOC of ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$, which are essentially the same as those of ${\mathrm{NdO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$ in the energy in our experiments [16], are also plotted in (b) for comparison. Calculations were performed using the optimized lattice parameters [13]. The calculated bands are shifted up by 0.5 eV to match the experimental band dispersions. (c) Corresponding EDCs. (d) Magnification of the box in (c).

Figure 2

(a) ARPES intensity plot at $E{}_F$ as a function of the two-dimensional wave vector taken at 30 K. The intensity is obtained by integrating the spectra within $\pm 15$ meV with respect to $E{}_F$. The data are symmetrized by assuming a fourfold symmetry with respect to $\Gamma$. Red and blue lines represent the extracted FSs. White lines labeled cut 1 and cut 2 indicate the momentum locations, along which the data are shown in Figs. 3 and 4, respectively. (b) Magnification of the dashed box in (a). Circles and squares show the experimentally determined $k{}_F$ points. Dashed black lines represent the LDA+SOC calculated FSs. (c, d) Calculated conduction bands at $X$ using one-${\mathrm{BiS}}_2$-layer models with and without SOC, respectively. (e, f) Same as (c) and (d), respectively, but using two-${\mathrm{BiS}}_2$-layer models. In (c)–(f), the zero energy is defined to the band bottom at $X$ and the horizontal dashed lines at 0.3 eV represent the approximate position of $E{}_F$.

Figure 3

(a) ARPES intensity plot along $XM$ [cut 1 from Fig. 2] taken at 30 K. Red and blue lines represent the dispersions extracted from the peak positions of the MDCs and EDCs, respectively. Dashed black lines represent the LDA+SOC calculated bands. (b) Corresponding intensity plot of second derivative along momentum. Dotted lines are the same as the red lines in (a). (c) Corresponding EDCs. Crosses indicate the peak positions of the EDCs. Black, blue, and green curves represent the EDCs at $X$, $k{}_{F1}$, and $k{}_{F2}$, respectively. $k{}_{F1}$ and $k{}_{F2}$ are the Fermi wave vectors of the inner and outer electronlike bands, respectively. (d) Corresponding MDCs. Short verticals indicate the peak positions of the MDCs. Blue and green curves represent the MDCs at $E{}_F$ and –0.4 eV, respectively. (e) EDC at $k{}_{F2}$. Blue line represents a linear extrapolation of the slope on the lower-binding-energy side of the hump. (f) MDC at $E{}_F$. The MDC is fitted to four Lorentzian peaks, indicating the band splitting along $XM$ due to SOC.

Figure 4

(a, b) ARPES intensity plots through the $X$ point [cut 2 from Fig. 2] taken at 30 and 230 K, respectively. (c) $E-k$ plot of the positions of the EDC and MDC peaks taken at 30 and 230 K, respectively. To approximately remove the effect of the Fermi function to the EDC peak position near $E{}_F$, the EDC peak position is extracted from the symmetrized curve with respect to $E{}_F$. (d, e) MDCs at $E{}_F$ and EDCs at $k{}_F$ of the left branch taken at various temperatures between 30 and 230 K, respectively. The thermal broadening effect on the EDCs in (e) is removed (see text for details). Inset of (e) plots the EDCs (raw data) in an energy window of [–0.05, 0.05 eV]. (f) Spectral weight (left axis) and binding energy of the maximum (right axis) of the broad hump against temperature. The spectral weight is obtained by subtracting the integration of the EDC at 230 K from that taken at the corresponding temperature.