Spectroscopic-imaging STM studies of superconductivity and nematicity in FeSe$_{1-x}$S$_x$

FeSe$_{1-x}$S$_x$ exhibits electronic nematic order that is suppressed with increasing sulfur content $x$. The nematic order disappears in the bulk above $x\sim$0.17, whereas superconducting transition temperature $T_c = 9\sim10$~K remains almost unchanged~[1]. We performed spectroscopic-imaging STM experiments on FeSe$_{1-x}$S$_x$ to investigate the change in the band structure and the superconducting gap across the nematic quantum critical point at $x\sim$0.17. We have found that anisotropy of the in-plane band structure diminishes with increasing $x$ but survives at least locally even at $x>$0.17. Superconducting gap is hardly affected by sulfur doping in the nematic phase but becomes blunt at $x>$0.17. This result may suggest that superconductivity and nematicity are interrelated. [1] S. Hosoi {\it et al}., PNAS {\bf 113}, 8139 (2016).