Superconductivity enhanced by Se-doping in Eu$_{3}$Bi$_{2}$S$_{4}$F$_{4}$

We investigated the negative chemical pressure effect of Eu$_{3}$Bi$_{2}$S$_{4}$F$_{4}$ by partially substituting S with Se. The ``parent'' compound Eu$_{3}$Bi$_{2}$S$_{4}$F$_{4}$ is a new member of the BiS$_{2}$-based superconductors. [H.F. Zhai et al., J. Am. Chem. Soc. 136, 15386$-$15393, (2014)] It shows anomalous Eu valence and superconductivity of $T_{c}=$1.5 K without chemical doping. With S/Se-doping, we found that a CDW-like anomaly is gradually suppressed to lower temperatures, and meanwhile the superconductivity (SC) is enhanced. For Eu$_{3}$Bi$_{2}$S$_{2}$Se$_{2}$F$_{4}$, $T_{c}$ reaches 3.4 K. Magnetization measurements reveal an average Eu valence of $\sim$ 2.06, which means that Se doping does not introduce extra electrons but instead, lowers down to a low electron doping level of $x $ $\sim$ 0.1. Therefore, the present system manifested itself as a rare example of existence of SC at very low doping levels.