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Optical probe on doping modulation of magnetic Weyl semimetal Co$_3$Sn$_2$S$_2$

The magnetic Weyl semimetal Co$_3$Sn$_2$S$_2$ is extensively investigated due to its giant anomalous Hall effect (AHE).Recent studies demonstrate that the AHE can be effectively tuned by multi-electron Ni doping.To reveal the underlying mechanism of this significant manipulation,it is crucial to explore the band structure modification caused by Ni doping. Here,we study the electrodynamics of both pristine and Ni-doped Co$_{3-x}$Ni$_x$Sn$_2$S$_2$ with $x=$0, 0.11 and 0.17 by infrared spectroscopy. We find that the inverted energy gap around the Fermi level($E_{F}$) gets smaller at $x=$0.11,which is supposed to enhance the Berry curvature and therefore increase the AHE.Then $E_{F}$ moves out of this gap at $x=$0.17. Additionally,the low temperature carrier density is demonstrated to increase monotonically upon doping,which is different from previous Hall measurement results. We also observe the evidences of band broadening and exotic changes of high-energy interband transitions caused by doping.Our results provide detailed information about the band structure of Co$_{3-x}$Ni$_x$Sn$_2$S$_2$ at different doping levels,which will help to guide further studies on the chemical tuning of AHE.