Physical characterization of chemically-doped YFe$_{\mathrm{2}}$Ge$_{\mathrm{2}}$ compounds at different Y, Fe and Ge sites

The discovery of superconductivity in the Fe pnictides in 2008 has triggered intensive research on the superconductivity of so called 122 ThCr$_{\mathrm{2}}$Si$_{\mathrm{2}}$-type AFe$_{\mathrm{2}}$As$_{\mathrm{2}}$ (A$=$alkali or alkaline earth metals) compounds, with many superconductors have been found in the past few years. On the other hand, experimental efforts are also carried out to search for superconductivity in the other non-pnictide systems with the same ThCr$_{\mathrm{2}}$Si$_{\mathrm{2}}$-type structures, i.e. RFe$_{\mathrm{2}}$Ge$_{\mathrm{2\thinspace }}$and RFe$_{\mathrm{2}}$Si$_{\mathrm{2}}$ where R$=$ rare earth elements. Superconductivity with transition temperature (T$_{\mathrm{c}})$ at 1.8K is indeed detected in the YFe$_{\mathrm{2}}$Ge$_{\mathrm{2}}$ through stringent synthesis procedure. Herein, we have carried out systematical doping studies at Y, Fe, and Ge sites, with the aim to further enhance the T$_{\mathrm{c}}$. The detail synthesis, x-ray analysis, electrical transport, and heat capacity measurements will be presented, and the results with potential quantum criticality will be discussed.