Josephson spectroscopy study of kagome superconductors toward the deep point-contact regime

Josephson scanning tunneling microscopy (JSTM) has emerged as an important technique for probing the superconducting order parameter at the atomic scale. However, the Josephson current in JSTM may behave quite differently when the coupling strength varies. Here, we push the junction to the deep point-contact regime, reaching a normal-state junction resistance of only 0.15 $h/2e^2 \simeq 2~{\rm k}Ω$. We demonstrate, using kagome superconductors, that the zero-bias conductance, a key characteristic of the Josephson current, deviates strongly from the quadratic dependence on the normal-state conductance upon entering the deep point-contact regime. Furthermore, we observe a striking saturation of the zero-bias conductance, which we show arises from the series resistance in the circuit. This also serves as a cautious reminder when interpreting zero-bias conductance saturation or quantization in studies of exotic physics such as that of Majorana zero modes if the tip-sample junction resistance is extremely small. Finally, we identify an optimum regime where JSTM can be used as an atomic-scale probe for studying pair-density wave states in materials with low superconducting transition temperature, such as AV3Sb5 kagome superconductors.