We systematically study the role of Weyl cone tilting in the spin Hall effect of light (SHEL) in doped Weyl semimetals (WSMs), and propose a new scheme to determine the type of a WSM and to sense the tilt degree of Weyl cones precisely. It is found that in the case of a small amount of doping, the SHEL in type-I WSMs shows almost no dependence on the tilt degree of Weyl cones, while the SHEL in type-II WSMs is extremely sensitive to variations in the degree of tilt. However, in the case of a large amount of doping, not only the SHEL in type-II WSMs but also the SHEL in type-I WSMs show strong dependences on the tilt degree. These trends are mainly attributed to the variation of the real part of the Hall conductivity with the tilt degree. Remarkably, by using a quantum weak measurement, the tiny SHEL shifts can be amplified and detected to a desirable accuracy. Based on the obviously different tilt-dependent characteristics of amplified SHEL shifts in WSMs, we propose a new scheme to determine the type of a WSM and to sense the tilt degree precisely. By adjusting the doping level, the sensing sensitivity can reach up to 1461.55 µm per degree of tilt. This study may provide an application reference for the fabrication of WSM parameter sensors and other topological photoelectric devices.
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