The exploration of topological superconductivity and Majorana zero modes has become a rapidly developing field. Many types of proposals to realize topological superconductors have been presented, and significant advances have been recently made. In this review, we conduct a survey on the experimental progress in possible topological superconductors and induced superconductivity in topological insulators or semimetals as well as artificial structures. The approaches to inducing superconductivity in topological materials mainly include high pressure application, the hard-tip point contact method, chemical doping or intercalation, the use of artificial topological superconductors, and electric field gating. The evidence supporting topological superconductivity and signatures of Majorana zero modes are also discussed and summarized.
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