Topological Insulators (TIs) are materials in which the bulk is insulating but the surface hosts metallic states due to non-zero topological invariants of the bulk band structure. A topological superconductor is analogous to a TI in that the superconducting gap function has a nontrivial topological invariant. Although a great success has been achieved in the study of topological insulators, progress in establishing bulk topological superconductivity has been slow until recently. In this talk, I will introduce our efforts in the quest of topological superconductivity in doped topological insulators CuxBi2Se3  and Sn1-xInxTe [2,3], as well as in strongly electron-correlated superconductor Rb2Cr3As3 .
In Cu0.3Bi2Se3, our 77Se nuclear magnetic resonance measurements showed that spin rotation symmetry is spontaneously broken in the hexagonal plane below the superconducting transition temperature Tc=3.4 K . This is the first evidence for such symmetry breaking found in any superconductors. Our results not only establish spin-triplet (odd parity) superconductivity in this compound, but also show that it is a topological superconductor belonging to DIII class. We will also report the doping mechanism and superconductivity in Sn1-xInxTe [2,3]. In Rb2Cr3As3 (Tc=4.8 K ), we found strong ferromagnetic spin fluctuations in the normal state and point nodes in the superconducting gap , which suggest that this compound is a solid-state analogue of superfluid 3He.
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