  Recently, the natural heterostructure of (PbSe)5(Bi2Se3)6 has been
theoretically predicted and experimentally confirmed as a topological
insulator. In this work, we induce superconductivity in (PbSe)5(Bi2Se3)6 by
implementing high pressure. As increasing pressure up to 10 GPa,
superconductivity with Tc ~ 4.6 K suddenly appears, followed by an abrupt
decrease. Remarkably, upon further compression above 30 GPa, a new
superconducting state arises, where pressure raises the Tc to an unsaturated
6.0 K within the limit of our research. Combining XRD and Raman spectroscopies,
we suggest that the emergence of two distinct superconducting states occurs
concurrently with the pressure-induced structural transition in this
topological heterostructure (PbSe)5(Bi2Se3)6.
