We present a review of the superconducting properties of Cu, Sr and Nb doped Bi2Se3 compounds with a focus on high pressure effects. The parent compound Bi2Se3 is a topological insulator at ambient pressure and exhibits pressure-induced crystallographic phase transitions and superconductivity above 10 GPa. The doped compounds are all bulk superconductors with Tc~3 K and have been investigated intensively in the past decade because of their candidature for topological superconductivity (TSC). A key role as regards topological superconductivity is played by spontaneous rotational symmetry breaking (RSB), which is observed, for instance, as an anisotropy in the upper critical field Bc2. We discuss the pressure variation of Tc and the concomitant effect on the upper critical field. An analysis of the basal-plane anisotropy of Bc2 is presented in the context of an odd-parity unconventional superconducting state.
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