  Quasi-two-dimensional layered BiSe, a natural super-lattice with
Bi2Se3-Bi2-Bi2Se3 units, has recently been predicted to be a dual topological
insulator, simultaneously weak topological insulator as well as topological
crystalline insulator. Here using structural, transport, spectroscopic
measurements and density functional theory calculations, we show that BiSe
exhibits rich phase diagram with the emergence of superconductivity with Tc ~8K
under pressure. Sequential structural transitions into SnSe-type energetically
tangled orthorhombic and CsCl-type cubic structures having distinct
superconducting properties are identified at 8 GPa and 13 GPa respectively. Our
observation of weak-antilocalization in magneto-conductivity suggests that
spin-orbit coupling (SOC) plays a significant role in retaining non-trivial
band topology in the trigonal phase with possible realization of 2D topological
superconductivity. Theoretical analysis reveals that SOC significantly enhances
superconducting Tc of the high-pressure cubic phase through an increase in
electron-phonon coupling strength. Simultaneous emergence of Dirac-like surface
states suggests cubic BiSe as a suitable candidate for the 3D-topological
superconductor.
