  Topological insulators embody a new state of matter characterized entirely by
the topological invariants of the bulk electronic structure rather than any
form of spontaneously broken symmetry. Unlike the 2D quantum Hall or quantum
spin-Hall-like systems, the three dimensional (3D) topological insulators can
host magnetism and superconductivity which has generated widespread research
activity in condensed-matter and materials-physics communities. Thus there is
an explosion of interest in understanding the rich interplay between
topological and the broken-symmetry states (such as superconductivity), greatly
spurred by proposals that superconductivity introduced into certain band
structures will host exotic quasiparticles which are of interest in quantum
information science. The observations of superconductivity in doped Bi_2Se_3
(Cu$_x$Bi$_2$Se$_3$) and doped Bi_2Te_3 (Pd$_x$-Bi$_2$Te$_3$ T$_c$ $\sim$ 5K)
have raised many intriguing questions about the spin-orbit physics of these
ternary complexes while any rigorous theory of superconductivity remains
elusive. Here we present key measurements of electron dynamics in
systematically tunable normal state of Cu$_x$Bi$_2$Se$_3$ (x=0 to 12%) gaining
insights into its spin-orbit behavior and the topological nature of the surface
where superconductivity takes place at low temperatures. Our data reveal that
superconductivity occurs (in sample compositions) with electrons in a bulk
relativistic kinematic regime and we identify that an unconventional doping
mechanism causes the topological surface character of the undoped compound to
be preserved at the Fermi level of the superconducting compound, where Cooper
pairing occurs at low temperatures. These experimental observations provide
important clues for developing a theory of topological-superconductivity in 3D
topological insulators.
