  Resolving the conductance of the topological surface states (TSSs) from the
bulk contribution has been a great challenge for studying the transport
property of topological insulators. By developing a non-purturbative diffusion
equation that describes fully the spin-charge dynamics in the strong spin-orbit
coupling regime, we present a proposal to read the charge transport information
of TSSs from its spin dynamics which can be isolated from the bulk contribution
by time-resolved second harmonic generation pump-probe measurement. We
demonstrate the qualitatively different Dyaknov-Perel spin relaxation behavior
between the TSSs and the two-dimensional spin-orbit coupling electron gas. The
decay time of both in-plane and out-of-plane spin polarization is naturally
proved to be identical to the charge transport time. The out-of-plane spin
dynamics is shown to be in the experimentally reachable regime of the
femtosecond pump probe spectroscopy and thereby we suggest experiments to
detect the charge transport property of the TSSs from their unique spin
dynamics.
