  We report on time-resolved mid-infrared-pump terahertz-transmission-probe
studies of the topological-insulator materials $(Bi_{1-x}Sb_{x})_{2}Te_{3}$, in
which by varying x charge carriers are chemically tuned to be of n-type or
p-type. Relaxation dynamics is found to be different in various aspects for
transitions below or above the bandgap, which are selectively excited by
changing the pump-pulse energy. For the below-bandgap excitation, an
exponential decay of the pump-probe signals is observed, which exhibits linear
dependence on the pump-pulse fluence. In contrast, the relaxation dynamics for
the above-bandgap excitation is characterized by a compressed exponential decay
and nonlinear fluence dependence at high pump flunences, which reflects
interaction of the excited nonequilibrium states.
