  We present a theoretical study on the high-field charge transport on the
surface of Bi$_2$Se$_3$ and reproduce all the main features of the recent
experimental results, i.e., the incomplete current saturation and the finite
residual conductance in the high applied field regime [Costache {\it et al.},
Phys. Rev. Lett. {\bf 112}, 086601 (2014)]. Due to the hot-electron effect, the
conductance decreases and the current shows the tendency of the saturation with
the increase of the applied electric field. Moreover, the electric field can
excite carriers within the surface bands through interband precession and leads
to a higher conductance. As a joint effect of the hot-electron transport and
the carrier excitation, the conductance approaches a finite residual value in
the high-field regime and the current saturation becomes incomplete. We thus
demonstrate that, contrary to the conjecture in the literature, the observed
transport phenomena can be understood qualitatively in the framework of surface
transport alone. Furthermore, if a constant bulk conductance which is
insensitive to the field is introduced, one can obtain a good quantitative
agreement between the theoretical results and the experimental data.
