Transient Surface Photoemission Involving Nonlinear Surface Sheet Polarization Developed on the Doped Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}$ Topological Insulator*

Time- and angle-resolved photoemission spectroscopy is performed on the doped Bi$_{\mathrm{2}}$Se$_{\mathrm{3}}^{\mathrm{\thinspace }}$topological insulator. We observe unusual variation in the efficiency of photoemission from femto-to-picosecond non-equilibrium particularly when two-dimensional electron gas (2DEG) states are developed on surface, while the surface confinement potential is virtually unchanged. The results indicate that a surface sheet polarization, which is induced nonlinearly by both the photon field and inversion-symmetry-breaking field, grows in magnitude as the 2DEG states become pronounced and opens a so-called surface photoemission channel, \textit{div}\textbf{\textit{A,}} \quad that can be varied transiently. Matrix element effects investigated by linearly-polarized angle-resolved photoemission also supports the presence of \textit{div}\textbf{\textit{A}}. The asymmetric charge distribution developed around vacuum-surface interface is considered as a key to understand and control Rashba splitting of the 2DEG states.