Resonant electronic Raman excitations with $A_{2g}$ symmetry in the topological insulator Bi$_2$Se$_3$*

Inelastic light scattering from Dirac fermions can lead to electronic excitations odd in time reversal symmetry~\footnote{E. Riccardi et al., PRL 116, 066805}$^,$\footnote{O. Kashuba and V.I. Fal'ko, PRB 80, 241404(R)}. Here, we report the observation of a sharp collective mode with energy of 150\,meV, below the edge of a gapped continuum, in bulk Bi$_2$Se$_3$. Both the gapped continuum and the collective mode have pseudovector-like symmetry of the $A_{2g}$ representation of the $D_{3d}$ group, and are only present when excitation energy is in resonance with interband transitions between the occupied and unoccupied Dirac surface states. The gapped continuum can be understood as the electron-hole excitations between the lower and upper Dirac cones near the Fermi surface, whereas the slightly below gap edge collective mode is the excitonic bound states of the electron-hole pairs. Such inter-Dirac-cone excitation flips the in-plane electron spin, but preserves the out-of-plane angular momentum, resulting in singlet excitonic states. Such exciton is dark in photoluminescence spectra, as opposed to the doublet states which can be populated with circularly polarized light. This is a demonstration of novel collective excitation from the surface states of 3D topological insulators.