Abstract
Plasmons dispersion and nonvertical interband transitions in Bi${}_{2}$Se${}_{3}$ single crystals were investigated by electron energy-loss spectroscopy in conjunction with (scanning) transmission electron microscopy [(S)TEM-EELS]. Both volume plasmons (\ensuremath{\pi} plasmon at 7 eV and \ensuremath{\pi} + \ensuremath{\sigma} plasmon at 17 eV) and surface plasmons (\ensuremath{\sim}5.5 and 10 eV) were demonstrated in STEM-EELS spectra and the corresponding spectral imaging in real space. In further EELS experiments in reciprocal space, the momentum-dependent spectra reveal very different dispersion behavior between \ensuremath{\pi} and \ensuremath{\pi} + \ensuremath{\sigma} plasmons, with \ensuremath{\pi} + \ensuremath{\sigma} plasmons showing a typical quadratic dependence, whereas the \ensuremath{\pi} plasmon exhibited a linear dispersion analogous to what was reported for graphene. Furthermore, a low energy excitation 0.7--1.6 eV was also observed which is attributed to direct nonvertical interband transitions along the \ensuremath{\Gamma}$F$ direction.
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