Evidence of reduced surface electron-phonon scattering in the conduction band of Bi${}_2$Se${}_3$ by nonequilibrium ARPES

The nature of the Dirac quasiparticles in topological insulators calls for a direct investigation of the electron-phonon scattering at the surface. By comparing time-resolved ARPES measurements of the topological insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ with different probing depths, we show that the relaxation dynamics of the electronic temperature of the conduction band is much slower at the surface than in the bulk. This observation suggests that surface phonons are less effective in cooling the electron gas in the conduction band.

Figure 1

(a) ARPES image of the band structure of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ around the $\Gamma$ point, measured with the surface-sensitive probe (17.5 eV) before ($-500$ fs) the optical excitation. Blue (green) lines outline the dispersion of the bulk (surface) states. (b) tr-ARPES image obtained as difference between the ARPES data at positive delay times ($+300$ fs) and the reference signal before optical excitation ($-500$ fs) with $s$-polarized light at 1.59 eV. (c), (d) Band structure and tr-ARPES image as panels (a), (b) measured with 6.2-eV photon energy. (e), (f) Evolution of the energy distribution curves (EDCs) taken from the ARPES data at the $\Gamma$ point at selected delay times in the two temporal regions $t$ $<$ 0.5 ps (c) and $t$ $>$ 1 ps (d).

Figure 2

EDCs at the $\Gamma$ point for different delay times: (a) surface-sensitive probe (17.5 eV); (b) bulk-sensitive probe (6.2 eV). The different broadening at negative delay time between (a) and (b) reflects the different energy resolution of the two setups. The broadening at positive delay times reflects instead an increase of $T_e$. In (a), the EDCs are shifted in energy to compensate the variations of $\mu$ (Fig. 1). The three EDCS at positive delays overlap, suggesting that $T_e$ reaches a steady value. In (b), by contrast, at long-time delays ($t>$ 5 ps), $T_e$ has already relaxed back to room temperature.

Figure 3

(a), (b) $\mu$ and $T_e$ as determined by fitting a Fermi-Dirac function to the EDCs at the $\Gamma$ point shown in Fig. 2. Blue (red) markers refer to 17.5-eV (6.2-eV) probe energy. In (b) the black solid line shows the best fit obtained with a single decay exponential plus a constant, with characteristic relaxation time ${\tau }_T=160$ fs. At large-delay times, a steady state with $T_0=640$ K is achieved. The pump fluence dependence of the maximum change of $\mu$ (d) and of the plateau value of $T_e$ (c), probed with $17.5$-eV photons, is reported.