Impact of ultrafast transport on the high-energy states of a photoexcited topological insulator

Ultrafast dynamics in three-dimensional topological insulators (TIs) opens new routes for increasing the speed of information transport up to frequencies a thousand times faster than in modern electronics. However, to date, disentangling the exact contributions from bulk and surface transport to the subpicosecond dynamics of these materials remains a difficult challenge. Here, using time- and angle-resolved photoemission, we demonstrate that driving a TI from the bulk-conducting into the bulk-insulating transport regime allows us to selectively switch on and off the emergent channels of ultrafast transport between the surface and the bulk. We thus establish that ultrafast transport is one of the main driving mechanisms responsible for the decay of excited electrons in prototypical TIs following laser excitation. We further show how ultrafast transport strongly affects the thermalization and scattering dynamics of the excited states up to high energies above the Fermi level. In particular, we observe how inhibiting the transport channels leads to a thermalization bottleneck that substantially slows down electron-hole recombination via electron-electron scatterings. Our results pave the way for exploiting ultrafast transport to control thermalization timescales in TI-based optoelectronic applications, and expand the capabilities of TIs as intrinsic solar cells.

Figure 1

(a) Geometry of the synchrotron- and laser-based photoemission experiments. The light incidence and electron emission planes are indicated in green (light) and blue (dark) colors, respectively. The detection plane is oriented along the $\overline{\mathrm{\Gamma }}\overline{K}$ direction of the SBZ, and the light impinges the sample under an angle of $\varphi ={45}^{\circ }$ with respect to the surface normal. The tr-ARPES measurements are taken by varying the time delay $\mathrm{\Delta }\mathrm{t}$ between infrared (1.5 eV) pump and ultraviolet (6 eV) probe pulses of vertical and horizontal linear polarization, respectively. (b)–(g) ARPES dispersions of (b),(c) ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and (d)–(g) ${\mathrm{Bi}}_{0.9}{\mathrm{Sb}}_{1.1}{\mathrm{Te}}_3$ taken under equilibrium conditions using linearly polarized synchrotron light of different photon energies.

Figure 2

Ultrafast dynamics of excited states following optical excitation by fs-laser pulses in (a)–(e) ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and (d)-(l) ${\mathrm{Bi}}_{0.9}{\mathrm{Sb}}_{1.1}{\mathrm{Te}}_3$. High-resolution tr-ARPES spectra at selected pump-probe delays are shown in (a),(b) and (f)–(i), respectively. Correspondingly, the time evolution of the momentum-resolved intensities at various energies above the Fermi level is shown in (c)–(e) and (j)–(l). Intensity contributions from a topologically trivial surface resonance, the bulk-conduction band and topological surface state are denoted as SR, BCB, and TSS, respectively. The metastable long-lived populations associated to the bulk and the surface are labeled ${\mu }_B$ and ${\mu }_S$ in (h),(i),(k), and (l).

Figure 3

(a)–(c) Normalized tr-ARPES intensities from different bands as a function of pump-probe delay for ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ (blue circles) and ${\mathrm{Bi}}_{0.9}{\mathrm{Sb}}_{1.1}{\mathrm{Te}}_3$ (green circles). For each band, the intensities are integrated within small energy-momentum windows that are at the same energy for the bulk-conducting and bulk-insulating case [see panels (a1)–(c2)]. Changes in the dynamics of (a) surface resonance (SR) states, (b) bulk-conduction band (BCB), and (c) topological surface state (TSS) are also emphasized in the corresponding insets. The labels ${\mu }_B$ and ${\mu }_S$ in (b) and (c) denote the metastable long-lived populations associated to the bulk and the surface, respectively.

Figure 4

(a) Comparison between tr-ARPES intensities extracted within the TSS at an energy of $\sim 60$ meV above and below the Fermi level in ${\mathrm{Bi}}_{0.9}{\mathrm{Sb}}_{1.1}{\mathrm{Te}}_3$, depicting the dynamics of electrons (blue) and holes (red). Once the metastable population in the bulk-conduction band completely relaxes (indicated by a vertical thick line), electrons and holes within the TSS are the only contribution to the measured signal. (b) Time evolution of the momentum-resolved intensity of the TSS bands below the Fermi level corresponding to the hole dynamics shown in (a).

Figure 5

Schematics of the different thermalization stages. In each panel, the surface density of states is shown on the right, while the surface-projected bulk density of states is shown on the left. The typical timescales of the studied processes as observed experimentally are given on the top. The surface states are plotted as semitransparent lines on the bulk density of states as a guide to the eye, and are not to be intended as real states in the bulk. The chemical potentials and effective chemical potentials are pictured as broken red lines. The dashed gray lines depict the chemical potential at previous delay times and used as a guide to the eye. The top row illustrates the thermalization stages in ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. (a) The laser excites electrons from below the Fermi energy to empty states above (for simplicity, all transitions are shown as originating from the top of the valence band; however, it is understood that the original state of the excited electrons has to be the appropriate one below the Fermi energy). (b) Two thermalization channels are active: Scattering (orange arrows) and transport (black arrows). (c) The recombination of electrons and holes is the last stage of thermalization. The bottom row depicts the thermalization stages in ${\mathrm{Bi}}_{0.9}{\mathrm{Sb}}_{1.1}{\mathrm{Te}}_3$. (d) Laser excitation. (e) Electron-electron and electron-phonon scatterings contribute to the thermalization, but the transport is quickly suppressed by the formation of charged regions. (f) The first stage of electron-hole recombination is facilitated by the fact that the scattered electron can still be within the bottom of the conduction band having high density of states. (g) The second stage is slowed down by the fact that the second electron involved in the scattering has to come from the Dirac cone, which has a low density of states.