Prolonged duration of nonequilibrated Dirac fermions in neutral topological insulators

Abstract

Topological insulators (TIs) possess spin-polarized Dirac fermions on their surface but their unique properties are often masked by residual carriers in the bulk. Recently, (Sb_1-x Bi _x )₂Te₃ was introduced as a non-metallic TI whose carrier type can be tuned from n to p across the charge neutrality point. By using time- and angle-resolved photoemission spectroscopy, we investigate the ultrafast carrier dynamics in the series of (Sb_1-x Bi _x )₂Te₃. The Dirac electronic recovery of ∼10 ps at most in the bulk-metallic regime elongated to >400 ps when the charge neutrality point was approached. The prolonged nonequilibration is attributed to the closeness of the Fermi level to the Dirac point and to the high insulation of the bulk. We also discuss the feasibility of observing excitonic instability of (Sb_1-x Bi _x )₂Te₃.

Figure 1

Band dispersions of (Sb_1−x Bi_x)₂Te₃ (x = 0, 0.29, and 0.43). (a) Representative TARPES images displaying the bands in the unoccupied side. The cut is along $\overline{\mathrm{\Gamma }}-\overline{K}$ direction. (b) Constant energy maps of the angular distribution of photoelectrons for the x = 0.43 sample.

Figure 2

Nonequilibrium carrier dynamics in the (Sb_1−x Bi_x)₂Te₃ crystals. (a–c) TARPES images recorded at various delay times for x = 0 (a), 0.29 (b) and 0.43 (c). (d–f) Frames set along the bands for x = 0 (d), 0.29 (e) and 0.43 (f). (g–l) Normalized intensity variations in the frames set in (d–f).

Figure 3

Pump-fluence dependency of the recovery time for x = 0.43. Intensity variations at the conduction-band bottom (B3) (a) and bottom of the upper Dirac cone (S6) (b) recorded at p = 0.13, 0.26 and 0.52 mJ/cm².

Figure 4

Recovery time recorded at various pumping fluences at the bottom of the bulk conduction-band (τ _b) and the bottom of the upper Dirac cone (τ _s) as functions of x.

Figure 5

Surface photovoltage effect for the bulk insulating sample x = 0.43. (a) TARPES images recorded without (left) and with pump at t = −1.33 ps (middle panel). The right panel shows the difference image between two images. (b) Angle-integrated energy distribution curves for the images shown in (a, left and middle panels). (c) Schematic of the downward surface band bending and SPV effect. (e) Time-dependent electronic energy U (red color, left axis) and energy shift of the Dirac point (blue color, right axis).