Observation of optical absorption correlated with surface state of topological insulator

We performed broadband optical transmission measurements of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and In-doped ${\left({\text{Bi}}_{1-x}{\text{In}}_x\right)}_2{\text{Se}}_3$ thin films, where in the latter the spin-orbit coupling (SOC) strength can be tuned by introducing In. Drude and interband transitions exhibit In-dependent changes that are consistent with evolution from the metallic $(x=0)$ to insulating $(x=1)$ nature of the end compounds. Most notably, an optical absorption peak located at $\hslash \omega =1\mathrm{eV}$ in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ is completely quenched at $x=0.06$, the critical concentration where the phase transition from TI into non-TI takes place. For this $x$, the surface state (SS) has vanished from the band structure as well. The correlation between the 1 eV optical peak and the SS in the $x$ dependencies suggests that the peak is associated with the SS. We further show that when ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ is electrically gated, the 1 eV peak becomes stronger (weaker) when electron is depleted from (accumulated into) the SS. These observations combined together demonstrate that under the $\hslash \omega =1\mathrm{eV}$ illumination electron is excited from a bulk band into the topological surface band of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. The optical population of the surface band is of significant importance not only for fundamental study but also for TI-based optoelectronic device application.

Figure 1

Optical conductivity of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin film ($d=50$ QL) ${\sigma }_1\left(\omega \right)$ shows the Drude, phonon, and interband transition. Note that log-log scale is used for the $0.2\le \hslash \omega \le 5$ eV range. Inset shows peak A in the real scale.

Figure 2

Evolution of peak A in In-substituted ${\left({\text{Bi}}_{1-x}{\text{In}}_x\right)}_2{\text{Se}}_3$ thin films. (a) Optical conductivity of ${\left({\text{Bi}}_{1-x}{\text{In}}_x\right)}_2{\text{Se}}_3$ for the In-concentration range of $0\le x\le 0.9$. (b) The second derivative of optical conductivity $\frac{d^2{\sigma }_1}{d{E}^2}$. The $x$-dependent behavior of peak A can be traced more clearly in this plot. Here $w$ and $d$ denote the distance between the two maxima and depth of the dip, respectively. (c) The width $w$ and depth $d$ are shown as a function of $x$. (d) The peak strength $S$ calculated from $S=\frac{1}{12}\sqrt{\frac{\pi }{6}}d{w}^3$ (see Supplemental Material Fig. S1 [20]). We also calculate $S$ by $S=\int {\sigma }_1^A\left(\omega \right)d\omega$, where ${\sigma }_1^A\left(\omega \right)={\sigma }_1\left(\omega \right)-{\sigma }_1^{\text{BG}}\left(\omega \right)$ (${\sigma }_1^{\text{BG}}$ = polynomial background) as shown in the inset. In (c) and (d), the critical concentration $x_c=0.06$ of the TI to non-TI (NTI) phase transition is highlighted by the vertical line.

Figure 3

Gate-driven change of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. (a) Schematic diagram of gate-controlled transmission measurement of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin film. $T(V_{\mathrm{G}}$) is taken with the bias voltage $V_{\mathrm{G}}$ applied between the film and Si. (b) $T\left(V_{\mathrm{G}}\right)/T\left(0\right)$ changes in the far-IR, mid-IR, and at 1 eV. (c) For peak A $T(V_{\mathrm{G}}$) increases/decreases for the negative/positive $V_{\mathrm{G}}$, respectively. (d) Optical conductivity of peak A, ${\sigma }_1^A\left(\omega \right)$, was calculated from $T(V_{\mathrm{G}}$) in (c) as described in the text.

Figure 4

Estimation of the growth of peak A at high gating voltage. (a) Gate-driven shift of the interband transition. The onset energy $E_{\text{op}}$ is determined by the linear extrapolation of data (dashed line). (b) Schematic diagram of the $\mathrm{VB}\to \mathrm{CB}$ interband transition. The $E_{\text{op}}$ corresponds to onset of the $\mathrm{VB}\to \mathrm{CB}$. Here the Fermi energy $E_{\text{F}}$ is measured from the CB bottom. DP stands for Dirac point. (c) The shift $\mathrm{\Delta }{E}_{\text{op}}=E_{\text{op}}\left(V_{\mathrm{G}}\right)-E_{\text{op}}\left(0\right)$ and the change of $S$ are plotted against $V_{\mathrm{G}}$. Here $S$ was calculated by integrating ${\sigma }_1\left(\omega \right)$ in Fig. 3 as $S=\int {\sigma }_1^A\left(\omega \right)d\omega$.

Figure 5

Schematic band structure and possible origin of peak A. For $V_{\mathrm{G}}=0$, an electron is excited from the bulk band branch into the empty surface state as highlighted by the blue arrows. For the positive gating, the Fermi level $E_{\text{F}}$ shifts up and the 1 eV transition becomes weaker. For the negative gating $E_{\text{F}}$ shifts down and the 1 eV transition becomes stronger. The amount of $E_{\text{F}}$ shift is exaggerated for clarity. The band diagram shown here was redrawn schematically based on experiment [3, 7, 35, 36, 37, 38, 39] and theory [40, 41, 42, 43]. CB = bulk conduction band, VB = bulk valence band, SS = surface state.