Figure 1

Sample layout and band bending diagram: (a) A Bi${}_2$Se${}_3$ 60(40)-QL film is capped with 10 nm of In${}_2$Se${}_3$, and encased in 590 nm (620 nm) of Parylene-C. A NiCr gate $\sim$400 $\Omega /\square$ and antireflection coating $\sim$275 $\Omega /\square$ were deposited by evaporation. Pairs of silver epoxy contacts were made to the Bi${}_2$Se${}_3$ film and NiCr gate. (b) Band bending diagram on the right side depicts the conduction-band edge from large negative gate voltages (red) to large positive gate voltages (purple) throughout the cross section of the film. The left diagram depicts the top topological surface state and associated bulk band (shown as a parabola) dispersion, and the dashed colored horizontal lines represent the associated surface Fermi levels due to the band bending. The specific Fermi levels at the surface depicted in blue and orange are referenced in the text as the flat band and conduction band edge (CBE) conditions, respectively.Reuse & Permissions

Figure 2

$\Delta {\theta }_F$ and $\Delta T$ data and model. All transmission and Faraday angle measurements were performed at $\omega /2\pi =0.74$ THz at discrete magnetic fields that are color coded according to the key in (a). Differential optical measurements are differences between two different gate voltages, one is fixed at $V_g^0=170$ V and the other $V_g$ is variable. Maximum reported gate voltages are near the break down limit of the devices. The differential transmission $\Delta T$ is normalized to the average transmission $T_{\text{avg}}$ of the two gate values only in (f). The conduction band edge (CBE) condition at the top surface is demarcated with a vertical dotted line in all figures. (a)–(c) Differential measurements of the Faraday angle and transmission are shown for the 60-QL film maintained at 10 K and (d)–(f) the 40-QL film maintained at 10 K. (g) and (h) A zoomed view of the Re$(\Delta {\theta }_F$) for the 60- and 40-QL films, respectively. (i) A model of the Re$(\Delta {\theta }_F$) for the 60-QL device incorporating the Drude parameters that reproduce all the optical data in Ref. 8.Reuse & Permissions