Large Tunable Rashba Spin Splitting of a Two-Dimensional Electron Gas in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$

We report a Rashba spin splitting of a two-dimensional electron gas in the topological insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ from angle-resolved photoemission spectroscopy. We further demonstrate its electrostatic control, and show that spin splittings can be achieved which are at least an order-of-magnitude larger than in other semiconductors. Together these results show promise for the miniaturization of spintronic devices to the nanoscale and their operation at room temperature.

Figure 1

(a)–(c) Electronic structure of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, measured using time-of-flight ARPES at increasing times after cleaving the sample [marked in Fig. 4a] ($h\nu =19.2\mathrm{eV}$, $T=10\mathrm{K}$). (d) Spin-ARPES total intensity MDC at the Fermi level ($h\nu =19.5\mathrm{eV}$, $T=60\mathrm{K}$) along the $\overline{\Gamma }\mathrm{\text{−}}\overline{M}$ direction, and (e) the measured (points) and fitted (lines) radial ($P_x$), tangential ($P_y$), and out-of-plane ($P_z$) components of the spin polarization along this cut. (f) Schematic representation of the in-plane component of the Fermi surface spin texture.

Figure 2

(a) Detailed measurement ($h\nu =16\mathrm{eV}$, $T=60\mathrm{K}$) of multiple 2DEG states (upper features) and the topological surface state (lower feature). Model Poisson-Schrödinger calculations (red solid lines) reproduce the ladder of 2DEG states within the surface quantum well. A Rashba splitting of $\alpha =0.36\mathrm{eV}\AA$ (estimated from the $k_F$ splitting) applied to the lowest calculated subband dispersion gives the green lines. Inset: EDC at $\overline{\Gamma }$ with 2DEG states marked by arrows. (b) Near-surface band bending (blue) with the calculated energy levels and modulus-squared wave functions of the quantum-confined states (red).

Figure 3

Rashba-split 2DEG in Ca-doped (nondegenerate) ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ induced by (a) 18 L of CO adsorption at 60 K and (b) $\ll 1\mathrm{ML}$ of Rb-deposition at 170 K. The measurement temperature in (a) and (b) is 60 K and 380 K, that is, well above room temperature, respectively. (c)–(e) Reversible nature of effective gating of undoped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, with the spin splitting (along $\overline{\Gamma }\mathrm{\text{−}}\overline{K}$) changing from (c) $\Delta k_F=0.034{\AA }^{-1}$ ($V_g\sim 0.28\mathrm{eV}$) to (d) $\Delta k_F=0.011{\AA }^{-1}$ ($V_g\sim 0.11\mathrm{eV}$) following annealing the sample at 250 K to remove some surface adsorbates to (e) $\Delta k_F=0.025{\AA }^{-1}$ as the effective gate potential is increased again to $V_g\sim 0.26\mathrm{eV}$.

Figure 4

(a) Evolution of the Fermi wave vector along $\overline{\Gamma }\mathrm{\text{−}}\overline{M}$ and $\overline{\Gamma }\mathrm{\text{−}}\overline{K}$ with time after cleaving the sample. (b) Extracted $k_F$ positions and band-bending which induces the 2DEG. (c) Sheet density and (d) $k_{\parallel }$ splitting at the Fermi level of the measured (points) and calculated (lines) Rashba-split 2DEG as a function of the effective gate potential, $V_g$.