Rashba Spin-Splitting Control at the Surface of the Topological Insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$

The electronic structure of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ is studied by angle-resolved photoemission and density functional theory. We show that the instability of the surface electronic properties, observed even in ultrahigh-vacuum conditions, can be overcome via in situ potassium deposition. In addition to accurately setting the carrier concentration, new Rashba-like spin-polarized states are induced, with a tunable, reversible, and highly stable spin splitting. Ab initio slab calculations reveal that these Rashba states are derived from 5-quintuple-layer quantum-well states. While the K-induced potential gradient enhances the spin splitting, this may be present on pristine surfaces due to the symmetry breaking of the vacuum-solid interface.

Figure 1

(a),(b) Time evolution of the ARPES dispersion of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ at $5\times {10}^{-11}\mathrm{torr}$ and $T=6\mathrm{K}$: (a) 3 h after cleaving; (b) 34 h after cleaving. (c) Exponential fit of the Dirac point (DP) binding energy versus time for 6 and 300 K cleaves (both measured at 6 K); saturation at $\Delta E^{\mathrm{DP}}\simeq 133$ and 116 meV is reached in 46 and 22 h, respectively.

Figure 2

Evolution of the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ $\overline{\Gamma }-\overline{K}$ electronic dispersion upon subsequent 0.5 min K-evaporation steps: (a1)–(a8) ARPES image plots, (b1)–(b8) corresponding energy distribution curves (EDCs). The sample was kept at $5\times {10}^{-11}\mathrm{torr}$ and 6 K.

Figure 3

ARPES $\overline{\Gamma }-\overline{K}$ band dispersion from ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ taken (a) immediately after a 3 min K evaporation, and (b) 30 h later (the sample was kept at $5\times {10}^{-11}\mathrm{torr}$ and 6 K the whole time). As also emphasized by the comparison of the corresponding $\overline{\Gamma }$ point EDCs in (c), the evaporated surface is highly stable. (d) Band dispersion measured at 220 K after a slow 36 h warming up on a sample initially K evaporated for 4 min at 6 K; the comparison with the data in Fig. 2a(8) reveals the suppression of the K-induced carrier doping. (e)–(g) Evolution vs K evaporation time of: (e) binding energy variation for DP ($\Delta E^{\mathrm{DP}}$) and bottom of RB1 ($\Delta E^{\mathrm{RB}1}$), as defined in (a); (f) sheet carrier density for DC ($n_{2\mathrm{D}}^{\mathrm{DC}}$) and RB1 ($n_{2\mathrm{D}}^{\mathrm{RB}1}$); (g) variation of the DC Fermi wave vector ($\Delta k_F^{\mathrm{DC}}$) and of the Rashba band splitting at $E_F$ ($\Delta k_F^{\mathrm{RB}1}$). Empty symbols in (e)–(g) are for $T=6\mathrm{K}$ and filled ones for $T=220\mathrm{K}$.

Figure 4

DFT results for (a) $k_z$-projected bulk and (b) 5QL slab of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ ($E_F$ is at energy 0). (c) Energy difference of the quantum-well (QW) slab states with respect to QW1, calculated for various thicknesses. The QW number increases with QL number, defining a bandwidth $W_{\mathrm{QL}}$ that asymptotically approaches the fully $k_z$-projected bulk $W_B=520\mathrm{meV}$. The 3 min K-deposition RB2-RB1 splitting of $123\pm 6\mathrm{meV}$ is accurately reproduced by the 5QL results.