Visualizing the evolution of surface localization in the topological state of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ by circular dichroism in laser-based angle-resolved photoemission spectroscopy

We use angle-resolved photoemission spectroscopy with a circularly polarized 7-eV laser, and find that the angle-resolved pattern of circular dichroism (CD) for the topological surface state of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ is dramatically changed with surface aging. Shortly after sample cleaving, the CD pattern exhibits a $\sin (\varphi$)-like modulation ($\varphi$ is the Fermi surface angle) reminiscent of the helical spin texture. Intriguingly, this pattern gradually changes with time, and eventually turns into a $\sin \left(2\varphi \right)$-like modulation on the aged surface. These two patterns are also revealed in quantum well states with different quantum numbers, indicating that the CD pattern is a valid measure to identify the surface confinement of electrons. Our experiments thus demonstrate the time evolution of electron localization in the topological surface state.

Figure 1

Geometry in our ARPES measurements. (a) Front view of ARPES experiments. The vertical node in CD is expected to emerge due to geometric symmetry along the mirror plane. (b) Side view of ARPES experiments. Circularly polarized light is illuminated to the samples at ${45}^{\circ }$ from the analyzer. Two conditions required to achieve geometric symmetry about the side view mirror plane (a dotted line) are depicted. Condition (1) is that the $p_z$ component of the photoemission matrix element is negligible [19]. Condition (2) is that the observed electrons have sixfold rotational symmetry. The scanning of angle space (or momentum space) was carried out by rotating the samples along the $x$ axis, as depicted by a curved arrow with the notation of “$\theta$ rotation” in (a) and (b).

Figure 2

(a1)–(a5) Time evolution of band dispersion ($I_{\mathrm{RC}}+I_{\mathrm{LC}}$) across $\overline{\mathrm{\Gamma }}$, measured along $\alpha$ at $\theta =0^{\circ }$ in Fig. 1. (b1)–(b5) The corresponding CD intensities ($I_{\mathrm{RC}}-I_{\mathrm{LC}}$). (c1), (c2) MDCs measured with left and right circularly polarized light for a fresh surface (0 h) and an aged surface (40 h), respectively. ($E-E{}_{\mathrm{D}}$: Energy distance from the Dirac point.) (d) CD intensities plotted as a function of momentum distance from $\overline{\mathrm{\Gamma }}$ [$\left|\mathrm{\Delta }\alpha \right|$ marked by the arrow in (c1)]: Negative and positive areas of MDCs extracted from (b1) at various binding energies, divided by the areas of the corresponding MDCs from (a1). The obtained values are plotted as a function of $\left|\mathrm{\Delta }\alpha \right|$ for each MDC peak. (e) Time evolution of the band shape close to the Dirac point.

Figure 3

(a1), (a2) Band dispersion ($I_{\mathrm{RC}}+I_{\mathrm{LC}}$) and the corresponding CD image ($I_{\mathrm{RC}}-I_{\mathrm{LC}}$), respectively, for a relatively fresh surface. ARPES maps [(b1)–(b6)] and CD maps [(c1)–(c6)] along the $\alpha -\theta$ plane measured at several binding energies [green lines in (a1) and (a2)]. (d) Band dispersion for the aged surface. ARPES maps [(e1)–(e6)] and CD maps [(f1)–(f6)] along the $\alpha -\theta$ plane measured at several binding energies [green lines in (d)].

Figure 4

(a1), (b1) Schematic band structures and CD patterns for the fresh and aged surfaces, respectively. (a2), (a3) Fermi surface angle ($\varphi$) dependence of CD intensities close to the Dirac point for fresh and aged surfaces, respectively. These values are estimated to be the areas of negative and positive peaks of MDCs extracted from Figs. 3 and 3 in each $\varphi$ direction, divided by the area of the corresponding MDC peaks from Figs. 3 and 3. (b2), (b3) CD intensities for quantum well states with a quantum number of $n=2$ and $n=1$, respectively, which were estimated similarly to those in (a2) and (a3). (c) Schematic for surface confinement effect.