Electronic Structure of the Topological Insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ Using Angle-Resolved Photoemission Spectroscopy: Evidence for a Nearly Full Surface Spin Polarization

We performed high-resolution spin- and angle-resolved photoemission spectroscopy studies of the electronic structure and the spin texture on the surface of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, a model TI. By tuning the photon energy, we found that the topological surface state is well separated from the bulk states in the vicinity of $k_z=Z$ plane of the bulk Brillouin zone. The spin-resolved measurements in that region indicate a very high degree of spin polarization of the surface state, $\sim 0.75$, much higher than previously reported. Our results demonstrate that the topological surface state on ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ is highly spin polarized and that the dominant factors limiting the polarization are mainly extrinsic.

Figure 1

ARPES from ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ at various photon energies. (a)–(c) ARPES intensity as a function of energy and momentum recorded at 30, 50, and 90 eV photon energy. The bands are labeled in (a). (d) The Fermi surface intensity map as a function of $k_x$ and $k_z$. The data were measured at photon energies ranging from 30 to 100 eV in 5 eV steps. The nondispersive feature along $k_z$ is from the surface state. Red dashed line corresponds to 50 eV photon energy. (e) The Fermi surface as a function of $k_x$ and $k_y$ measured at 50 eV photon energy. The red dashed circle is a guide to the shape of the Fermi surface.

Figure 2

Spin-integrated spectra of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ measured at 50 eV photon energy using the SARPES analyzer. (a) ARPES spectra along the momentum line $\Gamma M$ near the center of the surface BZ, measured in steps of 0.5°. The green line represents the surface state dispersion, extracted from momentum distribution curves (MDCs) from the ARPES spectrum shown in Fig. 1b. $A$ and $B$ indicate the $k$ positions where the spin-resolved measurements were performed. (b) energy distribution curves (EDCs) from (a). (c) MDC at the Fermi level from intensity contour in (a), interpolated to 4 times the number of original data points. (d) MDC from the Fermi surface map in Fig. 1e along the $k_y=0$ line. The Lorentzian fit gives a full with at half maximum of $0.009{\AA }^{-1}$, or 0.15°.

Figure 3

The spin-resolved photoemission of the surface state of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. (a)–(b) Spin-resolved spectra with the polarization vector along the $y$ and $x$ directions for point A from Fig. 2a. (c)–(d) same for point $B$. (e)–(h) Spin-resolved spectra for points $A$ and $B$ with the polarization vectors along the red arrows in Fig. 4. The corresponding spin polarizations are shown in (i)–(l) All the spectra were measured at photon energy 50 eV at $T=77\mathrm{K}$.

Figure 4

Vector analysis of spin polarization in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. The green (blue) arrows represent the spin polarization in the $y$ ($x$) direction, determined from Fig. 3. The red arrows correspond to the total spin polarization. The lengths of the arrows indicate the magnitudes of spin polarizations. The origins of the arrows correspond to the $k$ positions of points $A$ and $B$. The intensity map represents the constant energy contour at $-0.1\mathrm{eV}$ from spin-integrated ARPES data.