Surface and bulk electronic structure of the strongly correlated system SmB${}_6$ and implications for a topological Kondo insulator

Recent theoretical calculations and experimental results suggest that the strongly correlated material SmB${}_6$ may be a realization of a topological Kondo insulator. We have performed an angle-resolved photoemission spectroscopy study on SmB${}_6$ in order to elucidate elements of the electronic structure relevant to the possible occurrence of a topological Kondo insulator state. The obtained electronic structure in the whole three-dimensional momentum space reveals one electron-like $5d$ bulk band centered at the $X$ point of the bulk Brillouin zone that is hybridized with strongly correlated $f$ electrons, as well as the opening of a Kondo band gap ($\Delta$${}_B$ $\sim$ 20 meV) at low temperature. In addition, we observe electron-like bands forming three Fermi surfaces at the center $\overline{\Gamma }$ point and boundary $\overline{X}$ point of the surface Brillouin zone. These bands are not expected from calculations of the bulk electronic structure, and their observed dispersion characteristics are consistent with surface states. Our results suggest that the unusual low-temperature transport behavior of SmB${}_6$ is likely to be related to the pronounced surface states sitting inside the band hybridization gap and/or the presence of a topological Kondo insulating state.

Figure 1

(a) The first Brillouin zone of SmB${}_6$ and the projection on the cleaving surface. High-symmetry points are also indicated. (b), (c) Fermi surface mapping at $T$ $=$ 17 K by integrating ARPES intensity within $E_F\pm 5$ meV with $h\nu$ $=$ 26 and 46 eV, corresponding to $k_z=4\pi$ and 5$\pi$ at $\overline{\Gamma }$, respectively. (d), (e) ARPES intensity plots at $\overline{\Gamma }$ and $\overline{X}$ for the $k_z^B$ $=$ 4$\pi$ plane at $T$ $=$ 17 K. The red and blue curves are the dispersions of the $\beta$ and $\gamma$ bands extracted by MDC fitting. (f), (g) Analogous to (d) and (e), but for the $k_z^B$ $=$ 5$\pi$ plane.

Figure 2

(a), (b) ARPES intensity plots for cuts through $\overline{\Gamma }$-$\overline{X}$ and $\overline{X}$-$\overline{M}$, respectively, for the $k_z^B$ $=$ 4$\pi$ plane. Note the narrow energy window. The data were collected at $T$ $=$ 17 K. The red and blue curves are dispersions for the $\beta$ and $\gamma$ bands extracted by fitting the MDCs. The curves on the top are the MDCs taken at $E_F$, with labels for the peak positions. An EDC at the location in $k$ space marked by the red vertical line is also displayed. From this, the Kondo band gap is estimated to be ${\Delta }_B\sim$ 20 meV. (c), (d) Analogous to (a) and (b), but for the $k_z^B$ $=$ 5$\pi$ plane. (e)–(g) Plots of the curvatures of the MDC intensities along $\overline{\Gamma }$-$\overline{X}$ in either the first or second BZ (${\overline{\Gamma }}^{\prime }-{\overline{X}}^{\prime }$) evaluated in the $k_z^B$ $=$ 4$\pi$, 5$\pi$, and 6$\pi$ planes, respectively. (h) MDC curvature analysis at the second BZ center $\overline{\Gamma }$’ point for the $k_z^B$ $=$ 6$\pi$ plane. (i)–(l) Corresponding MDC plots for (e)–(h).

Figure 3

(a) ARPES intensity along the $\overline{X}$-$\overline{M}$ direction measured at $T=17$ K with various photon energies. (b) Plot of the ARPES intensity along $\overline{X}$-$\overline{M}$ as a function of photon energies from 22 to 75 eV, covering more than 1.5 BZs along $k_z^B$. (c) Corresponding MDCs at $E_F$. (d) Extracted dispersions of the $\beta$ band for different photon energies. (e) Plot of the curvature of the MDC intensity along $\overline{\Gamma }$-$\overline{M}$ for each photon energy. (f) Corresponding MDCs at $E_F$.

Figure 4

(a)–(f) ARPES intensity plots along $\overline{M}$-$\overline{X}$-$\overline{M}$ measured at $T$ $=$ 17, 30, 45, 70, 110,and 280 K, respectively. (g)–(l) ARPES intensity plots along $\overline{X}$-$\overline{\Gamma }$-$\overline{X}$ measured at T $=$ 17, 30, 45, 70, 110, and 150 K, respectively.