Polarity-Driven Surface Metallicity in ${\mathrm{SmB}}_6$

By a combined angle-resolved photoemission spectroscopy and density functional theory study, we discover that the surface metallicity is polarity driven in ${\mathrm{SmB}}_6$. Two surface states, not accounted for by the bulk band structure, are reproduced by slab calculations for coexisting ${\mathrm{B}}_6$ and Sm surface terminations. Our analysis reveals that a metallic surface state stems from an unusual property, generic to the (001) termination of all hexaborides: the presence of boron $2p$ dangling bonds, on a polar surface. The discovery of polarity-driven surface metallicity sheds new light on the 40-year old conundrum of the low-temperature residual conductivity of ${\mathrm{SmB}}_6$, and raises a fundamental question in the field of topological Kondo insulators regarding the interplay between polarity and nontrivial topological properties.

Figure 1

(a),(b) Time evolution of the ARPES dispersion of ${\mathrm{SmB}}_6$ measured along $\overline{M}-\overline{\Gamma }-\overline{M}$ at $5\times {10}^{-11}$ torr and $T=6\mathrm{K}$: (a) 1 h and (b) 5 h after cleaving. (c)–(e) Time evolution of the $k$-integrated ARPES maps: continuous sequence of 2-min-averaged data in (c), with only 1 curve out of 3 shown in (d),(e). Despite the strong dynamics, corresponding to a transfer of spectral weight from low to high energies [inset of (d)], the Sm $4f$ multiplets are remarkably stable (e).

Figure 2

(a) ${\mathrm{SmB}}_6$ bulk and projected (001) surface Brillouin zones. (b) ${\mathrm{SmB}}_6$ bulk band structure at $k_z=0$ (black; $f$ bands removed for clarity), with, in addition, the $\mathrm{B}\mathrm{\text{−}}2p$ dangling-bond-derived surface states (SS, red), as revealed by our combined ARPES and slab-DFT study. (c)–(e) ARPES dispersions along $\overline{M}-\overline{\Gamma }-\overline{M}$ (c), $\overline{X}-\overline{\Gamma }-\overline{X}$ (d), and $\overline{M}-\overline{X}-\overline{M}$ (e) measured at 6 K with 21.2 eV photons, corresponding to $k_z\approx 0$ [29]. (f) Enlarged dispersion along $\overline{M}-\overline{\Gamma }-\overline{M}$, where no bulk bands are predicted to cross $E_F$ (b); a pileup of intensity at $E_F$—evidenced by a 3 peak profile in the raw MDC at $E_F$ in (g), which reduces to a 2 peak structure when the raw data in (f) are normalized to compensate for the cross-section enhancement at $\overline{\Gamma }$—provides evidence for the existence of a surface electron pocket around the $\overline{\Gamma }$ point. In (c)–(f) the white-dashed lines highlight the observed $\mathrm{B}\mathrm{\text{−}}2p$ SS. Note that the spectra in (c) are measured on a fresh cleave, while all other data are from stabilized surfaces, including the LEED pattern in (h).

Figure 3

(a) Comparison between the DOS of ${\mathrm{BaB}}_6$ and a model material made of ${\mathrm{B}}_6$ only (note that the differences seen above $E_F$ and at $-12\mathrm{eV}$ stem from the Ba $5d$ and $5p$ states, respectively, which, however, play no role in the discussion of hexaborides’ ionicity). The overall DOS profiles agree with each other after a 1.31 eV upward $E_F$ shift for ${\mathrm{B}}_6$, corresponding to the addition of 2 electrons as indicated by the integration of the ${\mathrm{BaB}}_6$ DOS (blue). (b) Crystal structure of ${\mathrm{BaB}}_6$ with one unit cell showing the surface of constant charge density at the isovalue $0.025e/{\AA }^3$.

Figure 4

(a),(b) Symmetric, nonstoichiometric slabs—either Sm (a) or ${\mathrm{B}}_6$ (b) terminated on both sides—are nonpolar. (c) The nonsymmetric, stoichiometric slab—with one Sm and one ${\mathrm{B}}_6$ termination—is instead polar, because of the divergent electrostatic potential V associated with the alternating $-Q/+Q$ charged planes, leading to electronic reconstruction: the transfer of $Q/2$ electronic charge from the ${\mathrm{B}}_6$ to the Sm termination, resulting in a charge stacking analogous to (a),(b). (d)–(f) Slab band structures calculated for the geometries in (a)–(c), with a 5-unit-cell thickness. Two sets of SS—one metallic—are derived from the B $2p$ dangling bonds (red bands). The near-$E_F$ black bands are Sm $5d$ states, which in the slabs span the bulk $k_z$ dispersion; these do not contribute to the low-temperature conductivity due to the opening of the Kondo gap, consistent with scanning tunneling spectroscopy [42] ($f$ bands and related $5d$-$4f$ hybridization are here not accounted for, since the Sm $4f$ states are treated as core levels).