Dielectric capping effects on binary and ternary topological insulator surface states

Using a density-functional-based electronic structure method, we study the effect of crystalline dielectrics on the metallic surface states of Bismuth- and chalcogen-based binary and ternary three-dimensional topological insulator (TI) thin films. Crystalline quartz (SiO${}_2$) and boron nitride (BN) dielectrics were considered. Crystalline approximation to the amorphous quartz allows one to study the effect of oxygen coverage or environmental effects on the surface-state degradation, which has gained attention recently in the experimental community. We considered both symmetric and asymmetric dielectric cappings to the surfaces of TI thin films. Our studies suggest that BN and quartz cappings have negligible effects on the Dirac cone surface states of both binary and ternary TIs, except in the case of an oxygen-terminated quartz surface. Dangling bond states of oxygens in oxygen-terminated quartz dominate the region close to Fermi level, thereby distorting the TI Dirac cone feature and burying the Dirac point in the quartz valence-band region. Passivating the oxygen-terminated surface with atomic hydrogen removes these dangling bond states from the Fermi-surface region, and consequently the clear Dirac cone is recovered. Our results are consistent with recent experimental studies of TI surface degradation in the presence of oxygen coverage.

Figure 1

Schematic diagram of (a) 6 QLs Bi${}_2$Se${}_3$ and (b) 4 QLs Bi${}_2$Se${}_2$Te thin-film structures obtained by stacking QLs along the $z$ direction. (c) Two-dimensional Brillouin zone (BZ) of the (111) surface of thin-film TIs with three time-reversal invariant points $\overline{\Gamma }$, $\overline{M}$, and $\overline{K}$.

Figure 2

Schematic diagram of the supercell structure of BN and 6 QLs Bi${}_2$Se${}_3$. The colors corresponding to the atoms are labeled on the bottom right of the supercell. The green and brown arrows at the top and bottom interfaces indicate B on the top of Se. The top view of bottom interfacial atomic layers is shown on the bottom right of the supercell structure. The 1$\times$1 Bi${}_2$Se${}_3$ cell (green rhombus) is matched with $3d_{\text{B-N}}\times 3d_{\text{B-N}}$ BN. This corresponds to symmetric capping mentioned in the text. Also, Se on the top of N on both sides of the film corresponds to the symmetric case.

Figure 3

Same as Fig. 2 but now with the B on the top of Se on one side and N on the top of Se on the other side of the TI thin film. The colors corresponding to atoms are labeled on the bottom right of the supercell. The green, brown, and orange arrows indicate the relative positions of the Se atom with respect to B (bottom) and N (top). The top views of top and bottom interfacial atomic layers are shown on the top right and bottom right of the supercell, respectively. The $1\times 1$ Bi${}_2$Se${}_3$ cell (green rhombus) is matched with $3d_{\text{B-N}}\times 3d_{\text{B-N}}$ BN. This corresponds to asymmetric capping in the text.

Figure 4

Schematic diagram of oxygen-terminated quartz with dangling-bond states covered with hydrogen atoms (small green circles) interfaced on both sides of Bi${}_2$Se${}_3$. The Si-terminated surface also possesses dangling bonds, but only oxygen-terminated surface without the hydrogen coverage distorts the surface-state Dirac cone. The top view of bottom interfacial atomic layers is shown on the bottom right of the supercell structure. The $2\times 2$ Bi${}_2$Se${}_3$ cell (green rhombus) is matched with $1\times 1$ SiO${}_2$ at the interface.

Figure 5

Band structures of Bi${}_2$Se${}_3$/BN supercell along high-symmetry directions of the hexagonal BZ for symmetric capping case (a) B on the top of Se and (b) N on the top of Se on both sides of TI film without atomic relaxation. The Dirac cone and its degeneracy at the $\overline{\Gamma }$ point are not disturbed in the presence of crystalline BN thin film. (c) Same case of (a) with atomic relaxation. Atomic relaxation has little effect on the Dirac cone feature. The position of BN valence-band maximum can be found by the band structure of a BN slab without TI in the inset of (a) and the density of states (DOS) plots in Fig. 6.

Figure 6

The atom-projected DOS in the same energy range as the band structures in Fig. 5 for symmetric capping cases (a) B on the top of Se and (b) N on the top of Se on both sides of TI film without atomic relaxation. Se orbitals are not in resonance, with either B or N orbitals near the Fermi level suggesting that the Dirac cone, formed from the Bi and Se orbitals, is intact.

Figure 7

Band structures of Bi${}_2$Se${}_3$/BN supercell along high-symmetry directions of the hexagonal BZ for asymmetric capping cases (a) B on the top of Se on one side and vacuum on the other side of TI film and (b) B on the top of the Se atom on one side and N on the top of the Se atom on the other side without atomic relaxation. The Dirac cone and its degeneracy at the $\overline{\Gamma }$ point are not disturbed in the presence of crystalline BN thin film. The position of BN valence-band maximum can be found by the band structure of the BN slab without TI in the inset of (a) and the DOS plots in Fig. 8.

Figure 8

The atom-projected DOS in the same energy range as the band structures in Fig. 7 for asymmetric capping cases (a) B on the top of Se on one side and vacuum on the other side of TI film and (b) B on the top of Se on one side and N on the top of Se on the other side of TI film without relaxation. Se orbitals are not in resonance, with either B or N orbitals near the Fermi level suggesting that Dirac cone, formed from the Bi and Se orbitals, is intact.

Figure 9

Band structure of Bi${}_2$Se${}_3$ with Si-terminated quartz supercell along high-symmetry directions in the hexagonal BZ (a) without hydrogen coverage and (b) with hydrogen coverage. The Dirac cone of TI is preserved in both cases. Insets of (a) and (b) show the band structures of only Si-terminated SiO${}_2$ slabs without and with passivation, respectively. In the inset of (b), a clear band gap is seen, while additional bands by Si dangling bond lie inside the gap in the inset of (a).

Figure 10

The atom-projected DOS in the same energy range as the band structures in Fig. 9 for the Si-terminated quartz cases (a) without hydrogen passivation and (b) with hydrogen passivation. The orbitals of Si and Se do not overlap near the Fermi level. Left insets of (a) and (b) show the atom-projected DOS for only Si-terminated SiO${}_2$ slabs without and with passivation, respectively. States from Si orbitals are clearly shown in the left inset of (a).

Figure 11

(a) Band structure of Bi${}_2$Se${}_3$ with oxygen-terminated quartz supercell without atomic relaxation along high-symmetry directions in the hexagonal BZ suggesting that Dirac cone is significantly affected and (b) corresponding atom-projected DOS. The strong hybridization of Se and oxygen orbitals near the Fermi level is observed. Band structure of only oxygen-terminated SiO${}_2$ slab without passivation is in the inset of (a), and the corresponding atom-projected DOS plot is shown in the left inset of (b). The Fermi level is below the valence-band edge formed by oxygen orbitals. The Dirac point is marked with the arrow on the right inset of (b).

Figure 12

Same as Fig. 11 but now with hydrogen coverage of oxygen-dangling orbitals (a) band structure without atomic relaxation and (b) corresponding atom-projected DOS. The Dirac cone of TI is recovered due to noninteraction of Se and oxygen orbitals. (c) Same case with atomic relaxation. The Dirac cone feature is not affected by the atomic relaxation. Band structure of only oxygen-terminated SiO${}_2$ slab with passivation is in the inset of (a), and the corresponding atomic-projected DOS plot is shown in the left inset of (b). The Fermi level is inside the gap.

Figure 13

Band structure of Bi${}_2$Se${}_2$Te/BN supercell along high-symmetry directions of the hexagonal BZ for asymmetric capping cases (a) B on the top of Se on one side and vacuum on the other side of TI film and (b) B on the top of the Se atom on one side and N on the top of the Se atom on the other side, and for the symmetric capping case (c) B on the top of Se on both sides of TI film. The atomic relaxation is not considered. The Dirac cone and its degeneracy at the $\overline{\Gamma }$ point are not disturbed in the presence of crystalline BN thin film. The position of the BN valence-band edge can be estimated by the band structure of the BN slab without TI in the inset of (a).

Figure 14

Band structure of the Bi${}_2$Te${}_2$Se/BN supercell along high-symmetry directions of the hexagonal BZ for asymmetric capping cases (a) B on the top of Te on one side and vacuum on the other side of TI film and (b) B on the top of the Te atom on one side and N on the top of the Te atom on the other side, and for the symmetric capping case (c) B on the top of Te on both sides of the TI film. The atomic relaxation is not considered. The Dirac cone at the $\overline{\Gamma }$ point is not disturbed in the presence of crystalline BN thin film. The fourfold degeneracy is lifted to two twofold degeneracies at the $\overline{\Gamma }$ point in the inset of (b). The position of the BN valence-band maximum can be found by the band structure of the BN slab without TI in the inset of (a).

Figure 15

(a) Band structure of Bi${}_2$Te${}_2$Se with oxygen-terminated quartz supercell without atomic relaxation along high-symmetry directions in the hexagnoal BZ suggesting that Dirac cone is affected and (b) corresponding atom-projected DOS. The Dirac point of TI is buried into quartz valence bands. The band structure of only oxygen-terminated SiO${}_2$ slab without passivation is in the inset of (a). The Fermi level is below the valence-band edge formed by oxygen orbitals. The Dirac point is marked with an arrow in the inset of (b).