Topological surface states in epitaxial ${\left(\mathrm{Sn}{\mathrm{Bi}}_2{\mathrm{Te}}_4\right)}_n{\left({\mathrm{Bi}}_2{\mathrm{Te}}_3\right)}_m$ natural van der Waals superlattices

Topological insulators are good candidates for charge to spin conversion with high efficiency due to their spin-polarized topological surface states (TSSs). In this work, we provide experimental evidence for two-dimensional (2D) TSSs in ${\left(\mathrm{Sn}{\mathrm{Bi}}_2{\mathrm{Te}}_4\right)}_n {\left({\mathrm{Bi}}_2{\mathrm{Te}}_3\right)}_m$ natural van der Waals superlattices grown by molecular beam epitaxy using angle resolved photoelectron spectroscopy and magnetotransport. While the TSSs overlap with bulk conduction band (BCB) states at the Fermi energy, it is shown that by increasing the Sn composition, the influence of BCB states is reduced and becomes minimum for $\mathrm{Sn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$. The latter compound, found to be in the form of septuplet layers, shows weak antilocalization effect with a prefactor $\alpha \sim –0.41$, indicating that the TSSs and the bulk behave as one 2D channel in which magnetotransport properties are influenced by large spin-orbit coupling.

Figure 1

RHEED patterns of InAs(111) substrate and Sn-Bi-Te films along the InAs [1 $\overline{1}$ 0] and [11 $\overline{2}$] azimuths.

Figure 2

(a) High-resolution cross-section STEM image of layered $\mathrm{Sn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$ (sample S5). (b) Detail of one septuplet layer showing a seven-row arrangement of the form Te-MII-Te-MI-Te-MII-Te. The metal positions MI and MII are preferentially occupied by Sn and Bi, respectively.

Figure 3

(a) High-resolution cross-section image of $\mathrm{Sn}{\mathrm{Bi}}_4{\mathrm{Te}}_7$ (sample S3). (b) HR STEM shows alternating QL and SL layers in the form of a natural van der Waals (vdW) superlattice where each layer is separated by a vdW gap. (c) High-angle annular dark field (HAADF) image and (d) the intensity line profile along a yellow arrow in (c) showing a possible atom exchange between Sn and Bi in the middle row of the SL.

Figure 4

(a) The calculated band structure of bulk $\mathrm{Sn}{\mathrm{Bi}}_4{\mathrm{Te}}_7$ along the ΚΓ$L$ and HAL directions showing the band inversion (green and orange lines). (b) The first BZ, (c) the projected Brillouin zone along the $\overline{K}\overline{\mathrm{\Gamma }}\overline{M}$ direction of the two different terminations, and (d) the band structures of the non-inversion-symmetric two and four layers. The green and red symbols correspond to the atomic orbitals of the top and bottom surfaces, respectively. It should be noted that no overlap between the CB and VB is predicted and the calculated Fermi level does not cross either the conduction or the valence band.

Figure 5

(a) The BZ of $\mathrm{Sn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$. (b) The calculated band structure of bulk $\mathrm{Sn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$ along the ΚΓ$L$ and KZX directions and showing the band inversion (green and orange lines). (c) The projection of the Brillouin zone along the $\overline{K}\overline{\mathrm{\Gamma }}\overline{M}$ direction and (d) the band structure of two, four, seven, and 14 SLs.

Figure 6

(a) ARPES spectra of $\mathrm{Sn}{\mathrm{Bi}}_4{\mathrm{Te}}_7$ for photon energy $E_{\mathrm{photon}}=20\mathrm{eV}$ along $\overline{\mathrm{\Gamma }}\overline{M}$ and (b) the Fermi surface of the same sample. (c) The photon energy dependent $k_z-k_y$ Fermi surface map at $E_{\mathrm{F}}$ ($k_y$ parallel to $\overline{\mathrm{\Gamma }}\overline{K}$). The traces of the topological surface states (TSS) are recorded at the $k_y$ values at which the dashed red line in (b) cuts the trace of the surface state. BCB denotes the bulk conduction band states.

Figure 7

(a)–(d) ARPES measurements of band dispersions and their $k_x\text{−}{k}_y$ Fermi surface maps for four samples with different Sn compositions recorded along $\overline{K}\overline{\mathrm{\Gamma }}\overline{K}$. The shifts of the conduction band minimum are indicated with horizontal blue dotted lines. TSS and BCB in (b) denote the topological surface states and bulk conduction band, respectively.

Figure 8

Schematic illustration showing the evolution of crystal and band structure as a function of Bi/Sn ratio.

Figure 9

Magnetotransport measurements of $\mathrm{Sn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$ at 6 K. (a) Hall resistance $\left(R_{xy}\right)$ displaying characteristic bent shape (nonlinear) due to multiband conduction. (b) Longitudinal resistance $\left(R_{xx}\right)$ as a function of the in-plane and out-of-plane field revealing the WAL effect. (c) Magnetoconductance $\mathrm{\Delta }G$ normalized by $e^2/\left(\pi h\right)$ as a function of the magnetic field, where blue and red lines correspond to fitting curves.