Probing Topological Surface States and Conduction via Extended Defects in (Bi$_{1-x}$Sb$_x$)$_2$Te$_3$ Films

TL;DR

The paper addresses how extended defects influence conduction in non-degenerate topological insulators, focusing on $60^{\circ}$ twin boundaries in (Bi$_{1-x}$Sb$_x$)$_2$Te$_3$. By combining STM/STS, low-temperature magnetotransport, STEM/EDS, and DFT with a BHZ tight-binding framework, it shows that $60^{\circ}$ twins host in-gap DOS corresponding to a 2D carrier density of $n_{twin,2D} \approx 3.22\times 10^{13}$ cm$^{-2}$ and establishes an upper bound on twin-boundary conductivity, $\sigma_{twin} \le 7.3\times 10^{-4}$ S, implying a mobility up to $\mu_{twin} \approx 142$ cm$^{2}$/V·s. A lattice-twin model and BHZ analysis further indicate that reduced tunneling across twin boundaries can yield gapless, topologically protected states along the boundaries, suggesting that engineered extended defects can play a constructive role in TI electronics. These findings illuminate a new conduction pathway in non-degenerate TIs and point to defect-controlled strategies for designing TI-based devices with robust surface conduction channels.

Abstract

(Bi$_{1-x}$Sb$_x$)$_2$Te$_3$ alloys are non-degenerate topological insulators (TIs) whose Dirac point (DP) can be tuned within the bulk bandgap by varying the composition, effectively reducing bulk conduction while allowing surface carrier conduction. Magnetotransport measurements of a series of (Bi$_{1-x}$Sb$_x$)$_2$Te$_3$ thin films indicate electron-dominated conduction, with weak anti-localization attributed to topological surface states (TSSs). Due to the similarity of phase coherence lengths and twin boundary spacings ($\sim$100 nm), we consider the role of twin boundaries as additional conducting paths. Density functional theory calculations reveal an enhanced density of states near the Fermi level at $60^\circ$ twin boundaries, with 2D carrier concentration in excess of $3 \times 10^{13}$ cm$^{-2}$. Furthermore, an analysis of the longitudinal magnetoconductivity yields an upper bound of $7.3 \times 10^{-4}$ S for twin boundary conductivity, resulting in a carrier mobility as high as $142$ cm$^2$/(V$\cdot$s). We discuss the role of twin boundaries in facilitating a transition from a massive Dirac cone dispersion to gapless, topologically protected surface states. Understanding the role of twin boundaries on carrier conduction in non-degenerate TIs is critical for the development of novel TI-based electronic devices.

Figures (8)

• Figure 1: Scanning tunneling microscopy (STM) and scanning tunneling spectroscopy of (Bi$_{1-x}$Sb$_{x}$)$_{2}$Te$_{3}$ films: (a) large-scale STM images of pp ($\Delta z$ = 15.5 nm), pn thin ($\Delta z$ = 9.5 nm), pn thick ($\Delta z$ = 9.8 nm), and nn ($\Delta z$ = 15.8 nm). For all films, large terraces with single quintuple layer (QL) steps are observed, indicating layer-by-layer growth of the van der Waals bonded layers. (b) The differential conductance ($dI/dV$) as a function of bias voltage, corresponding to the energy relative to the Fermi level $E_{F}$. $dI/dV$ for (c) pn thick and (d) nn as a function of bias voltage, corresponding to the energy relative to the $E_{F}$ revealing two distinct states of surface and bulk conduction.
• Figure 2: Magnetotransport data for nn (31 QL): (a) Hall resistance and (b) sheet resistance as a function of magnetic field at 10 K and 1.7 K. (c) Magnetoconductivity as a function of temperature (open symbols) with Hikami-Larkin-Nagaoka fit (solid lines). (d) Phase coherence length as a function of temperature (square symbols) and a fit proportional to $T^{-0.25}$ (solid line). At $T = 0.4$ K, we calculate $\alpha = 0.83$.
• Figure 3: Phase coherence lengths, $l_\phi$, as a function of temperature for the pp (4 QLs), pn thin (19 QLs), pn thick (31 QLs), and nn (31 QLs). For $T > 1$ K, similar $T$-dependencies are apparent for all samples.
• Figure 4: High-angle annular dark-field scanning transmission electron micrographs (HAADF-STEM) revealing quintuple layers (QLs) within (Bi$_{1-x}$Sb$_{x}$)$_{2}$Te$_{3}$ films: (a) $[1\overline{1}00]$ projection of pp (4 QL); $[11\overline{2}0]$ projections of (b) pn thin (19 QL), (c) pn thick (31 QL) and (d) nn (31 QL). The QLs consist of 5 atomic layers, separated by van der Waals gaps. High resolution (e) $[1\overline{1}00]$ and (f) $[11\overline{2}0]$ projections of the atomic structures, HAADF-STEM images, and energy-dispersive x-ray spectroscopy elemental maps of Bi (blue), Sb (red), and Te (green).
• Figure 5: Example high-angle annular dark-field scanning transmission electron micrographs (HAADF-STEM) in the vicinity of the (Bi$_{1-x}$Sb$_{x}$)$_{2}$Te$_{3}$/Al$_{2}$O$_{3}$ interface. For the (a) $[11\overline{2}0]$ and (b) $[10\overline{1}0]$ projections, constant Sb-Sb separations are 4.118 Å and 2.389 Å, respectively. For a single domain antimonene monolayer, illustrated in yellow, two distinct Sb-Sb separations are apparent in the $[10\overline{1}0]$ projection. Since a constant Sb-Sb separation is instead observed, multiple domains of antimonene monolayers, illustrated in yellow and pink, are expected.