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