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We report $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{NMR}$ measurements in ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}:\mathrm{Ca}$ and ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}:\mathrm{Mn}$ single crystals using $^{8}\mathrm{Li}^{+}$ implanted to depths on the order of 100 nm. Above $\ensuremath{\sim}200\phantom{\rule{4pt}{0ex}}\mathrm{K}$, spin-lattice relaxation reveals diffusion of $^{8}\mathrm{Li}^{+}$, with activation energies of $\ensuremath{\sim}0.4\phantom{\rule{4pt}{0ex}}\mathrm{eV}$ $(\ensuremath{\sim}0.2\phantom{\rule{4pt}{0ex}}\mathrm{eV})$ in ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}:\mathrm{Ca}$ $({\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}:\mathrm{Mn})$. At lower temperatures, the NMR properties are those of a heavily doped semiconductor in the metallic limit, with Korringa relaxation and a small, negative, temperature-dependent Knight shift in ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}:\mathrm{Ca}$. From this, we make a detailed comparison with the isostructural tetradymite ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{2}\mathrm{Se}$ [McFadden et al., Phys. Rev. B 99, 125201 (2019)]. In the magnetic ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}:\mathrm{Mn}$, the effects of the dilute Mn moments predominate, but remarkably the $^{8}\mathrm{Li}^{+}$ signal is not wiped out through the magnetic transition at 13 K, with a prominent critical peak in the spin-lattice relaxation that is suppressed in a high applied field. This detailed characterization of the $^{8}\mathrm{Li}^{+}$ NMR response is an important step toward using depth-resolved $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{NMR}$ to study the low-energy properties of the chiral topological surface state in the ${\mathrm{Bi}}_{2}{\mathrm{Ch}}_{3}$ tetradymite topological insulator.

The thermal excitation of electrons to higher, unoccupied states leads in certain cases to the paradox situation that the chemical potential needs to be shifted to lower energies. Here, a manipulation of Dirac fermions through the temperature dependence of the chemical potential is analyzed while maintaining sufficient insulating character in the bulk. The appearance of a bulk conduction band and consequently, a remarkable energy shift of the Dirac point is observed in ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{2}\mathrm{Se}$ at low temperatures (20 K), compared to the high temperatures (200--300 K), as revealed by hard x-ray photoelectron spectroscopy as well as momentum-resolved photoelectron microscopy. The temperature-induced shift of the Dirac cone and the appearance of bulk bands are related to the paradoxical shift of the chemical potential. The experiments are completely reversible, i.e., repeated cooling and heating of the sample up to room temperature recovers the original spectra. Such bulk related energy shifts must be considered not only in photoelectron spectroscopy but also in analysis of other measurable physical quantities and while designing devices for applications.

We report on the electronic and magnetic properties of Co atoms adsorbed on topological insulator (TI) surfaces, such as ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}, {\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$, and on magnetically doped ${\mathrm{Bi}}_{1.9}{\mathrm{Mn}}_{0.1}{\mathrm{Te}}_{3}$ and ${\mathrm{Bi}}_{1.98}{\mathrm{Fe}}_{0.02}{\mathrm{Se}}_{3}$ in comparison to a nontopological insulator surface, ${\mathrm{Bi}}_{2}{\mathrm{S}}_{3}$. Co atoms are used as probes of impurity affected surface electronic properties of TI and non-TI tetradymite semiconductors. X-ray spectroscopy, x-ray magnetic circular dichroism, and scanning tunneling microscopy and spectroscopy were employed. We found that the electronic properties of Co adatoms do not depend much on the substrate. In particular, no TI specific phenomenon was found. Magnetic dichroism measurements reveals an in-plane easy axis of adsorbed Co atoms on all topological insulators and ${\mathrm{Bi}}_{2}{\mathrm{S}}_{3}$, but not on the ferromagnetic substrate ${\mathrm{Bi}}_{1.9}{\mathrm{Mn}}_{0.1}{\mathrm{Te}}_{3}$, for which an out-of-plane easy axis was found.

Formation energies of native defects in Bi${}_{2}$(Te${}_{x}$Se${}_{3\ensuremath{-}x}$), with comparison to ideal Bi${}_{2}$Te${}_{2}$S, are calculated in density-functional theory to assess transport properties. Bi${}_{2}$Se${}_{3}$ is found to be $n$ type for both Bi- and Se-rich growth conditions, while Bi${}_{2}$Te${}_{3}$ changes from $n$ to $p$ type going from Te- to Bi-rich conditions, as observed. Bi${}_{2}$Te${}_{2}$Se and Bi${}_{2}$Te${}_{2}$S are generally $n$ type, explaining observed heavily doped $n$-type behavior in most samples. A (0/\ensuremath{-}) transition level at 16 meV above valence-band maximum for Bi on Te antisites in Bi${}_{2}$Te${}_{2}$Se is related to the observed thermally active transport gap causing a $p$-to-$n$ transition at low temperature. Bi${}_{2}$(Te${}_{x}$Se${}_{3\ensuremath{-}x}$) with $xg2$ are predicted to have high bulk resistivity due to effective carrier compensation when approaching the $n$-to-$p$ crossover. Predicted behaviors are confirmed from characterization of our grown single crystals.

Defects in the topological insulator Bi${}_{2}$Te${}_{2}$Se are studied by scanning tunneling microscopy. Small numbers of Te${}_{\mathrm{Bi}}$ antisite defects are found and are postulated to be the origin of $n$-type carriers in this tetradymite composition near the $n$-to-$p$ crossover. Based on this defect chemistry, we design an alternative method for obtaining resistive Bi${}_{2+x}$Te${}_{2\ensuremath{-}x}$Se samples, by the introduction of compensating $p$-type carriers through Bi${}_{\mathrm{Te}}$ antisite defects induced by making the material slightly Bi rich. Our resistivity and Hall coefficient measurements of Bi${}_{2+x}$Te${}_{2\ensuremath{-}x}$Se crystals grown by the Bridgeman-Stockbarger method show that the carrier concentration at base temperature is significantly reduced from that of stoichiometric samples. Analysis of the measurements reveals the possible underlying chemical distribution along the boules during growth.

We describe the crystal growth, crystal structure, and basic electrical properties of Bi${}_{2}$Te${}_{1.6}$S${}_{1.4}$, which incorporates both S and Te in its tetradymite quintuple layers in the motif -[Te${}_{0.8}$S${}_{0.2}$]-Bi-S-Bi-[Te${}_{0.8}$S${}_{0.2}$]-. This material differs from other tetradymites studied as topological insulators due to the increased ionic character that arises from its significant S content. Bi${}_{2}$Te${}_{1.6}$S${}_{1.4}$ forms high quality crystals from the melt and is the S-rich limit of the ternary Bi-Te-S \ensuremath{\gamma}-tetradymite phase at the melting point. The native material is $n$ type with a low resistivity; Sb substitution, and with adjustment of the Te to S ratio, results in a crossover to $p$ type and resistive behavior at low temperatures. An angle-resolved photoemission study shows that topological surface states are present, with the Dirac point more exposed than it is in Bi${}_{2}$Te${}_{3}$ and similar to that seen in Bi${}_{2}$Te${}_{2}$Se. Single crystal structure determination indicates that the S in the outer chalcogen layers is closer to the Bi than the Te, and therefore that the layers supporting the surface states are corrugated on the atomic scale.

To optimize the bulk-insulating behavior in the topological insulator materials having a tetradymite structure, we have synthesized and have characterized single-crystal samples of ${\mathrm{Bi}}_{2\text{\ensuremath{-}}x}{\mathrm{Sb}}_{x}{\mathrm{Te}}_{3\text{\ensuremath{-}}y}{\mathrm{Se}}_{y}$ solid solution at various compositions. We have elucidated that there are a series of intrinsic compositions where the acceptors and donors compensate each other and present a maximal bulk-insulating behavior. At such compositions, the resistivity can become as large as several $\ensuremath{\Omega}$ cm at low temperatures, and one can infer the role of the surface-transport channel in the nonlinear Hall effect. In particular, the composition of ${\mathrm{Bi}}_{1.5}{\mathrm{Sb}}_{0.5}{\mathrm{Te}}_{1.7}{\mathrm{Se}}_{1.3}$ achieves the lowest bulk carrier density and appears to be best suited for surface-transport studies.

We report on a diluted magnetic semiconductor based on the ${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$ tetradymite structure doped with very low concentrations of vanadium (1--3 at. %). The anomalous transport behavior and robust magnetic hysteresis loops observed in magnetotransport and magnetic measurements are experimental manifestations of the ferromagnetic state in these materials. The $p\ensuremath{-}d$ exchange between holes and vanadium $3d$ spins is estimated from the behavior of the magnetoresistance. A Curie temperature of at least 22 K is observed for ${\mathrm{Sb}}_{1.97}{\mathrm{V}}_{0.03}{\mathrm{Te}}_{3}.$ This discovery offers possibilities for exploring magnetic properties of other tetradymite structure semiconductors doped with a wide range of $3d$ transition metals.