Considerable evidence suggests that variations in the properties of topological insulators (TIs) at the nanoscale and at interfaces can strongly affect the physics of topological materials. Therefore, a detailed understanding of surface states and in
terface coupling is crucial to the search for and applications of new topological phases of matter. Currently, no methods can provide depth profiling near surfaces or at interfaces of topologically inequivalent materials. Such a method could advance the study of interactions. Herein we present a non-invasive depth-profiling technique based on $beta$-NMR spectroscopy of radioactive $^8$Li$^+$ ions that can provide one-dimensional imaging in films of fixed thickness and generates nanoscale views of the electronic wavefunctions and magnetic order at topological surfaces and interfaces. By mapping the $^8$Li nuclear resonance near the surface and 10 nm deep into the bulk of pure and Cr-doped bismuth antimony telluride films, we provide signatures related to the TI properties and their topological non-trivial characteristics that affect the electron-nuclear hyperfine field, the metallic shift and magnetic order. These nanoscale variations in $beta$-NMR parameters reflect the unconventional properties of the topological materials under study, and understanding the role of heterogeneities is expected to lead to the discovery of novel phenomena involving quantum materials.
In this study we present an alternative approach to separating contributions to the NMR shift originating from the Knight shift and chemical shielding by a combination of experimental solid-state NMR results and ab initio calculations. The chemical a
nd Knight shifts are normally distinguished through detailed studies of the resonance frequency as function of temperature and carrier concentration, followed by extrapolation of the shift to zero carrier concentration. This approach is time-consuming and requires studies of multiple samples. Here, we analyzed $^{207}$Pb and $^{125}$Te NMR spin-lattice relaxation rates and NMR shifts for bulk and nanoscale PbTe. The shifts are compared with calculations of the $^{207}$Pb and $^{125}$Te chemical shift resonances to determine the chemical shift at zero charge carrier concentration. The results are in good agreement with literature values from carrier concentration-dependent studies. The measurements are also compared to literature reports of the $^{207}$Pb and $^{125}$Te Knight shifts of $n$- and $p$-type PbTe semiconductors. The literature data have been converted to the currently accepted shift scale. We also provide possible evidence for the self-cleaning effect property of PbTe nanocrystals whereby defects are removed from the core of the particles, while preserving the crystal structure.
Non-invasive local probes are needed to characterize bulk defects in binary and ternary chalcogenides. These defects contribute to the non-ideal behavior of topological insulators. We have studied bulk electronic properties via $^{125}$Te NMR in Bi$_
2$Te$_3$, Sb$_2$Te$_3$, Bi$_{0.5}$Sb$_{1.5}$Te$_3$, Bi$_2$Te$_2$Se and Bi$_2$Te$_2$S. A distribution of defects gives rise to asymmetry in the powder lineshapes. We show how the Knight shift, line shape and spin-lattice relaxation report on carrier density, spin-orbit coupling and phase separation in the bulk. The present study confirms that the ordered ternary compound Bi$_2$Te$_2$Se is the best TI candidate material at the present time. Our results, which are in good agreement with transport and ARPES studies, help establish the NMR probe as a valuable method to characterize the bulk properties of these materials.
