Tight-binding theory of NMR shifts in topological insulators Bi2Se3 and Bi2Te3

Motivated by recent nuclear magnetic resonance (NMR) experiments, we present a microscopic sp3 tight-binding model calculation of the Knight shift and the orbital shift in bulk Bi2Se3 and Bi2Te3. As byproducts, we obtain approximate values for the contact hyperfine couplings and the electronic g factors. Overall, our study unveils a number of points that may guide the interpretation of NMR measurements in topological materials. First, the contact Knight shift in layered crystals has a large uniaxial anisotropy. Second, dipolar interactions make a significant contribution to the isotropic NMR shift. Third, the contribution of the Van Vleck spin susceptibility to the Knight shift is significant. Fourth, the carrier-density-dependent part of the orbital shift is comparable to that of the contact and dipolar shifts. The first three of the preceding statements are hallmarks of strong spin-orbit interactions. In addition, we find that the contact hyperfine interaction makes a significant contribution to the isotropic shift reported in Bi209 NMR experiments, even though the electronic states at the Fermi level have a rather weak s-orbital character. In contrast, the contribution from the contact hyperfine interaction to the NMR shift of Se77 and Te125 is weak compared to the dipolar and orbital shifts therein.