  Motivated by recent nuclear magnetic resonance (NMR) experiments, we present
a microscopic sp3 tight-binding model calculation of the NMR shifts in bulk
Bi2Se3, and Bi2Te3. We compute the contact, dipolar, orbital and core
polarization contributions to the carrier-density-dependent part of the NMR
shifts in Bi209, Te125 and Se77. The spin-orbit coupling and the layered
crystal structure result in a contact Knight shift with strong uniaxial
anisotropy. Likewise, because of spin-orbit coupling, dipolar interactions make
a significant contribution to the isotropic part of the NMR shift. The contact
interaction dominates the isotropic Knight shift in Bi209 NMR, 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. In all cases, the orbital shift is at least comparable to the contact
and dipolar shifts, while the shift due to core polarization is subdominant
(except for Te nuclei located at the inversion centers). By artificially
varying the strength of spin-orbit coupling, we evaluate the evolution of the
NMR shift across a band inversion but find no clear signature of the
topological transition.
