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

TL;DR

This paper develops a microscopic tight-binding model to analyze NMR shifts in topological insulators Bi2Se3 and Bi2Te3, revealing the roles of spin-orbit coupling and crystal structure in NMR responses.

Contribution

It provides a detailed calculation of NMR shifts considering various interactions, and explores the impact of spin-orbit coupling on topological transitions.

Findings

Contact hyperfine interaction dominates Bi209 NMR shifts.

Dipolar interactions significantly influence Se77 and Te125 NMR shifts.

No clear NMR signature of topological transition was observed.

Abstract

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.