Probing the bulk electronic states of Bi2Se3using nuclear magnetic resonance

Abstract

We report a nuclear magnetic resonance (NMR) study of Bi${}_{2}$Se${}_{3}$ single crystals grown by three different methods. All the crystals show nine well-resolved peaks in their ${}^{209}$Bi NMR spectra of the nuclear quadrupolar splitting, albeit with an intensity anomaly. Spectra at different crystal orientations confirm that all the peaks are purely from the nuclear quadrupolar effect, with no other hidden peaks. We identify the short nuclear transverse relaxation time (${T}_{2}$) effect as the main cause of the intensity anomaly. We also show that the ${}^{209}$Bi signal originates exclusively from bulk, while the contribution from the topological surface states is too weak to be detected by NMR. However, the bulk electronic structure in these single crystals is not the same, as identified by the NMR frequency shift and nuclear spin-lattice relaxation rate ($1/{T}_{1}$). The difference is caused by the different structural defect levels. We find that the frequency shift and $1/{T}_{1}$ are smaller in samples with fewer defects and a lower carrier concentration. Also, the low-temperature power law of the temperature-dependent $1/{T}_{1}$ ($\ensuremath{\propto}{T}^{\ensuremath{\alpha}}$) changes from the Korringa behavior $\ensuremath{\alpha}=1$ in a highly degenerate semiconductor (where the electrons obey Fermi statistics) to $\ensuremath{\alpha}<1$ in a less degenerate semiconductor (where the electrons obey Boltzmann statistics).