NMR Probe of Metallic States in Nanoscale Topological Insulators

A ${}^{125}\mathrm{Te}$ NMR study of bismuth telluride nanoparticles as a function of particle size revealed that the spin-lattice relaxation is enhanced below 33 nm, accompanied by a transition of NMR spectra from the single to the bimodal regime. The satellite peak features a negative Knight shift and higher relaxivity, consistent with core polarization from $p$-band carriers. Whereas nanocrystals follow a Korringa law in the range 140–420 K, micrometer particles do so only below 200 K. The results reveal increased metallicity of these nanoscale topological insulators in the limit of higher surface-to-volume ratios.

Figure 1

Comparison of the Korringa product of the ${}^{125}\mathrm{Te}$ spin-lattice relaxation time with the temperature as a function of the inverse temperature for 19-nm nanoparticles of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and the m&p sample. Inset shows a log-log plot for $1/(T_1{T}^{1/2})$ vs inverse temperature in the case of nanosized as well as m&p samples. The quantity $1/(T_1{T}^{1/2})$ is proportional to carrier density.

Figure 2

${}^{125}\mathrm{Te}$ spin-lattice relaxation rate as a function of the mean particle size of ball-milled ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ nanoparticles. The mean particle size was estimated from PXRD data. The inset schematically describes the diameter [$d$], the particle core volume bulk, $V_B$, the volume of its shell [surface, $V_S$] as well as the shell thickness [$t$]. The shell is the volume where metallic surface states reside (a). The mean particle size of the nanoparticles per each milling time process estimated from PXRD data (b). PXRD data of 19 nm (732 min) and m&p sample reveals crystallinity (b, inset). Comparison of ${}^{125}\mathrm{Te}$ NMR spectrum of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ nanoparticles versus polycrystalline ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ (m&p sample). As the particle size decreases, a shoulder peak emerges and grows. We postulate that this shoulder peak is related to the metallic surface states (c). A representative SEM image of particles with average size 55 nm (d).

Figure 3

${}^{125}\mathrm{Te}$ NMR central peak width as a function of the mean particle size of the ball-milled ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ nanoparticles. The central and shoulder peaks are seen in Fig. 2. The mean particle size was estimated from PXRD data. The inset shows the splitting of the ${}^{125}\mathrm{Te}$ resonance into central (upper curve, black color) and shoulder (lower curve, red color) peaks for nanoparticles. The splitting increases with decreasing particle size.

Figure 4

${}^{125}\mathrm{Te}$ NMR spectra of 19-nm ball-milled ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ at various delay times during the saturation recovery process and the spin-lattice saturation recovery relaxation data for the “shoulder” (red line, triangle symbols) and the central (blue line, circle symbols) peak, respectively. For clarity, all spectra have been rescaled to the same vertical range.