Anisotropic and strong negative magnetoresistance in the three-dimensional topological insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$

We report on high-field angle-dependent magnetotransport measurements on epitaxial thin films of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, a three-dimensional topological insulator. At low temperature, we observe quantum oscillations that demonstrate the simultaneous presence of bulk and surface carriers. The magnetoresistance of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ is found to be highly anisotropic. In the presence of a parallel electric and magnetic field, we observe a strong negative longitudinal magnetoresistance that has been considered as a smoking gun for the presence of chiral fermions in a certain class of semimetals due to the so-called axial anomaly. Its observation in a three-dimensional topological insulator implies that the axial anomaly may be in fact a far more generic phenomenon than originally thought.

Figure 1

(a) Temperature dependence of the electrical resistivity ${\rho }_{xx}$ for ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ MBE-grown films with different thicknesses. (b) Mobility $\mu$ and carrier density $n$ as a function of $T$ for sample A. (c), (d) ${\rho }_{xx}$ and ${\rho }_{xy}$ as a function of $B$ at $T=4.2$ K for A and D, respectively. The quoted carrier density is extracted from the low-field Hall resistance.

Figure 2

Longitudinal resistivity ${\rho }_{xx}$ as a function of (a) perpendicular and (b) in-plane magnetic field at 4.2 K for sample A, respectively. (c), (d) Second derivative of ${\rho }_{xx}\left(B\right)$ as a function of $1/B$ and $1/B_{\parallel }$ to highlight the SdH oscillations. (e) Extracted frequencies from the FFT analysis as a function of angle showing contributions from surface and bulk carriers. The straight (dashed) lines correspond to the $1/cos\mathrm{\Theta }$ dependence expected for a purely two-dimensional system. (f), (g) FFTs for a perpendicular and parallel field sweep, respectively, with the primary oscillation frequencies highlighted.

Figure 3

Anisotropic magnetotransport in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ at $T=300$ K: (a) Schematic diagram of the electrical transport measurements for configurations [i] and [ii]. (b), (c) Magnetoresistance of sample A as a function of $B$ for both configurations, indicating a strong negative MR if $I\parallel B_x$. (d) Longitudinal ${\sigma }_{xx}$ and Hall conductivities ${\sigma }_{xy}$ as a function of the magnetic field and (e) extracted $\mu B$ and $\mu$ using the Drude model. (f) Hall resistivity ${\rho }_{xy}$ as a function of $B$ for both configurations (solid line for [i], open symbols for [ii]). (g) The conductivity ${\sigma }_{xx}$ as a function of $B$ (solid line) at $\varphi ={90}^{\circ }$ is found to be $\propto B^2$ (triangles).

Figure 4

(a) Normalized longitudinal magnetoresistivity ${\rho }_{xx}\left(B\right)/{\rho }_{xx}\left(0\right)$ for sample A at different temperatures [inset: ${\rho }_{xx}\left(B\right)/{\rho }_{xx}\left(0\right)$ at $B=25$ T]. ${\rho }_{xx}\left(B\right)/{\rho }_{xx}\left(0\right)$ for different angles $\varphi$ at (b) $T=4.2$ K and (c) $T=300$ K. (d) Normalized magnetoconductivity ${\sigma }_{xx}\left(B\right)/{\sigma }_{xx}\left(0\right)$ at $T=300$ K for all samples A, B, C, and D for $\varphi ={90}^{\circ }$. All samples follow a ${\sigma }_{xx}\left(B\right)/{\sigma }_{xx}\left(0\right)\propto B^2$ dependence (see fits). The inset shows the fitting parameter $a$ as a function of $\mu$ for all samples.