Classical linear magnetoresistance in exfoliated ${\mathrm{NbTe}}_2$ nanoflakes

Recently, the transition metal dichalcogenide ${\mathrm{NbTe}}_2$ was predicted to be a candidate material of topological semimetal. Here we report the magnetotransport data measured in two devices fabricated from ${\mathrm{NbTe}}_2$ nanoflakes. A nonsaturating linear magnetoresistance was observed in both devices at various temperatures. A close analysis shows that the observed linear magnetoresistance is not consistent with the Abrikosov quantum theory; instead, it can be well explained in the framework of the effective-medium theory which describes the classical magnetoresistance of inhomogeneous systems. Our results indicate that the linear magnetoresistance of ${\mathrm{NbTe}}_2$ is most likely a classical magnetoresistance induced by disorders and inhomogeneities. This speculation is supported by the abundant domain structures observed in ${\mathrm{NbTe}}_2$ crystals in transmission electron microscopy measurements.

Figure 1

(a) Illustration of crystal structure of monoclinic ${\mathrm{NbTe}}_2$. Balls in yellow and turquoise color denote Te and Nb atoms, respectively. (Left) Stacking sequence of the Te-Nb-Te monolayers, viewed along [010]${}_{\text{m}}$ direction. (Right) Top view along the direction perpendicular to the Te-Nb-Te monolayers. (b) X-ray diffraction pattern of ${\mathrm{NbTe}}_2$ crystal, showing Bragg peaks of $\left(00l\right)$ surfaces. (c) Typical bright-field TEM image displays the complex domain structures of ${\mathrm{NbTe}}_2$. The coherent twinned planes are marked by dotted dashed lines and the boundaries regions marked by circles are selected to produce electron diffraction patterns. [(d) and (e)] The [103]${}_{\text{m}}$-oriented electron diffraction patterns of the two circled regions in (c). It is noteworthy that two patterns exhibit distinct spot splitting of (91-3) and (-3-11) owing to their specific twinned orientations. (f) Atomically resolved high-angle annual dark-field TEM image across the coherent twinned plane, revealing different atomic configurations in adjacent domains.

Figure 2

[(a) and (b)] Optical images of devices 1 and 2, illuminated with polarized light. Electrodes of device 1 and 2 are made of Pd and Au, respectively. [(c) and (d)] AFM images of devices 1 and 2. The thickness of the ${\mathrm{NbTe}}_2$ flakes in devices 1 and 2 was measured to be 59 and 110 nm, respectively.

Figure 3

Temperature dependence of resistivity. The resistivity of both devices decrease with decreasing temperature, showing a metallic behavior. The residual resistivity ratio was measured to be 6.7 and 6.8 for devices 1 and 2, respectively.

Figure 4

[(a) and (b)] The $R_{yx}\left(B\right)$ curves of devices 1 and 2, measured at $T⩾100$ K. In this temperature range, the high-field slope of $R_{yx}\left(B\right)$ increases with decreasing $T$. [(c) and (d)] The $R_{yx}\left(B\right)$ curves of both devices measured at 1.5 K $⩽T⩽$ 50 K. In this temperature range, the high-field slope of $R_{yx}\left(B\right)$ decreases with decreasing $T$. [(e) and (f)] The low-field $R_{yx}\left(B\right)$ data of both devices measured at $1.5\mathrm{K}⩽T⩽300$ K. The low-field slope of $R_{yx}\left(B\right)$ curves increases monotonically with decreasing $T$ in the entire temperature range. (g) Temperature dependence of Hall carrier density $n_{\text{H}}$, calculated using the low-field slopes of $R_{yx}\left(B\right)$ shown in (e) and (f). Dashed lines show a guide to the eye. (h) Temperature dependence of Hall mobility ${\mu }_{\text{H}}$, calculated using ${\mu }_{\text{H}}=1/\left(e\rho n_{\text{H}}\right)$.

Figure 5

[(a) and (b)] Magnetoresistance of devices 1 and 2, measured at various temperatures. The dashed lines are the fits to the empirical equation $R_{\text{MR}}\left(B\right)=\sqrt{k^2{B}^2+a^2}-a$ and the dashed-dotted lines are the fits to the effective-medium theory. [(c) and (d)] Magnetoresistance of devices 1 and 2 plotted against the dimensionless magnetic field $\beta$. (e) Temperature dependence of the linear and quadratic coefficients (left axis) and crossover field (right axis) obtained from the empirical fitting of the magnetoresistance data, explained in detail in the text. (f) Temperature dependence of parameters $\langle \mu \rangle$ and $\mathrm{\Delta }\mu$ obtained by fitting the effective medium model to the magnetoresistance data. The dashed line shows a guide to the eye. (Inset) Temperature dependence of $\mathrm{\Delta }n/\langle n\rangle$ obtained from the effective-medium-theory fitting. The details of the fitting are explained in the text.

Figure 6

[(a) and (b)] Comparison between the experimental $R_{yx}\left(B\right)$ data (solid lines) and the theoretically calculated $R_{yx}\left(B\right)$ curves (dashed lines) assuming that the observed linear magnetoresistance originates from the Abrikosov quantum linear magnetoresistance of a small Fermi pocket with high mobility. The free parameter in the model has been carefully tuned to give the best fit to the experimental data, as discussed in detail in the text.