Evidence of anisotropic three-dimensional weak-localization in TiSe$_{2}$ nanoflakes

Abstract

TiSe$_2$ is a typical transition-metal dichalcogenide known for its charge-density wave order. In this study, we report the observation of an unusual anisotropic negative magnetoresistance in exfoliated TiSe$_2$ nanoflakes at low temperatures. Unlike the negative magnetoresistance reported in most other transition-metal dichalcogenides, our results cannot be explained by either the conventional two-dimensional weak localization effect or the Kondo effect. A comprehensive analysis of the data suggests that the observed anisotropic negative magnetoresistance in TiSe$_2$ flakes is most likely caused by the three-dimensional weak localization effect. Our findings contribute to a deeper understanding of the phase-coherent transport processes in TiSe$_2$.

Figures (8)

• Figure 1: (a) X-ray diffraction pattern of a typical TiSe$_{2}$ crystal, showing Bragg peaks of (00$l$) surfaces. Inset: as-grown TiSe$_2$ crystals. The spacing of grid lines is 1 mm. (b) Temperature dependence of resistivity ($\rho$$_{xx}$) of devices A and B. The values of sheet resistance $R_{\textrm{sh}}$ are shown on the right axes. Inset: optical photo of device A with a 10-$\mu$m scale bar. (c) Second derivative of $\rho_{xx}(T)$ curves. The charge-density-wave transition temperatures were determined to be $T_\textrm{CDW}=190$ K and 194 K for device A and B, respectively. (d) Low-temperature $\rho_{xx}(T)$ curves of devices A and B, normalized to the $\rho_{xx}$ values at $T=20$ K. The resistivity upturn at low temperature is suppressed by an in-plane magnetic field $B_{\parallel}=10$ T.
• Figure 2: [(a)-(b)] Normalized out-of-plane magnetoresistance of devices A and B, measured at various temperatures. [(c)-(d)] Normalized in-plane magnetoresistance of devices A and B, measured at various temperatures.
• Figure 3: [(a)-(d)] The $\rho_{yx}(B_\perp)$ and $\rho_{xx}(B_\perp)$ curves of device A and B. The values of sheet resistance $R_{\textrm{sh}}$ are shown on the right axes of (c) and (d). Dashed lines are fitted curves obtained using the two-band Drude model. [(e)-(f)] Comparison of the negative magnetoresistivity measured in perpendicular and in-plane magnetic fields. The classical contribution to the out-of-plane magnetoresistivity has been removed by subtracting the fitted curves shown in (c) and (d).
• Figure 4: [(a)-(b)] Low-field magnetoconductance of devices A and B at various temperatures. Here $\Delta G(B)$ is the change of sheet conductance after subtracting the classical background. Dashed lines represent the best fits to the data using the HLN formula [Eq. (3)]. [(c)-(d)] The obtained fitting parameters $\alpha_\textrm{2D}$ and $L_{\phi}$ plotted as a function of temperature. Error bars represent the ranges within which the fitting results appear acceptable by eye. At low temperatures, $\alpha_\textrm{2D}$ significantly exceeds the threshold $\alpha_\textrm{2D}=1$ expected from the 2D weak localization theory.
• Figure 5: Fitting to the magnetoconductivity data using the 3D weak localization theory. [(a)-(d)] Low-field $\Delta \sigma(B)$ curves of devices A and B, measured in perpendicular and in-plane magnetic fields and at various temperatures. Here $\Delta \sigma \equiv \sigma(B) - \sigma(0)$. Dashed lines are fits to the $\Delta\sigma(B)$ data using the 3D weak localization theory [Eq. (5)]. [(e)-(f)] Temperature dependence of obtained fitting parameters $\alpha_{\textrm{3D}}$, $L_{\phi\parallel}$ and $L_{\phi \perp}$ for devices A and B. Error bars indicate the ranges within which the deviation between the fitting curves and the data looks acceptable.