Anisotropy of linear magnetoresistance in Kagome metal ZrV$_6$Sn$_6$

Abstract

The Kagome lattice has attracted extensive attention due to the diverse magnetic properties and non-trivial electronic states generated by its unique atomic arrangement, which provides an excellent system for exploring macroscopic quantum behavior. Here, we report the anomalous transport properties in 166-type Kagome metal ZrV$_6$Sn$_6$ single crystals. The quadratic and linear magnetoresistance (LMR) can be observed depending on the directions of the field and the current. Integrating Hall resistivity and quantum oscillation measurements, we found that the LMR could match well with the Abrikosov model. However, this model encounters difficulties in explaining the anisotropy of the magnetoresistance. To solve the issue, we extrapolate the Abrikosov model to the case of two-dimensional linear dispersion. It was found that when the field is parallel to the linear dependence momentum, the quantized energy is $ε_n^{\pm}$ = $\pm v\sqrt{p^2+2eHn/c}$, resulting in LMR. By contrast, when it is parallel to the non-linear dependence momentum, the energy is $ε_n^{\pm}$ = $\pm v\sqrt{2eHn/c}$, without yielding LMR. Through the combination of experiment and theory, the modified Abrikosov model could interpret the macroscopic quantum transport in ZrV$_6$Sn$_6$ crystal. The present research provides a new perspective for understanding the LMR behavior.

Figures (4)

• Figure 1: (a) Crystal structure of ZrV$_6$Sn$_6$. (b), (c): HRTEM images with corresponding crystal structure of ZrV$_6$Sn$_6$ single-crystal. (d) Temperature-dependent resistivity $\rho$ of ZrV$_6$Sn$_6$ single-crystal when the current is parallel to the $a$-axis and $c$-axis, respectively. Inset: Sample measurement sketch with the $x$, $y$, and $z$ axes correspond to the $a$, $b$, and $c$ axes, respectively.
• Figure 2: The ($MR$) for ZrV$_6$Sn$_6$ single-crystal. (a), (b): The field-dependence of $MR$ at various temperatures. Configuration A (a): Current along $a$-axis and field along $c$-axis. Configuration B (b): Current along $c$-axis and field along $a$-axis. Inset: The temperature-dependence of crossover field ($B_c$). $B_c$ is the intersection point of the linear fitted by the high-field curve and the low-field curve in the field-dependence of derivative of $MR_{zz}$. (c), (d): The field-dependence of $MR$ at 20 K for the current along $a$-axis and $c$-axis , respectively, and field rotating within the normal plane of the current. Inset: Sample measurement sketch for different current and field configurations. (e): The angle-dependence of power $n$, which could fitted by $MR$ = $a$$(T)^n$ in inset of (e).
• Figure 3: The high-field magnetoresistance at low temperature in Configuration A (a) and Configuration B (b). (c): A plot of $MR_{zz}$ versus $\mu_{0}H/\rho_{zz}$($T$,0) at different temperatures. (d): The temperature-dependence of increments of longitudinal resistance (black circles) and the transverse resistance (blue circles) at 8.5 T, and their ratio (red dots).
• Figure 4: (a), (b): Band structure of the 3D Dirac point and the 2D Dirac point, respectively. (c): The quantized energy-momentum dispersion of the 3D Dirac point when the field is along a certain direction $p_\gamma$. (d), (e): The quantized energy-momentum dispersion of the 2D Dirac point when the field is along $p_z$ for Configuration A and $p_x$ for Configuration B, respectively.