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

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.