Evolution of Anisotropic In-plane Resistivity with doping level in Ca$_{1-x}$Na$_x$Fe$_2$As$_2$ Single Crystals

We measured the in-plane resistivity anisotropy in the underdoped Ca$_{1-x}$Na$_x$Fe$_2$As$_2$ single crystals. The anisotropy (indicated by $\rho_{\rm b} - \rho_{\rm a}$) appears below a temperature well above magnetic transition temperature $T_{\rm N}$, being positive ($\rho_{\rm b} - \rho_{\rm a} > 0$) as $x\leq$ 0.14. With increasing the doping level to $x$ = 0.19, an intersection between $\rho_{\rm b}$ and $\rho_{\rm a}$ is observed upon cooling, with $\rho_{\rm b} - \rho_{\rm a} < 0$ at low-temperature deep inside a magnetically ordered state, while $\rho_{\rm b} - \rho_{\rm a}> 0$ at high temperature. Subsequently, further increase of hole concentration leads to a negative anisotropy $\rho_{\rm b} - \rho_{\rm a} < 0$ in the whole temperature range. These results manifest that the anisotropic behavior of resistivity in the magnetically ordered state depends strongly on the competition of the contributions from different mechanisms, and the competition between the two contributions results in a complicated evolution of the anisotropy of in-plane resistivity with doping level.