Antagonistic in-plane resistivity anisotropies from competing fluctuations in underdoped cuprates

One of the prime manifestations of an anisotropic electronic state in underdoped cuprates is the in-plane resistivity anisotropy $\Delta\rho\equiv(\rho_{a}-\rho_{b})/\rho_{b}$. Here we use a Boltzmann-equation approach to compute the contribution to $\Delta\rho$ arising from scattering by anisotropic charge and spin fluctuations, which have been recently observed experimentally. While the anisotropy in the charge fluctuations is manifested in the correlation length, the anisotropy in the spin fluctuations emerges only in the structure factor. As a result, we find that spin fluctuations favor $\Delta\rho>0$, whereas charge fluctuations promote $\Delta\rho<0$, which are both consistent with the doping dependence of $\Delta\rho$ observed in YBa$_{2}$Cu$_{3}$O$_{7}$. We also discuss the role played by CuO chains in these materials, and propose transport experiments in strained HgBa$_{2}$CuO$_{4}$ and Nd$_{2}$CuO$_{4}$ to probe directly the different resistivity anisotropy regimes.