Screening of point charge impurities in highly anisotropic metals:   application to $\mu^+$ spin relaxation in underdoped cuprates
  We calculate the screening charge density distribution due to a point charge, such as that of a positive muon ($\mu^+$), placed between the planes of a highly anisotropic layered metal. In underdoped hole cuprates the screening charge converts the charge density in the metallic-plane unit cells in the vicinity of the $\mu^+$ to nearly its value in the insulating state. The current-loop ordered state observed by polarized neutron diffraction then vanishes in such cells, and also in nearby cells over a distance of order the intrinsic correlation length of the loop-ordered state. This in turn strongly suppresses the loop-current field at the $\mu^+$ site. We estimate this suppressed field in underdoped YBa$_2$Cu$_3$O$_{6+x}$ and La$_{2-x}$Sr$_x$CuO$_4$, and find consistency with the observed 0.2--0.3 G field in the former case and the observed upper bound of $\sim$0.2 G in the latter case. This resolves the controversy between the neutron diffraction and $\mu$SR experiments. The screening calculation also has relevance for the effect of other charge impurities in the cuprates, such as the dopants themselves. 
Arkady Shekhter, Lei Shu, Vivek Aji, D. E. MacLaughlin, C. M. Varma