Topological Doping and Superconductivity in Cuprates: An Experimental Perspective

Hole doping into a correlated antiferromagnet leads to topological stripe correlations, involving charge stripes that separate antiferromagnetic spin stripes of opposite phase. Topological spin stripe order causes the spin degrees of freedom within the charge stripes to feel a geometric frustration with their environment. In the case of cuprates, where the charge stripes have the character of a hole-doped two-leg spin ladder, with corresponding pairing correlations. Anti-phase Josephson coupling across the spin stripes can lead to pair-density-wave order, in which broken translation symmetry of the superconducting wave function is accommodated by pairs with finite momentum. This scenario has now been experimentally verified by recently reported measurements on La$_{2-x}$Ba$_x$CuO$_4$ with $x=1/8$. While pair-density-wave order is not common as a cuprate ground state, it provides a basis for understanding the uniform $d$-wave order that is more typical in superconducting cuprates.