  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.
