Topological scenario for stripe formation in manganese oxides

The spin-charge-orbital complex structures of manganites are studied using topological concepts. The key quantity is the "winding number" w associated with the Berry-phase connection of an e(g) electron parallel transported through Jahn-Teller centers, along zigzag one-dimensional paths in an antiferromagnetic environment of t(2g) spins. From these concepts, it is shown that the "bi-stripe" and "Wigner-crystal" states observed experimentally have different w's. Predictions for the spin structure of the charge-ordered states for heavily doped manganites are discussed.