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.