Superconductivity of a Metallic Stripe Embedded in an Antiferromagnet

Abstract

We study a simple model for the metallic stripes found in $La_{1.6-x}Nd_{0.4}Sr_xCuO_4$: two chain Hubbard ladder embedded in a static antiferromagnetic environments. We consider two cases: a ``topological stripe'', for which the phase of the Neel order parameter shifts by $π$ across the ladder, and a ``non-topological stripe'', for which there is no phase shift across the ladder. We perform one-loop renormalization group calculations to determine the low energy properties. We compare the results with those of the isolated ladder and show that for small doping superconductivity is enhanced in the topological stripe, and suppressed in the non-topological one. In the topological stripe, the superconducting order parameter is a mixture of a spin singlet component with zero momentum and a spin triplet component with momentum $π$. We argue that this mixture is generic, and is due to the presence of a new term in the quantum Ginzburg-Landau action. Some consequences of this mixing are discussed.