Topological doping and the stability of stripe phases

We analyze the properties of a general Ginzburg-Landau free energy with competing order parameters, long-range interactions, and global constraints (e.g., a fixed value of a total ``charge'') to address the physics of stripe phases in underdoped high-Tc and related materials. For a local free energy limited to quadratic terms of the gradient expansion, only uniform or phase-separated configurations are thermodynamically stable. ``Stripe'' or other non-uniform phases can be stabilized by long-range forces, but can only have non-topological (in-phase) domain walls where the components of the antiferromagnetic order parameter never change sign, and the periods of charge and spin density waves coincide. The antiphase domain walls observed experimentally require physics on an intermediate lengthscale, and they are absent from a model that involves only long-distance physics. Dense stripe phases can be stable even in the absence of long-range forces, but domain walls always attract at large distances, i.e., there is a ubiquitous tendency to phase separation at small doping. The implications for the phase diagram of underdoped cuprates are discussed.