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-$T_c$ 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 nonuniform phases can be stabilized by long-range forces, but can only have nontopological (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 length scale, 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.