Smectic Coexisting with nematic in cuprate

In the pseudogap phase of cuprate superconductors, incredibly rich and exotic things have been observed, among which are the checkerboard pattern that breaks the C4v symmetry within an unit cell and the stripes that break an additional translational symmetry. These are called electronic nematic and smectic phases, respectively. According to this study, there should be an interesting interplay between the two on cuprates, due to topological defects. The authors formalize the coupling in a gauge invariant way.

Coupling to the smectic fields can then occur either through phase or amplitude fluctuations of the smectic. Here, we focus on the former, which means that couples to local shifts of the wave vectors and . Replacing the gradient in the x direction by a covariant-derivative-like coupling gives(4)and similarly for the gradient in the y direction, to yield a GL term coupling the nematic to smectic states. The vector represents by how much the wave vector, , is shifted for a given fluctuation. Hence, we propose a GL functional (for modulations along ) based on symmetry principles and and being small:(5)where … refers to terms we can neglect for the present purpose (SOM d). If we were to replace by where is the electromagnetic vector potential, Eq. 5 becomes the GL free energy of a superconductor; its minimization in the long-distance limit yields and thus quantization of its associated magnetic flux (22, 23). Analogously, minimization of Eq. 5 implies surrounding each topological defect (SOM e). Here, the vector is proportional to and lies along the line where = 0. The resulting key prediction is that will vanish along the line in the direction of that passes through the core of the topological defect, with becoming greater on one side and less on the other (Fig. 4B). Additional coupling to the smectic amplitude can shift the location of the topological defect away from the line of = 0 (SOM e).