A Phenomenological Effective-Field Theory for a Charged Spin-1 Condensate in Anisotropic Layered Superconductors

We formulate a gauge-invariant phenomenological theory for a charged three-component condensate in an anisotropic layered superconductor. The construction is conditional on a material-specific pairing calculation selecting an isolated, predominantly triplet channel; it does not infer triplet pairing from layering or spin–orbit coupling alone. The order parameter is represented equivalently by a spin-1 spinor, a complex d-vector, and a pure-vector complex quaternion. Only the mapping and the density-spin bilinear are retained in the main text. A static Ginzburg–Landau functional then yields axial-polar, planar-polar, easy-axis polarized, and broken-axisymmetry mean-field states. Conservative Gross–Pitaevskii dynamics are introduced only as an additional composite-boson limit, not as a generic consequence of the Ginzburg–Landau theory. In that limit, analytic spectra are given for the axial-polar and easy-axis phases: the transverse spin branch softens at the axial-polar to broken-axisymmetry boundary, whereas crystal locking gaps the transverse magnon of the polarized phase. We do not claim a closed analytic spectrum for the mixed broken-axisymmetry phase. The static transverse current-response kernel provides a quantitative link between penetration-depth anisotropy and the gradient tensor. Ideal Bose condensation and BKT formulas are stated only in their controlled three- and two-dimensional limits. The framework therefore supplies a compact, falsifiable set of phase, mode, and response relations without introducing additional quaternionic degrees of freedom.