Critical phenomena at the complex tensor ordering phase transition

TL;DR

This paper studies the critical behavior of phase transitions to complex tensor order in spin-orbit coupled superconductors, revealing fluctuation effects and the influence of anisotropy through renormalization group analysis.

Contribution

It formulates a bosonic field theory for complex tensor order and analyzes fluctuation effects, including first-order transitions and fixed points, in a unified RG framework.

Findings

Fluctuation-induced first-order transition in isotropic systems.

Weakly first-order transition near a fixed point in Luttinger semimetals.

Cubic anisotropy maps the theory to frustrated magnetism.

Abstract

We investigate the critical properties of the phase transition towards complex tensor order that has been proposed to occur in spin-orbit coupled superconductors. For this purpose we formulate the bosonic field theory for fluctuations of the complex irreducible second-rank tensor order parameter close to the transition. We then determine the scale dependence of the couplings of the theory by means of the perturbative Renormalization Group (RG). For the isotropic system we generically detect a fluctuation-induced first-order phase transition. The initial values for the running couplings are determined by the underlying microscopic model for the tensorial order. As an example we study three-dimensional Luttinger semimetals with electrons at a quadratic band touching point. Whereas the strong-coupling transition of the model receives substantial fluctuation corrections, the weak-coupling transition at low temperatures is rendered only weakly first-order due to the presence of a fixed point in the vicinity of the RG trajectory. If the number of fluctuating complex components of the order parameter is reduced by cubic anisotropy, the theory maps onto the field theory for frustrated magnetism.