The role of electromagnetic gauge-field fluctuations in the selection between chiral and nematic superconductivity

TL;DR

This paper investigates how electromagnetic gauge-field fluctuations influence the stability of nematic versus chiral superconducting states on a triangular lattice, revealing that fluctuations can favor nematic order over the traditionally preferred chiral order.

Contribution

The study derives an effective free energy incorporating gauge-field fluctuations, showing that these fluctuations can stabilize nematic superconductivity, especially in systems with anisotropic order parameter stiffness.

Findings

Gauge-field fluctuations induce a cubic term favoring nematic order.

Fluctuations can shift the phase diagram, promoting nematic over chiral states.

Results are applicable to various candidate nematic superconductors, including twisted bilayer graphene.

Abstract

Motivated by the observation of nematic superconductivity in several systems, we revisit the problem of the leading pairing instability of two-component unconventional superconductors on the triangular lattice -- such as $(p_{x},\,p_{y})$-wave and $(d_{x^{2}-y^{2}},\,d_{xy})$-wave. Such a system has two possible superconducting states: the chiral state (e.g. $p+ip$ or $d+id$), which breaks time-reversal symmetry, and the nematic state (e.g. $p+p$ or $d+d$), which breaks the threefold rotational symmetry of the lattice. Weak-coupling calculations generally favor the chiral over the nematic superconducting state, raising the question of what mechanism can stabilize the latter. Here, we show that the electromagnetic field fluctuations can play a crucial role in selecting between these two states. Specifically, we derive and analyze the effective free energy for the two-component superconducting order parameter after integrating out the gauge-field fluctuations, which is formally justified if the spatial order parameter fluctuations can be neglected. A non-analytic cubic term arises, as in the case of a conventional $s$-wave superconductor. However, unlike the latter, the cubic term depends on the relative phase and on the relative amplitudes between the two order parameter components, in such a way that it generally favors the nematic state. This result is a direct consequence of the fact that the stiffness of the superconducting order parameter is not isotropic. Competition with the quartic term, which favors the chiral state, leads to a renormalized phase diagram in which the nematic state displaces the chiral state over a wide region in the parameter space. We analyze the stability of the fluctuation-induced nematic phase, generalize our results to tetragonal lattices, and discuss their applicability to candidate nematic superconductors, including twisted bilayer graphene.