  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.
