  Multiband superconductors are sources of rich physics arising from multiple
order parameters, which show unique collective dynamics including Leggett mode
as relative phase oscillations. Previously, it has been pointed out that the
Leggett mode can be optically excited in the linear response regime, as
demonstrated in a one-dimensional model for multiband superconductors[T.
Kamatani, et al., Phys. Rev. B 105, 094520 (2022)]. Here we identify the linear
coupling term in the Ginzburg-Landau free energy to be the so-called Lifshitz
invariant, which takes a form of
$\boldsymbol{d}\cdot\left(\Psi^{*}_{i}\nabla\Psi_{j} -
\Psi_{j}\nabla\Psi^{*}_{i}\right)$, where $\boldsymbol{d}$ is a constant vector
and $\Psi_{i}$ and $\Psi_{j}$ $(i\neq j)$ represent superconducting order
parameters. We have classified all pairs of irreducible representations of
order parameters in the crystallographic point groups that allow for the
existence of the Lifshitz invariant. We emphasize that the Lifshitz invariant
can appear even in systems with inversion symmetry. The results are applied to
a model of $s$-wave superconductors on a Kagome lattice with various bond
orders, for which in some cases we confirm that the Leggett mode appears as a
resonance peak in a linear optical conductivity spectrum based on microscopic
calculations. We discuss a possible experimental observation of the Leggett
mode by a linear optical response in multiband superconductors.
