Stable Higgs Modes in Fulde-Ferrell-Larkin-Ovchinnikov States*

Higgs boson is an elementary particle in the Standard Model that was discovered experimentally in 2012. The Higgs boson is massive thus requiring a huge particle collider to enable its discovery. An elementary excitation, analogous to Higgs boson, can also appear in superconductors as a consequence of the U(1) symmetry breaking. Akin to its cousin in particle physics, the Higgs boson in superconductors is very massive, which renders it short lived by decaying into quasiparticle continuum. This raises a question of how to stabilize the Higgs mode in superconductors. Here we study the Higgs mode in thin-film superconductors with spatially inhomogeneous superconducting order parameter, known as the Fulde-Ferrell-Larkin-Ovchinnikov state. By deriving an effective action for the small amplitude fluctuation in the ground state manifold, we obtain the dispersion for the Higgs mode. We find that the Higgs mode becomes massless and more stable at finite momentums.