# Higgs Modes in the Pair Density Wave Superconducting State

## TL;DR

This paper investigates the unique Higgs modes in the spatially modulated pair density wave superconducting state, revealing two Higgs modes with distinct damping behaviors, which can be experimentally detected to confirm PDW states.

## Contribution

It introduces a phenomenological model showing that unidirectional PDW superconductors possess two Higgs modes with different damping characteristics, unlike conventional superconductors.

## Key findings

- Two Higgs modes are present in PDW superconductors.
- Damping of Higgs modes requires exceeding an energy threshold.
- One Higgs mode remains largely undamped due to kinematic constraints.

## Abstract

The pair density wave (PDW) superconducting state has been proposed to explain the layer- decoupling effect observed in the compound La$_{2-x}$Ba$_x$CuO$_4$ at $x=1/8$ (Phys. Rev. Lett. 99, 127003). In this state the superconducting order parameter is spatially modulated, in contrast with the usual superconducting (SC) state where the order parameter is uniform. In this work, we study the properties of the amplitude (Higgs) modes in a unidirectional PDW state. To this end we consider a phenomenological model of PDW type states coupled to a Fermi surface of fermionic quasiparticles. In contrast to conventional superconductors that have a single Higgs mode, unidirectional PDW superconductors have two Higgs modes. While in the PDW state the Fermi surface largely remains gapless, we find that the damping of the PDW Higgs modes into fermionic quasiparticles requires exceeding an energy threshold. We show that this suppression of damping in the PDW state is due to kinematics. As a result, only one of the two Higgs modes is significantly damped. In addition, motivated by the experimental phase diagram, we discuss the mixing of Higgs modes in the coexistence regime of the PDW and uniform SC states. These results should be observable directly in a Raman spectroscopy, in momentum resolved electron energy loss spectroscopy, and in resonant inelastic X-ray scattering, thus providing evidence of the PDW states.