Time-reversal symmetry breaking, collective modes, and Raman spectrum in pair-density-wave states

TL;DR

This paper explores the collective amplitude modes in pair-density-wave states, especially how coexisting superconductivity affects these modes and their potential detection via Raman spectroscopy.

Contribution

It introduces the concept of a PDW/SC phase that breaks time-reversal symmetry and identifies a sharp Higgs mode observable in Raman experiments.

Findings

Pure PDW state has two overdamped Higgs modes.

PDW/SC phase exhibits three Higgs modes, including a sharp, Raman-visible mode.

SC reduces damping of the sharp Higgs mode, making it experimentally detectable.

Abstract

Inspired by empirical evidence of the existence of pair-density-wave (PDW) order in certain underdoped cuprates, we investigate the collective modes in systems with unidirectional PDW order with momenta $\pm {Q}$ and a $d$-wave form-factor with special focus on the amplitude (Higgs) modes. In the pure PDW state, there are two overdamped Higgs modes. We show that a phase with co-existing PDW and uniform ($d$-wave) superconducting (SC) order, PDW/SC, spontaneously breaks time-reversal symmetry - and thus is distinct from a simpler phase, SC/CDW, with coexisting SC and charge-density-wave (CDW) order. The PDW/SC phase exhibits three Higgs modes, one of which is sharply peaked and is predominantly a PDW fluctuation, symmetric between ${Q}$ and -${Q}$, whose damping rate is strongly reduced by SC. This sharp mode should be visible in Raman experiments.