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<p>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 ± <Emphasis Type="BoldItalic">Q</Emphasis> and a <i>d</i>-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 (<i>d</i>-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 <Emphasis Type="BoldItalic">Q</Emphasis> and −<Emphasis Type="BoldItalic">Q</Emphasis>, whose damping rate is strongly reduced by SC. This sharp mode should be visible in Raman experiments.</p>

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

  • 期刊论文

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  • 发表日期：

    2025年8月1日

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  • Yi-Ming Wu,
  • Andrey V. Chubukov,
  • Yuxuan Wang,
  • Steven A. Kivelson

摘要

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 ± 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.