A pair-density wave (PDW) is a modulation of superconducting pairing; a charge-density wave (CDW) is a modulation of electronic charge density. Both can produce periodic patterns, but they describe different physical quantities—and one signal alone does not establish the other.
How PDWs and CDWs differ
The distinction is the order parameter: what is varying in space. In a PDW, the superconducting pairing field varies. In a CDW, the electronic charge density varies. A periodic image or Fourier peak is not enough to tell which order is present unless the measured quantity is identified.
| Feature | Pair-density wave (PDW) | Charge-density wave (CDW) |
|---|---|---|
| Modulated quantity | Superconducting order parameter: the pairing field associated with Cooper pairs | Electronic charge density |
| Defining character | A superconducting state with spatially varying pairing, commonly described by finite center-of-mass momentum components | A periodic component of charge density at a wavevector, often denoted Q |
| Does it require the other order? | No. It may coexist with uniform superconductivity or CDW order. | No. It may coexist with superconductivity and can also be induced by PDW order. |
| What a measurement must establish | A pair-sensitive observable or evidence tied to the superconducting pairing field; a gap modulation alone does not identify its cause | A charge-sensitive observable; charge modulation alone does not reveal whether the CDW is primary or induced |
These definitions are used in the 2023 Nature study of UTe2, which discusses a unidirectional PDW with pairing components at +P and −P and contrasts it with a charge modulation at Q.
How the two orders can coexist and induce one another
PDW and CDW are distinct, but they are not mutually exclusive. Couplings among uniform superconductivity, PDW order and charge order can produce intertwined patterns. In the simple construction with PDW components at +P and −P, charge modulations can appear at wavevectors related to the PDW, including P and 2P in cases discussed in the UTe2 article. Conversely, when uniform superconductivity and CDW order are present, a PDW can be induced at the CDW wavevector.
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A 2025 theoretical study also describes secondary uniform charge-4e superconducting order and a CDW at 2Q arising with PDW order. Those are results of that paper’s model and treatment; they are not a universal measured relationship or a fixed ratio that applies to every material.
What experiments can—and cannot—show
Interpretation depends on the observable, not merely on whether a pattern looks periodic. The UTe2 study discusses several approaches:
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- Josephson critical-current mapping: a pair-sensitive measurement used to visualize condensed electron-pair density.
- Tunnelling spectra and superconducting-gap maps: used to examine spatial variation of the gap. A gap modulation is not, by itself, proof that the underlying order is a PDW.
- Spatially resolved electronic density of states: used to investigate charge-density order, including periodic features in Fourier analysis. A charge-sensitive signal does not establish whether that charge order is primary or induced.
When assessing a claim, ask what quantity was mapped, which probe measured it, and what alternative origins the authors considered. A CDW signal alone does not prove a primary PDW; evidence for a modulated charge density and evidence for modulated pairing answer different questions.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Why the hierarchy remains unsettled in cuprates
The presence of related signals does not settle which order is fundamental, whether one is induced by another, or how either relates to other forms of order. A 2020 review describes an active debate over whether PDW order is a “mother order” or another competing order in cuprates. A 2024 review likewise says that the origin of CDW order and its relationship to spin order and spatial correlations remain open questions. These conclusions concern cuprates; claims about other materials should be evaluated on their own evidence.
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For broader context, see the 2020 review “The Physics of Pair-Density Waves: Cuprate Superconductors and Beyond”, the 2023 UTe2 study “Detection of a pair density wave state in UTe2”, the 2025 theoretical paper “Anomalous superfluid density in pair-density-wave superconductors”, and the 2024 review “Charge Correlations in Cuprate Superconductors.”
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