A pair-density wave (PDW) is a superconducting state in which the pairing field varies across space; a charge-density wave (CDW) is a periodic variation in electronic charge density. The difference is what is modulated—not simply whether an experiment detects a repeating pattern.
How a PDW differs from a CDW
| Comparison | Pair-density wave (PDW) | Charge-density wave (CDW) |
|---|---|---|
| Modulated quantity | The superconducting pairing order parameter: the field describing Cooper-pair formation. | Electronic charge density. |
| Physical meaning | A superconducting state with a spatially varying pairing field, commonly described by finite-momentum pairing components. | A charge-order state with a periodic density component at a wavevector, often denoted Q. |
| What a measured pattern establishes | It depends on the observable. Pair-sensitive measurements can support a PDW interpretation; a gap modulation alone does not automatically establish modulated pairing. | A charge-sensitive pattern can establish a charge modulation, but not whether that modulation is primary or induced by another order. |
| Relationship to the other order | Can coexist with uniform superconductivity and CDW order, and can be associated with induced charge modulations. | Can coexist with superconductivity and may be induced by PDW order. |
A conventional superconductor has a spatially uniform order parameter. In a unidirectional PDW example, the pairing field includes finite-momentum components at +P and −P. A unidirectional CDW instead has a periodic charge-density component at Q. These definitions distinguish the orders even when their experimental signatures appear related. (Nature, 2023)
How the two orders can be connected
PDW and CDW are distinct but not mutually exclusive. Coupling between orders can make one accompany or induce the other. In the cases discussed in the UTe2 study, a PDW together with uniform superconductivity can generate charge modulations at wavevectors associated with the PDW, including P and 2P. Conversely, uniform superconductivity together with a CDW can induce modulated pairing at the CDW wavevector. The precise relationship depends on the state and model; it is not a rule that every observed CDW must come from a PDW.
A 2025 theoretical study likewise describes a PDW producing secondary uniform charge-4e superconducting order and a CDW at 2Q. Those are model-specific secondary correlations, not a universal measured ratio or a general experimental finding. (npj Quantum Materials, 2025)
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What experiments can—and cannot—show
A repeating signal by itself does not identify which order parameter is responsible. The interpretation depends on what a probe measures and how the signal is connected to the proposed order.
- Pair-sensitive measurements: The UTe2 study discusses Josephson critical-current mapping as a way to visualize condensed electron-pair density. Such a measurement is more directly relevant to pairing than a charge-sensitive map.
- Gap maps: Tunnelling spectra and spatial maps of the superconducting gap can reveal gap structure or modulation. A varying gap is not, on its own, proof that the pairing order parameter forms a PDW.
- Charge-sensitive measurements: Spatially resolved electronic density of states and Fourier peaks can reveal periodic charge-related structure. That signal establishes a modulation, not its microscopic cause or whether it is the primary order.
When evaluating a claim, ask which quantity was mapped, which probe produced the signal, and whether the evidence distinguishes primary order from an induced modulation. The Nature paper discusses these definitions and measurement approaches in its UTe2 context; that material-specific discussion should not be treated as a universal measurement prescription. (Nature, 2023)
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Why the hierarchy remains unsettled in cuprates
In cuprate superconductors, researchers continue to debate whether PDW order is a fundamental “mother” order or another competing order. The status of CDW order is also not settled: a 2024 review describes open questions about its origin and its relationship to spin order and spatial correlations. These are material-specific questions about which order is primary and how different orders interact—not a reason to treat PDW and CDW as synonyms. (Annual Review of Condensed Matter Physics, 2020; Annual Review of Condensed Matter Physics, 2024)
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