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The defining difference is the momentum carried by the Cooper pairs. In the conventional Bardeen–Cooper–Schrieffer (BCS) reference case, pairs have zero center-of-mass momentum and the superconducting order is uniform in space. In a pair-density wave (PDW), pairs have finite center-of-mass momentum, producing a superconducting order parameter that varies periodically across the material.
What does finite-momentum pairing mean?
A Cooper pair has a total, or center-of-mass, momentum. In the conventional BCS reference state, that momentum is zero: the superconducting order parameter has no built-in spatial modulation. In a PDW, the pairs carry finite momentum, so the condensate’s order parameter repeats in space.
For a simple unidirectional PDW, the order parameter can be represented as Δ(r) proportional to cos(Q·r). The vector Q is the modulation wavevector: its direction sets the modulation direction, and its magnitude sets the spatial period. The modulation is in the superconducting pair condensate itself, not merely in the density of individual electrons.
How do PDW and conventional superconductivity compare?
| Feature | Conventional BCS reference | Pair-density wave |
|---|---|---|
| Pair center-of-mass momentum | Zero | Finite |
| Superconducting order in real space | Uniform | Spatially modulated |
| What defines the state | Zero-momentum pairing and a spatially uniform order parameter | Finite-momentum pairing and a periodically varying order parameter |
| Relation to charge order | No modulation is required by the reference state | May coexist with or induce charge-density-wave or other order |
This is a comparison of defining features, not a claim that every material in either category has the same microscopic mechanism or gap symmetry. In particular, the distinction between uniform and modulated order is separate from whether the superconducting gap has s-wave or d-wave symmetry.
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Is a pair-density wave the same as a charge-density wave?
No. A charge-density wave (CDW) is a spatial modulation of electronic charge density. A PDW is a spatial modulation of superconducting order because the Cooper pairs have finite momentum. PDW order can be intertwined with, coexist with, or induce charge order, but a charge modulation by itself does not establish finite-momentum superconducting pairing.
Is a PDW the same as an FFLO state?
They share a central feature: both involve finite-momentum pairing and spatially nonuniform superconducting order. The terms are related, but they are not interchangeable in every context. The 2020 Annual Review of Condensed Matter Physics review treats FFLO states as weak-coupling examples within the broader discussion of PDW physics. Classic FFLO proposals involve conditions including high magnetic field and low temperature, while PDW can refer to a wider range of mechanisms and states.
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Terminology also depends on the specific state. A 2026 theoretical paper distinguishes a unidirectional PDW from a Fulde–Ferrell state associated with magnetic field and broken time-reversal symmetry. For a particular material, the useful questions are what produces the finite pair momentum, what symmetries are present, and how the authors define the state—not simply whether it is called PDW or FFLO.
What evidence has been reported?
The experimental picture is material-specific, and the status of PDW order remains an active question. A 2020 review discusses growing evidence in cuprate superconductors as well as debate over the microscopic picture and whether PDW order is a primary, or “mother,” order or a competing one. That review is useful context, not proof that the debates have been resolved.
In 2023, a Nature Physics report on centrosymmetric bilayer MoS2 presented evidence for finite-momentum pairing under its experimental conditions. The authors reported that the state occurred below the Pauli limit, was driven by the orbital effect, and did not rely on Fermi-surface segmentation. This is evidence for that system and its reported conditions; it does not make every finite-momentum state in other materials an identical FFLO or PDW state.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.What can superfluid-density measurements tell us?
A 2026 study in npj Quantum Materials analyzes a generic two-dimensional, unidirectional PDW model. The theoretical work finds an extensive parameter region with negative calculated superfluid density. In the model’s stable regime, it predicts a small longitudinal response, strong anisotropy, and unusual temperature dependence, including a transverse response proportional to T² at low temperature.
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These are model-dependent predictions and possible diagnostics, not universal measured properties of PDW materials. The study’s emphasis on stability is important: the existence of a modulated pairing solution in a model does not by itself show that it is stable or realized in a particular superconductor.
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