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A superconductor is called chiral when its superconducting order parameter has a handed structure, often formed from two components with a relative phase of +i or −i. Choosing one of those signs breaks time-reversal symmetry: reversing time would turn the state into its opposite-handed partner. That is different from conventional BCS superconductivity, which is generally introduced without this extra symmetry breaking. “Unconventional” is the broader category; not every unconventional superconductor is chiral, and chirality does not by itself prove a particular pairing type.
What does “chiral” mean in a superconductor?
The superconducting order parameter describes the paired-electron state, including how its amplitude and phase vary with direction and position. In a familiar proposed chiral form, two components combine as px + ipy or px − ipy. These combinations have opposite handedness. The plus and minus signs are not cosmetic: they distinguish two possible states related by time reversal.
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Time reversal is the operation that reverses the direction of time in the equations, including the directions of motion and magnetic moments. A state that is unchanged by that operation preserves time-reversal symmetry. A chiral state is not unchanged: time reversal maps it to the state of opposite chirality. The two-component structure is essential to this example; a single component alone does not make it chiral.
Chirality describes a symmetry property of the order parameter, not a synonym for “p-wave,” “triplet,” or “topological.” The px ± ipy example is often discussed as odd-parity, spin-triplet pairing, but chiral proposals can also be even-parity. Whether a material has nodes or a fully open energy gap depends on the specific order parameter and material, not on the word “chiral” alone.
How does it compare with conventional superconductivity?
Conventional BCS superconductivity is commonly described using an isotropic, even-parity s-wave order parameter. Unconventional states depart from that standard picture in their pairing symmetry or other properties, and may break additional symmetries. As G. M. Luke and colleagues explain in their 1998 Nature report, additional symmetry breaking can be associated with anisotropic pairing and multiple superconducting phases. But “conventional versus chiral” is not a simple one-to-one division: chirality is one possible feature of an unconventional state.
| Feature | Conventional BCS example | Unconventional, not necessarily chiral | Chiral state |
|---|---|---|---|
| Order parameter | Often introduced as a single-component, isotropic s-wave state. | May have anisotropic pairing, nodes, or more than one superconducting phase. | Has a handed, typically multi-component structure; a familiar proposed form is px ± ipy. |
| Time-reversal symmetry | Generally preserved in the standard example. | May be preserved or broken; unconventional does not automatically mean chiral. | Broken: time reversal maps one chirality to the opposite one. |
| Parity or spin pairing | The standard BCS example is even-parity and spin-singlet. | Can take different forms depending on the material. | Not fixed by chirality alone; chiral states are not all odd-parity or spin-triplet. |
| What identifies it? | Pairing properties and symmetry consistent with the conventional model. | Measurements that constrain the material’s pairing symmetry and gap structure. | Evidence for a handed multi-component state and time-reversal-symmetry breaking, interpreted together with other constraints. |
These are representative categories, not a universal checklist for every material. In particular, anisotropic gaps and nodes are not interchangeable with chirality: they concern how the gap varies across momentum directions, whereas chirality concerns the order parameter’s handedness and symmetry.
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Why is Sr2RuO4 associated with chiral superconductivity?
Strontium ruthenate, Sr2RuO4, became the best-known proposed chiral p-wave superconductor after experiments reported signals interpreted as time-reversal-symmetry breaking. Those signals make the material important to the discussion, but they do not by themselves establish that its order parameter is the classic px ± ipy state.
Evidence for spontaneous internal fields
In 1998, Luke and colleagues used muon spin-relaxation measurements and reported spontaneous internal magnetic fields appearing below Sr2RuO4’s superconducting transition. They interpreted that result as evidence that the superconducting state breaks time-reversal symmetry and, alongside other symmetry considerations, suggested p-wave pairing. The measurement detects internal fields; it does not directly image or identify the order parameter. Read the original Nature report.
Evidence under uniaxial stress
A 2021 muon spin-relaxation study reported that applying uniaxial stress separated the onset of superconductivity from the onset of time-reversal-symmetry breaking. The authors described this split as consistent with qualitative expectations for a chiral order parameter. It is relevant evidence for chirality, not a final identification of the pairing state. See the 2021 Nature Physics paper.
A constraint from NMR
Also in 2021, a field-dependent NMR Knight-shift study, “Evidence for even parity unconventional superconductivity in Sr2RuO4”, argued that purely odd-parity triplet pairing states could be eliminated from consideration. That challenges the classic p-wave, odd-parity triplet proposal. It does not make every possible chiral state impossible, because chirality alone does not require odd parity.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.What is established—and what remains unsettled?
The evidence has not converged on a definitive order-parameter identity for Sr2RuO4. A 2012 review surveyed evidence for p-wave pairing, triplet superconductivity, and broken time-reversal symmetry, while emphasizing discrepancies between experiments and predictions for chiral p-wave pairing; it concluded that the case remained unresolved and alternatives should be considered. A 2017 review likewise addressed the puzzle and conflicting experimental constraints. See the 2012 review record and the 2017 review.
The practical lesson is to separate three claims: a material shows a signal interpreted as time-reversal-symmetry breaking; that signal is consistent with chirality; and the material has a particular chiral p-wave order parameter. The first two can be supported by measurements without proving the third. The cited studies through 2021 constrain the possibilities but leave the classic Sr2RuO4 assignment contested. Proposed consequences such as Majorana modes or quantum-computing applications depend on identifying the actual state and should not be treated as established properties of this material.
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