science

Fulde–Ferrell–Larkin–Ovchinnikov phase

Fulde–Ferrell–Larkin–Ovchinnikov phase is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Fulde–Ferrell–Larkin–Ovchinnikov phase rather than just read about it. In short: The Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase (also occasionally called the Larkin–Ovchinnikov–Fulde–Ferrell phase, or LOFF) can arise in a superconductor under large magnetic fields. Among its characteristics are Cooper pairs with nonzero total momentum and a spatially non-uniform order parameter, leading to normally conducting areas in the system.

Key takeaways

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Reference excerpt

The Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase (also occasionally called the Larkin–Ovchinnikov–Fulde–Ferrell phase, or LOFF) can arise in a superconductor under large magnetic fields. Among its characteristics are Cooper pairs with nonzero total momentum and a spatially non-uniform order parameter, leading to normally conducting areas in the system.

History Two independent publications in 1964, one by Peter Fulde and Richard A. Ferrell and the other by Anatoly Larkin and Yuri Ovchinnikov, theoretically predicted a new state appearing in a certain regime of superconductors at low temperatures and in high magnetic fields. This particular superconducting state is nowadays known as the Fulde–Ferrell–Larkin–Ovchinnikov state, abbreviated FFLO state (also LOFF state). Since then, experimental observations of the FFLO state have been searched for in different classes of superconducting materials, first in thin films and later in more exotic superconductors such as heavy-fermion and organic superconductors. Good evidence for the existence of the FFLO state was found in organic superconductors using nuclear magnetic resonance (NMR) and studies of heat capacity.

In recent years, the concept of the FFLO state has been used in the field of atomic physics and experiments to detect the state in atomic ensembles in optical lattices. Moreover, there are indicators of the FFLO phase existence in two-component Fermi gases confined in a harmonic potential. These signatures are suppressed neither by phase separation nor by vortex lattice formation.

Theory If a BCS superconductor with a ground state consisting of Cooper pair singlets (and center-of-mass momentum q = 0) is subjected to an applied magnetic field, then the spin structure is not affected until the Zeeman energy is strong enough to flip one spin of the singlet and break the Cooper pair, thus destroying superconductivity (paramagnetic or Pauli pair breaking). If instead one considers the normal, metallic state at the same finite magnetic field, then the Zeeman energy leads to different Fermi surfaces for spin-up and spin-down electrons, which can lead to superconducting pairing where Cooper pair singlets are formed with a finite center-of-mass momentum q, corresponding to the displacement of the two Fermi surfaces. A non-vanishing pairing momentum leads to a spatially modulated order parameter with wave vector q.

Experiment For the FFLO phase to appear, it is required that Pauli paramagnetic pair-breaking is the relevant mechanism to suppress superconductivity (Pauli limiting field, also Chandrasekhar-Clogston limit). In particular, orbital pair breaking (when the vortices induced by the magnetic field overlap in space) has to be weaker, which is not the case for most conventional superconductors. Certain unusual superconductors, on the other hand, may favor Pauli pair breaking: materials with large effective electron mass or layered materials (with quasi-two-dimensional electrical conduction).

Heavy-fermion superconductors Heavy-fermion superconductivity is caused by electrons with a drastically enhanced effective mass (the heavy fermions, also heavy quasiparticles), which suppresses orbital pair breaking. Furthermore, certain heavy-fermion superconductors, such as CeCoIn5, have a layered crystal structure, with somewhat two-dimensional electronic transport properties. Indeed, in CeCoIn5 there is thermodynamic evidence for the existence of an unconventional low temperature phase within the superconducting state. Subsequently, neutron diffraction experiments showed that this phase also exhibits incommensurate antiferromagnetic order and that the superconducting and magnetic ordering phenomena are coupled to one another.

Organic superconductors Most organic superconductors are strongly anisotropic, in particular there are charge-transfer salts based on the molecule BEDT-TTF (or ET, "bisethylendithiotetrathiofulvalene") or BEDT-TSF (or BETS, "bisethylendithiotetraselenafulvalene") that are highly two-dimensional. In one plane, the electric conductivity is high compared to a direction perpendicular to the plane. When applying large magnetic fields exactly parallel to the conducting planes, penetration depth demonstrates and specific heat confirms the existence of the FFLO state. This finding was corroborated by NMR data that proved the existence of an inhomogeneous superconducting state, most probably the FFLO state.

References

Worked examples

Example 1 — a first encounter with Fulde–Ferrell–Larkin–Ovchinnikov phase

Start with the simplest possible case. Write down what Fulde–Ferrell–Larkin–Ovchinnikov phase claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Fulde–Ferrell–Larkin–Ovchinnikov phase before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Fulde–Ferrell–Larkin–Ovchinnikov phase ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Fulde–Ferrell–Larkin–Ovchinnikov phase

In research: Fulde–Ferrell–Larkin–Ovchinnikov phase appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Fulde–Ferrell–Larkin–Ovchinnikov phase in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Fulde–Ferrell–Larkin–Ovchinnikov phase is common in secondary-school and first-year university syllabi. It links to neighbouring topics Superconductivity, so understanding it makes those chapters shorter.
In everyday life: Look for Fulde–Ferrell–Larkin–Ovchinnikov phase outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Fulde–Ferrell–Larkin–Ovchinnikov phase in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Fulde–Ferrell–Larkin–Ovchinnikov phase means in your own words.
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Work through the three examples above with pen and paper.
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Frequently asked questions

What is Fulde–Ferrell–Larkin–Ovchinnikov phase in simple terms?

Why does Fulde–Ferrell–Larkin–Ovchinnikov phase matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Fulde–Ferrell–Larkin–Ovchinnikov phase?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Fulde–Ferrell–Larkin–Ovchinnikov phase.