Fulde-Ferrell-Larkin-Ovchinnikov phase
Encyclopedia
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase can arise in a superconductor
in large magnetic field. Among its characteristics are Cooper pair
s with nonzero total momentum and a spatially non-uniform order parameter.
and the other by Anatoly Larkin and Yuri Ovchinnikov,
theoretically predicted a new state in a certain regime of superconductors 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 observation of the FFLO state has been searched for in different classes of superconducting materials, first in thin films and later in exotic superconductors such as heavy-fermion
and organic
superconductors,
but so far there is no undisputed experimental evidence. In recent years, the concept of the FFLO state was taken up in the field of atomic physics and experiments to detect the FFLO state in atomic ensembles in optical lattices.
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 surface
s for spin-up and spin-down electrons, which can lead to superconducting pairing where Cooper pair singlets are formed with a center-of-mass momentum q which is finite, corresponding to the displacement of the two Fermi surfaces.
The non-vanishing q of the Cooper pairs leads to a spatially modulated order parameter (periodic with wave vector q).
induced by the magnetic field overlap in space) has to be weaker, which is not the case for conventional superconductors. Certain unconventional superconductor
s, on the other hand, may favor Pauli pair breaking: materials with large effective electron mass or layered materials (with quasi-two-dimensional electrical conduction).
is caused by electrons with a drastically enhanced effective mass (the heavy fermion
s, 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. Therefore, detailed studies close to the critical field have been performed on CeCoIn5, and there is evidence that certain regimes in the phase diagram of this material should be interpreted in terms of the FFLO state.
s have very anisotropic conductivity; in particular there are compounds which are good realizations of quasi-two-dimensional electronic transport. Also here there are candidate materials for the FFLO phase, and for the organic superconductors of the κ-(ET)2X and λ(BETS)2X there is experimental data indicating an FFLO region in the phase diagram of these materials.
Superconductivity
Superconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...
in large magnetic field. Among its characteristics are Cooper pair
Cooper pair
In condensed matter physics, a Cooper pair or BCS pair is two electrons that are bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper...
s with nonzero total momentum and a spatially non-uniform order parameter.
History
Two independent publications in the year 1964, one by Peter Fulde and Richard A. Ferrelland the other by Anatoly Larkin and Yuri Ovchinnikov,
theoretically predicted a new state in a certain regime of superconductors 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 observation of the FFLO state has been searched for in different classes of superconducting materials, first in thin films and later in exotic superconductors such as heavy-fermion
Heavy fermion superconductor
Heavy fermion superconductors are a type of Unconventional superconductor.The first heavy fermion superconductor, CeCu2Si2, was discovered by Frank Steglich in 1978....
and organic
Organic superconductor
In physical chemistry and condensed matter physics, an organic superconductor is an organic compound which exhibits superconductivity at low temperatures...
superconductors,
but so far there is no undisputed experimental evidence. In recent years, the concept of the FFLO state was taken up in the field of atomic physics and experiments to detect the FFLO state in atomic ensembles in optical lattices.
Theory
If a BCSBCS theory
BCS theory — proposed by Bardeen, Cooper, and Schrieffer in 1957 — is the first microscopic theory of superconductivity since its discovery in 1911. The theory describes superconductivity as a microscopic effect caused by a "condensation" of pairs of electrons into a boson-like state...
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
Zeeman effect
The Zeeman effect is the splitting of a spectral line into several components in the presence of a static magnetic field. It is analogous to the Stark effect, the splitting of a spectral line into several components in the presence of an electric field...
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 surface
Fermi surface
In condensed matter physics, the Fermi surface is an abstract boundary useful for predicting the thermal, electrical, magnetic, and optical properties of metals, semimetals, and doped semiconductors. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline...
s for spin-up and spin-down electrons, which can lead to superconducting pairing where Cooper pair singlets are formed with a center-of-mass momentum q which is finite, corresponding to the displacement of the two Fermi surfaces.
The non-vanishing q of the Cooper pairs leads to a spatially modulated order parameter (periodic with wave vector q).
Experiment
For the FFLO phase to appear, it is required that Pauli pair breaking is the relevant mechanism to suppress superconductivity (Pauli limiting field, also Chandrasekhar-Clogston limit). In particular, orbital pair breaking (when the vorticesAbrikosov vortex
In superconductivity, an Abrikosov vortex is a vortex of supercurrent in a type-II superconductor. The supercurrent circulates around the normal core of the vortex. The core has a size \sim\xi — the superconducting coherence length...
induced by the magnetic field overlap in space) has to be weaker, which is not the case for conventional superconductors. Certain unconventional superconductor
Unconventional superconductor
Unconventional superconductors are materials that display superconductivity which does not conform to either the conventional BCS theory or the Nikolay Bogolyubov's theory or its extensions....
s, 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 superconductivityHeavy fermion superconductor
Heavy fermion superconductors are a type of Unconventional superconductor.The first heavy fermion superconductor, CeCu2Si2, was discovered by Frank Steglich in 1978....
is caused by electrons with a drastically enhanced effective mass (the heavy fermion
Heavy Fermion
In solid-state physics, heavy fermion materials are a specific type of intermetallic compound, containing elements with 4f or 5f electrons. Electrons, a kind of fermion, found in such materials are sometimes referred to as heavy electrons...
s, 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. Therefore, detailed studies close to the critical field have been performed on CeCoIn5, and there is evidence that certain regimes in the phase diagram of this material should be interpreted in terms of the FFLO state.
Organic superconductors
Some organic superconductorOrganic superconductor
In physical chemistry and condensed matter physics, an organic superconductor is an organic compound which exhibits superconductivity at low temperatures...
s have very anisotropic conductivity; in particular there are compounds which are good realizations of quasi-two-dimensional electronic transport. Also here there are candidate materials for the FFLO phase, and for the organic superconductors of the κ-(ET)2X and λ(BETS)2X there is experimental data indicating an FFLO region in the phase diagram of these materials.