The Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase (also occasionally called the Larkin–Ovchinnikov–Fulde–Ferrell phase, or LOFF) can arise in a
superconductor in large magnetic field. Among its characteristics are
Cooper pair
In condensed matter physics, a Cooper pair or BCS pair (Bardeen–Cooper–Schrieffer pair) is a pair of electrons (or other fermions) 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
In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...
, leading to normal conducting areas in the superconductor.
History
Two independent publications in 1964, one by
Peter Fulde
Peter Fulde (born 6 April 1936 in Breslau, now Wroclaw) is a physicist working in condensed matter theory and quantum chemistry.
Fulde received a PhD degree at the University of Maryland in 1963. After spending more than one year as a postdo ...
and
Richard A. Ferrell
and the other by
Anatoly Larkin
Anatoly Ivanovich Larkin (russian: Анатолий Иванович Ларкин; October 14, 1932 – August 4, 2005) was a Russian theoretical physicist, universally recognised as a leader in theory of condensed matter, and who was also a cele ...
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 exotic superconductors such as
heavy-fermion
and
organic
Organic may refer to:
* Organic, of or relating to an organism, a living entity
* Organic, of or relating to an anatomical organ
Chemistry
* Organic matter, matter that has come from a once-living organism, is capable of decay or is the product ...
[H. Shimahara: Theory of the Fulde-Ferrell-Larkin-Ovchinnikov State and Application to Quasi-Low-Dimensional Organic Superconductors, in: A.G. Lebed (ed.): The Physics of Organic Superconductors and Conductors, Springer, Berlin (2008).] superconductors. Good evidence for the existence of the FFLO state was found in organic superconductors using Nuclear Magnetic Resonance (NMR) and heat capacity.
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. 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
Phase separation is the creation of two distinct phases from a single homogeneous mixture. The most common type of phase separation is between two immiscible liquids, such as oil and water. Colloids are formed by phase separation, though n ...
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 surface In condensed matter physics, the Fermi surface is the surface in reciprocal space which separates occupied from unoccupied electron states at zero temperature. The shape of the Fermi surface is derived from the periodicity and symmetry of the cryst ...
s 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
In fluid dynamics, a vortex ( : vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in th ...
induced by the magnetic field overlap in space) has to be weaker, which is not the case for most conventional superconductors. Certain unusual
superconductors
Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
, on the other hand, may favor Pauli pair breaking: materials with large
effective electron mass
In solid state physics, a particle's effective mass (often denoted m^*) is the mass that it ''seems'' to have when responding to forces, or the mass that it seems to have when interacting with other identical particles in a thermal distribution ...
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 fermion
In solid-state physics, heavy fermion materials are a specific type of intermetallic compound, containing elements with 4f or 5f electrons in unfilled electron bands. Electrons are one type of fermion, and when they are found in such materials, th ...
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.
Indeed, in
CeCoIn5 there is thermodynamic evidence for the existence of an unconventional low temperature phase within the superconducting state. Subsequently, the neutron-diffraction experiments showed that this phase exhibits also incommensurate anti-ferromagnetic order and that the superconducting and magnetic ordering phenomena are coupled with each other.
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
Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with ...
data that proved the existence of an inhomogeneous superconducting state, most probable the FFLO state.
References
{{DEFAULTSORT:Fulde-Ferrell-Larkin-Ovchinnikov phase
Superconductivity