This review presents a summary and evaluation of the experimental properties of unconventional superconductivity in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ as they were known in the spring of 2002. At the same time, the paper is intended to be useful as an introduction to the physics of spin-triplet superconductivity. First, the authors show how the normal-state properties of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ are quantitatively described in terms of a quasi-two-dimensional Fermi liquid. Then they summarize its phenomenological superconducting parameters in the framework of the Ginzburg-Landau model, and discuss the existing evidence for spin-triplet pairing. After a brief introduction to the vector order parameter, they examine the most likely symmetry of the triplet state. The structure of the superconducting energy gap is discussed, as is the effect of symmetry-breaking magnetic fields on the phase diagram. The article concludes with a discussion of some outstanding issues and desirable future work. Appendixes on additional details of the normal state, difficulty in observing the bulk Fermi surface by angle-resolved photoemission, and the enhancement of superconducting transition temperature in a two-phase ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}\ensuremath{-}\mathrm{Ru}$ system are included.

The superconductivity of Sr 2 RuO 4 and the physics of spin-triplet pairing

Inhomogeneous superconductivity arises when the species participating in the pairing phenomenon have different Fermi surfaces with a large enough separation. In these conditions it could be more favorable for each of the pairing fermions to stay close to its Fermi surface and, unlike the usual BCS state, for the Cooper pair to have a nonzero total momentum. For this reason, in this state the gap varies in space, the ground state is inhomogeneous, and a crystalline structure might be formed. This situation was considered for the first time by Fulde and Ferrell (1964) and Larkin and Ovchinnikov (1964), after whom the corresponding state is called the LOFF state. The spontaneous breaking of the space symmetries in the vacuum state is a characteristic feature of this phase and is associated with the presence of long-wavelength excitations of zero mass. The situation described here is of interest both in solid-state and in elementary-particle physics, in particular in quantum chromodynamics at high density and low temperature. This review presents the theoretical approach to the LOFF state and its phenomenological applications using the language of the effective field theories.

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Inhomogeneous superconductivity in condensed matter and QCD

Intermetallic compounds containing $f$-electron elements display a wealth of superconducting phases, which are prime candidates for unconventional pairing with complex order parameter symmetries. For instance, superconductivity has been found at the border of magnetic order as well as deep within ferromagnetically and antiferromagnetically ordered states, suggesting that magnetism may promote rather than destroy superconductivity. Superconducting phases near valence transitions or in the vicinity of magnetopolar order are candidates for new superconductive pairing interactions such as fluctuations of the conduction electron density or the crystal electric field, respectively. The experimental status of the study of the superconducting phases of $f$-electron compounds is reviewed.

Superconducting phases of f -electron compounds

The Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state is a novel superconducting state in a strong magnetic field characterized by the formation of Cooper pairs with nonzero total momentum ( k ↑,- k + ...

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Fulde–Ferrell–Larkin–Ovchinnikov State in Heavy Fermion Superconductors

This review presents a summary and evaluations of the superconducting properties of the layered ruthenate Sr 2 RuO 4 as they are known in the autumn of 2011. This paper appends the main progress th...

Evaluation of Spin-Triplet Superconductivity in Sr2RuO4

UPd2Al3 is a new heavy-fermion superconductor with a recordTc of 2 K. In addition, it shows a transition to long-range antiferromagnetic order atTN=14 K. Its Sommerfeld coefficient is reduced from γp=210mJ/K2 mole in the paramagnetic to γ0=150mJ/K2 mole in the antiferromagnetic phase.

Heavy-fermion superconductivity atT c =2K in the antiferromagnet UPd2Al3

An elastic neutron scattering study was performed on the new superconducting heavy fermion systems UPd2Al3 and UNi2Al3. The neutron diffraction patterns reveal unambiguously long range antiferromagnetic order in UPd2Al3 with an ordered magnetic momentμ

 U
 = (0.85±0.03)μ

 B
 , which coexists with the superconducting state. This is by far the largestμ

 U
 value observed for any heavy fermion superconductor. For UNi2Al3, no long-range magnetic order could be observed for temperaturesT≧1.5 K, yielding an upper limit of the ordered moment of 0.2μ

 B
 .

Neutron diffraction study of the heavy fermion superconductors UM2Al3 (M=Pd, Ni)

Measurements of the dc susceptibility \ensuremath{\chi}(T), dc magnetization, magnetoresistivity, and magnetostriction are utilized to delineate the magnetic B-T phase diagram of the antiferromagnetically ordered (${\mathit{T}}_{\mathit{N}}$=14 K) heavy-fermion superconductor (${\mathit{T}}_{\mathit{c}}$=2 K) ${\mathrm{UPd}}_{2}$${\mathrm{Al}}_{3}$. The single-crystal data reveal three antiferromagnetic phases for B\ensuremath{\perp}c, but only one for B\ensuremath{\parallel}c. The anisotropic \ensuremath{\chi}(T) in the paramagnetic state suggests a tetravalent configuration of uranium.

Tetravalency and magnetic phase diagram in the heavy-fermion superconductor UPd2Al3.

Both magnetic and superconducting characteristics of the new heavy fermion superconductors (HFS), UNi 2 Al 3 and UPd 2 Al 3 have been investigated extensively by means of 27 Al NMR and NQR. Systematic studies of the nuclear-spin-lattice relaxation time T 1 , the Knight shift and the spectrum of 27 Al have revealed different types of magnetic fluctuations and spin structure between these two compounds. UNi 2 Al 3 shows a band-type itinerant antiferromagnetic behavior, while UPd 2 Al 3 belongs to a heavy fermion antiferromagnet with an ordinary size of U-derived moment. In the superconducting state, the relaxation behavior in UPd 2 Al 3 is similar to those observed in the other HFS reported so far, providing an evidence for an unconventional anisotropic superconductivity with line of gap zeros on the Fermi surface as well. Knight shift has been found to decrease considerably below T c , showing that the pseudo spin is well defined, not affected by the impurity scattering.

NMR and NQR studies of magnetism and superconductivity in the antiferromagnetic heavy fermion superconductors UM2Al3 (M=Ni and Pd)

We report the first measurements of the electrical resistivity, the magnetic susceptibility and the specific heat of the new hexagonal compound CePd 2 Al 3 . The results indicate that CePd 2 Al 3 h is a new heavy fermion system with an electronic specific heat coefficient (γ) of 380 mJ/mol·K 2 and antiferromagnetic ordering below T N =2.8 K.

C. Schank

Papers

Heavy-fermion superconductivity atT c =2K in the antiferromagnet UPd2Al3

Neutron diffraction study of the heavy fermion superconductors UM2Al3 (M=Pd, Ni)

Tetravalency and magnetic phase diagram in the heavy-fermion superconductor UPd2Al3.

NMR and NQR studies of magnetism and superconductivity in the antiferromagnetic heavy fermion superconductors UM2Al3 (M=Ni and Pd)

A New Antiferromagnetic Heavy Fermion Compound: CePd2Al3