Recent developments in unconventional superconductivity theory

The review of recent developments in the unconventional superconductivity theory is given. In the fist part I consider the physical origin of the Kerr rotation polarization of light reflected from the surface of superconducting $Sr_2RuO_4$. Then the comparison of magneto-optical responses in superconductors with orbital and spin spontaneous magnetization is presented. The latter result is applied to the estimation of the magneto-optical properties of neutral superfluids with spontaneous magnetization. The second part is devoted to the natural optical activity or gyrotropy properties of noncentrosymmetric metals in their normal and superconducting states. The temperature behavior of the gyrotropy coefficient is compared with the temperature behavior of paramagnetic susceptibility determining the noticeable increase of the paramagnetic limiting field in noncentrosymmetric superconductors. In the last chapter I describe the order parameter and the symmetry of superconducting state in the itinerant ferromagnet with orthorhombic symmetry. Finally the Josephson coupling between two adjacent ferromagnet superconducting domains is discussed.Comment: 15 page

Half-quantum vortices

Unlike to superfluid ⁴He the superfluid ³He-A support the existence of vortices with half-quantum of circulation as well as single quantum vortices. The singular single quanta vortices as well as nonsingular vortices with 2 quanta of circulation have been revealed in rotating ³He-A. However, the half-quantum vortices in open geom-etry always possess an extra energy due to spin-orbit coupling leading to formation of domain wall at distances larger than dipole length ∼10⁻³ cm from the vortex axis. Fortunately the same magnetic dipole–dipole interaction does not prevent the existence of half-quantum vortices in the polar phase of superfluid ³He recently discovered in peculiar porous media “nematically ordered” aerogel. Here we discuss this exotic possibility. The discoveries of half-quantum vortices in triplet pairing superconductor Sr₂RuO₄ as well in the exciton–polariton condensates are the other parts of the story about half-quantum vortices also described in the paper

Magnetoelectric effect and the upper critical field in superconductors without inversion center

Solving the Ginzburg–Landau equation we demonstrate that the paramagnetic limiting of superconducting state in the superconductors without space inversion symmetry is significantly weakened. It is caused by so called magnetoelectric mechanism proving to be effective or not depending of the magnetic field direction and the crystal symmetry

Antiferromagnetic order in CeCoIn₅ oriented by spin-orbital coupling

An incommensurate spin-density wave ( Q phase) confined inside the superconducting state at high basal plane magnetic field is an unique property of the heavy-fermion metal CeCoIn₅. The neutron scattering experiments and the theoretical studies point out that this state come out from the soft mode condensation of magnetic resonance excitations. We show that the fixation of direction of antiferromagnetic modulations by a magnetic field reported by Gerber et al. [Nat. Phys. 10, 126 (2014)], is explained by spin-orbit coupling. This result, obtained on the basis of quite general phenomenological arguments, is supported by the microscopic derivation of the χzz susceptibility dependence on the mutual orientation of the basal plane magnetic field and the direction of modulation of spin polarization in a multiband metal

On the theory of superconductivity in ferromagnetic superconductors with triplet pairing

We point out that ferromagnetic superconductors with triplet pairing and strong spin-orbit coupling are even in the simplest case at least two-band superconductors. The Gor'kov type formalism for such superconductors is developed and the Ginzburg-Landau equations are derived. The dependence of the critical temperature on the concentration of ordinary point-like impurities is found. Its nonuniversality could serve as a qualitative measure of the two-band character of ferromagnetic superconductors. The problem of the upper critical field determination is also discussed.Comment: 8 pages, no figure; important changes with respect to the previous versions due to the correction of a mistake: in this new version, a more general form is considered for the order parameter (the two-components of the order parameter were considered before as equal, which is in general not true) ; submitted to Physical Review

Giant Quantum Oscillations of the Longitudinal Magnetoresistance in Quasi two-dimensional Metals

We have investigated in frame of the quantum transport theory the magnetic quantum oscillations of the longitudinal magnetoresistance $\rho_{zz}$ in quasi two-dimensional metals for a magnetic field perpendicular to the layers. Giant Shubnikov-de Haas oscillations are found when the cyclotron energy $\hbar \omega_{c}$ is much larger than the interlayer transfer integral $t$ (the two-dimensional limit). In large magnetic fields and at low temperatures, the minima of the magnetoconductivity $\sigma_{zz}=\rho_{zz}^{-1}$ exhibit a thermally activated behavior in presence of negligibly small chemical potential oscillations, as observed in the organic layered conductor \beta''\mathrm{-(BEDT-TTF)}_{2}\mathrm{SF}_{5}\mathrm{CH}_{2}\mathrm{CF}_{2}\m athrm{SO}_{3}. The questions concerning the absence of strong chemical potential oscillations in such compound and the impurity self-energy are discussed.Comment: 4 pages, intended for publication in special issue of Physica B for RHMF 2003 Conference, Toulous

Polarization Effects in Superfluid 4^4He

A theory of thermoelectric phenomena in superfluid $^4He$ is developed. It is found an estimation of the dipole moment of helium atom arising due to electron shell deformation caused by pushing forces from the side of its surrounding atoms. The corresponding electric signal generated in a liquid consisting of electrically neutral atoms by the ordinary sound waves is found extremely small. The second sound waves in superfluid $^4He$ generate the polarization of liquid induced by the relative accelerated motion of the superfluid and the normal component. The derived ratio of the amplitudes of temperature and electric polarization potential was proved to be practically temperature independent. Its magnitude is in reasonable correspondence with the experimental observations. The polarity of electric signal is determined by the sign of temperature gradient in accordance with the measurements. The problem of the roton excitations dipole moment is also discussed.Comment: 8 pages, no figure

Mixed-parity superconductivity in centrosymmetric crystals

A weak-coupling formalism for superconducting states possessing both singlet (even parity) and triplet (odd parity) components of the order parameter in centrosymmetric crystals is developed. It is shown that the quasiparticle energy spectrum may be non-degenerate even if the triplet component is unitary. The superconducting gap of a mixed-parity state may have line nodes in the strong spin-orbit coupling limit. The pseudospin carried by the superconducting electrons is calculated, from which follows a prediction of a kink anomaly in the temperature dependence of muon spin relaxation rate. The anomaly occurs at the phase boundary between the bare triplet and mixed-parity states. The stability of mixed-parity states is discussed within Ginzburg-Landau theory. The results may have immediate application to the superconducting series Pr(Os,Ru)4Sb12.Comment: 5 pages, 2 figures. Final version accepted to PR

Possible symmetries of the superconducting order parameter in a hexagonal ferromagnet

We study the order parameter symmetry in a hexagonal crystal with co-existing superconductivity and ferromagnetism. An experimental example is provided by carbon-based materials, such as graphite-sulfur composites, in which an evidence of such co-existence has been recently discovered. The presence of a non-zero magnetization in the normal phase brings about considerable changes in the symmetry classification of superconducting states, compared to the non-magnetic case.Comment: 4 pages, REVTe

Impurity Effects on the A_1-A_2 Splitting of Superfluid 3He in Aerogel

When liquid 3He is impregnated into silica aerogel a solid-like layer of 3He atoms coats the silica structure. The surface 3He is in fast exchange with the liquid on NMR timescales. The exchange coupling of liquid 3He quasiparticles with the localized 3He spins modifies the scattering of 3He quasiparticles by the aerogel structure. In a magnetic field the polarization of the solid spins gives rise to a splitting of the scattering cross-section of for `up' vs. `down' spin quasiparticles, relative to the polarization of the solid 3He. We discuss this effect, as well as the effects of non-magnetic scattering, in the context of a possible splitting of the superfluid transition for $\uparrow\uparrow$ vs. $\downarrow\downarrow$ Cooper pairs for superfluid 3He in aerogel, analogous to the A_1-A_2 splitting in bulk 3He. Comparison with the existing measurements of T_c for B< 5 kG, which show no evidence of an A_1-A_2 splitting, suggests a liquid-solid exchange coupling of order J = 0.1 mK. Measurements at higher fields, B > 20 kG, should saturate the polarization of the solid 3He and reveal the A_1-A_2 splitting.Comment: 7 pages, 3 figure