Pairing In Superconductors Research Articles

Competition between superconducting pair potential and Rashba spin–orbit interaction in a hybrid mesoscopic ring

We numerically investigate an isolated hybrid ring consisting of two segments, one is an s-wave superconductor and the other is two dimensional electron gas with Rashba spin–orbit interaction. Considering an Aharonov–Bohm flux through the hole of the ring, we calculate the elementary excitation spectrum and the persistent current at zero temperature and finite temperature. It is found that there is a competition between superconducting pair potential and Rashba spin–orbit interaction. At zero temperature the competition is mainly determined by the length of the superconducting segment d S . When the superconducting segment is short, quasi-particles is easy to tunnel through the superconducting segment and Rashba spin–orbit interaction effect is dominant which results in the elementary excitation spectrum splits and the persistent current obtains an additional peak. On the contrary, when the superconducting segment is long enough, the quasi-particles are difficult to tunnel through the superconducting segment and they enter the superconducting segment via Andreev reflection process. In this case Rashba spin–orbit interaction does not cause the split of the elementary excitation spectrum inside the energy gap, and thus the persistent current has no additional peak. At finite temperature, when the superconducting segment is short, although the spin split effect still exists, the peak of the persistent current resulting from Rashba spin–orbit interaction gradually disappears as the temperature rises.

Superconducting phases off-electron compounds

Intermetallic compounds containing f-electron elements display a wealth of superconducting phases, that 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 ferro- and antiferromagnetically ordered states, suggesting that magnetism may promote rather than destroy superconductivity. Superconductivity near valence transitions, or in the vicinity of magneto-polar 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.

Antiferromagnetic Order and π-Triplet Pairing in the Fulde–Ferrell–Larkin–Ovchinnikov State

The antiferromagnetic Fulde-Ferrell-Larkin-Ovchinnikov (AFM-FFLO) state of coexisting d-wave FFLO superconductivity and incommensurate AFM order is studied on the basis of Bogoliubov-de Gennes (BdG) equations. We show that the incommensurate AFM order is stabilized in the FFLO state by the appearance of the Andreev bound state localized around the zeros of the FFLO order parameter. The AFM-FFLO state is further enhanced by the induced \pi-triplet superconductivity (pair density wave). The AFM order occurs in the FFLO state even when it is neither stable in the normal state nor in the BCS state. The order parameters of the AFM order, d-wave superconductivity, and \pi-triplet pairing are investigated by focusing on their spatial structures. Roles of the spin fluctuations beyond the BdG equations are discussed. Their relevance to the high-field superconducting phase of CeCoIn_5 is discussed.

Vortex states in iron-based superconductors with collinear antiferromagnetic cores

Magnetism in the FeAs stoichiometric compounds and its interplay with superconductivity in vortex states are studied by self-consistently solving the Bogoliubov-de Gennes equations based on a two-orbital model with including the on-site interactions between electrons in the two orbitals. It is revealed that for the parent compound, magnetism is caused by the strong Hund's coupling, and the Fermi-surface topology aids to select the spin-density-wave (SDW) pattern. The superconducting (SC) order parameter with ${s}_{\ifmmode\pm\else\textpm\fi{}}={\ensuremath{\Delta}}_{0}\text{ }\text{cos}({k}_{x})\text{cos}({k}_{y})$ symmetry is found to be the most favorable pairing for both the electron- and hole-doped cases while the local density of states exhibits the characteristic of nodal gap for the former and full gap for the latter. In the vortex state, the emergence of the field-induced SDW depends on the strength of the Hund's coupling and the Coulomb repulsions. The field-induced SDW gaps the finite-energy contours on the electron- and hole-pocket sides, leading to the dual structures with one reflecting the SC pairing and the other being related to the SDW order. These features can be discernable in STM measurements for identifying the interplay between the field-induced SDW order and the SC order around the core region.

Evolution of superconductor pairing interactions from weak to strong coupling on a honeycomb lattice

We study the evolution of the pairing from weak to strong coupling on a honeycomb lattice by Quantum Monte Carlo. We show numerical evidence of the BCS-BEC crossover as the coupling strength increases on a honeycomb lattice with small fermi surface by measuring a wide range of observables: double occupancy, spin susceptibility, local pair correlation, and kinetic energy. Although at low energy, the model sustains Dirac fermions, we do not find significant qualitative difference in the BCS-BEC crossover as compared to those with an extended Fermi surface, except at weak coupling, BCS regime.

Nonequilibrium Dynamics of Weakly and Strongly Paired Superconductors

We study small oscillations of the order parameter in weakly and strongly paired superconductors driven slightly out of equilibrium, in the collisionless approximation. While it was known for quite some time that the amplitude of the oscillations in a weakly paired superconductor decays as t(-1/2), we show that in a superconductor sufficiently strongly paired so that its fermions form bound states usually referred to as molecules, these oscillations decay as t(-3/2). The transition between these two regimes happens when the chemical potential of the superconductor vanishes; thus, the behavior of the oscillations can be used to distinguish weakly and strongly paired superconductors. Finally, we interpret the result in the strongly paired superconductor as the probability of the molecular decay as a function of time.

Unconventional superconductivity pairing induced by antiferromagnetic spin fluctuations in layered organic superconductors

Abstract The unconventional character of the superconductivity in organic compounds κ - ( ET ) 2 X is ascribed to an antiferromagnetic spin fluctuation induced pairing. Since the band structure involves two bands ( ± ), we assume that the large amplitude spin fluctuations arise from the band with the best nesting properties (band + ), while superconductivity pairing occurs in the other band ( - ) . We show that the nesting properties may mimic either a chemical pressure (deuterization) or a hydrostatic one. Indeed, a change of the nesting ratio t 1 / t 2 , according to our model, induces a modification of the Fermi surface topology. The spin fluctuations strength in the system is affected and consequently the calculated effective coupling constant of superconductivity for the even-parity singlet pairing channel. Our theory appears to be qualitatively consistent with major experimental reports.

The Fulde–Ferrell–Larkin–Ovchinnikov phase in the presence of pair hoppinginteraction

The recent experimental support for the presence of the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO)phase in CeCoIn5 directed attention towards the mechanisms responsible for this type of superconductivity.We investigate the FFLO state in a model where on-site/inter-site pairingcoexists with the repulsive pair hopping interaction. The latter interactionis interesting in that it leads to pairing with non-zero momentum of theCooper pairs even in the absence of the external magnetic field (the so-calledη pairing). It turns out that, depending on the strength of the pair hopping interaction, themagnetic field can induce one of two types of the FFLO phase with different spatialmodulations of the order parameter. It is argued that the properties of the FFLO phase maygive information about the magnitude of the pair hopping interaction. We also show thatη pairing and d-wave superconductivity may coexist in the FFLO state. It holds true also forsuperconductors which, in the absence of magnetic field, are of pure d-wave type.

Colloquium: Modeling the unconventional superconducting properties of expandedA3C60fullerides

The trivalent alkali fulleride solids of generic composition ${A}_{3}{\mathrm{C}}_{60}$, where ${\mathrm{C}}_{60}$ is the fullerene molecule and $A=\mathrm{K}$, Rb, and Cs, are a well-established family of molecular superconductors. The superconductive electron pairing is of regular $s$-wave symmetry and is accounted for by conventional coupling of electrons to phonons, in particular by well-understood Jahn-Teller intramolecular ${\mathrm{C}}_{60}$ vibrations. A source of renewed interest in these systems is the surprising indication of strong electron-electron repulsion phenomena, which has emerged in compounds where the ${\mathrm{C}}_{60}\text{\ensuremath{-}}{\mathrm{C}}_{60}$ distance is expanded, by either a large cation size or other chemical or physical means. Several examples are now known where this kind of expansion, while leading to a high superconducting temperature at first, gradually or suddenly causes a decline of superconductivity and its eventual disappearance in favor of a Mott insulating state. This type of insulating state is the hallmark of strong electron correlations in cuprate and organic superconductors, and its appearance suggests that fullerides might also be members of that family. Our approach to fullerides is theoretical, and based on the solution of a Hubbard-type model, where electrons hop between molecular sites. In a Hubbard model of fullerides, unlike models for the strongly correlated cuprates, all important electron correlations occur within the molecular site, so it is efficiently soluble in the dynamical mean-field theory (DMFT) approximation. DMFT solutions confirm that superconductivity in this model fulleride, although of $s$-wave symmetry rather than $d$-wave, shares many of the properties that are characteristic of high-${T}_{c}$ cuprates. The calculations are heavy, and while the working model used is several years old, the new results presented pertain to the interesting case of three electrons per ${\mathrm{C}}_{60}$ molecule, appropriate to ${A}_{3}{\mathrm{C}}_{60}$, and have become possible only recently due to a stronger computational effort. The zero-temperature phase diagram is calculated as a function of the ratio of intramolecular repulsion parameter $U$ to the electron bandwidth $W$, the increase of $U∕W$ representing the main effect of lattice expansion. The phase diagram is close to that of actual materials, with a dome-shaped superconducting order parameter region preceding the Mott transition for increasing cell volume. Unconventional properties of expanded fulleride superconductors predicted by this model include (i) an energy pseudogap in the normal phase; (ii) a gain of electron kinetic energy and of conducting Drude weight at the onset of superconductivity, as in high-${T}_{c}$ cuprates; (iii) a spin susceptibility and a specific-heat behavior that are not drastically different from those of a regular phonon superconductor, despite strong correlations; and (iv) the emergence of more than one energy scale governing the renormalized single-particle dispersion, electronic entropy, and specific-heat jump. These predictions, which if confirmed should establish fullerides as members of the wider family of strongly correlated superconductors, are discussed in light of existing and foreseeable experiments.

Interband superconductivity: Contrasts between Bardeen-Cooper-Schrieffer and Eliashberg theories

recently discovered iron pnictide superconductors apparently present an unusual case of interband-channel pairing superconductivity. Here we show that in the limit where the pairing occurs within the interband channel, several surprising effects occur quite naturally and generally: different density of states on the two bands leads to several unusual properties, including a gap ratio which behaves inversely to the ratio of density of states; the weak-coupling limits of the Eliashberg and the BCS theories, commonly taken as equivalent, in fact predict qualitatively different dependence of the 1/2 and /Tc ratios on coupling constants. We show analytically that these effects follow directly from the interband character of superconductivity. Our results show that in the interband-only pairing model the maximal gap ratio is as strong-coupling effects act only to reduce this ratio. Our results show that pnictide BCS calculations must use renormalized coupling constants to get accurate results. Our results also suggest that if the large experimentally reported gap ratios (up to a factor 2) are correct, the pairing mechanism must include more intraband interaction than what is usually assumed.

Coexistence of Ferromagnetism with Spin Triplet Superconductivity

The experimental results for ZrZn2, URhGe, and in some pressure ranges also for UGe2, showed that the ferromagnetic superconductors are weak itinerant ferromagnets. Guided by these results we describe the phenomenon of coexistence between equal spin triplet pairing superconductivity and ferromagnetism using the extended Stoner model, which includes in Hamiltonian the on-site Coulomb interaction, U , and occupation dependent hopping integral. We use the Hartree–Fock approximation and the Green functions technique. In the Hartree–Fock approximation the on-site Coulomb interaction plays the role of the on-site exchange (Hund’s) field. All inter-site

Angular momentum mixing in single flavor color superconductivity with transverse pairing

Because of the equal strength of the pairing potential mediated by one-gluon exchange for all partial waves to the leading order QCD running coupling constant and the nonlinearity of the gap equation, the non-spherical pairing in single flavor color superconductivity (CSC) cannot be restricted in a single non- s-wave channel and the mixing among different angular momenta will occur. In this paper, we examine the angular momentum mixing in single flavor CSC of massless quarks with transverse pairing, in which the pairing quarks have opposite helicity. We find that the free energy of all non-spherical pairing states are lowered by angular momentum mixing compared with that contain p-wave only, though the amount of the free energy drop is numerically small. Consequently the most stable pairing state in the ultra-relativistic limit remains the spherical color-spin-locked state (CSL).

Colloquium: Andreev reflection and Klein tunneling in graphene

A colloquium-style introduction to two electronic processes in a carbon monolayer (graphene) is presented, each having an analog in relativistic quantum mechanics. Both processes couple electronlike and holelike states, through the action of either a superconducting pair potential or an electrostatic potential. The first process, Andreev reflection, is the electron-to-hole conversion at the interface with a superconductor. The second process, Klein tunneling, is the tunneling through a $p\text{\ensuremath{-}}n$ junction. The absence of backscattering, characteristic of massless Dirac fermions, implies that both processes happen with unit efficiency at normal incidence. Away from normal incidence, retro-reflection in the first process corresponds to negative refraction in the second process. In the quantum Hall effect, both Andreev reflection and Klein tunneling induce the same dependence of the two-terminal conductance plateau on the valley isospin of the carriers. Existing and proposed experiments on Josephson junctions and bipolar junctions in graphene are discussed from a unified perspective.

Local dynamical lattice instabilities: Prerequisites for resonant pairing superconductivity

Fluctuating local diamagnetic pairs of electrons, embedded in a Fermi sea, are candidates for non-phonon-mediated superconductors without the stringent conditions on ${T}_{c}$ which arise in phonon-mediated BCS classical low-${T}_{c}$ superconductors. The local accumulations of charge, from which such diamagnetic fluctuations originate, are irrevocably coupled to local dynamical lattice instabilities and form composite charge-lattice excitations of the system. For a superconducting phase to be realized, such excitations must be itinerant spatially phase-coherent modes. This can be achieved by resonant pair tunneling in and out of polaronic cation-ligand sites. Materials in which superconductivity driven by such local lattice instability can be expected have a ${T}_{c}$ which is controlled by the phase stiffness rather than the amplitude of the diamagnetic pair fluctuations. Above ${T}_{c}$, a pseudogap phase will be maintained up to ${T}^{\ensuremath{\ast}}$, at which this pairing amplitude disappears. We discuss the characteristic local charge and lattice properties which characterize this pseudogap phase and which form the prerequisites for establishing a phase-coherent macroscopic superconducting state.

Study on the competition between density waves, singlet, and triplet pairing superconductivity in organic conductors (TMTSF) 2X

We study the effect of dimerization of TMTSF molecules and the effect of magnetic field (Zeeman splitting) on the phase competition in quasi one-dimensional organic superconductors (TMTSF) 2X by applying the random phase approximation method. As for the dimerization effect, we conclude that due to the decrease of the dimerization, which corresponds to applying the pressure and cooling, spin and charge density wave states are suppressed and give way to a superconducting state. As for the magnetic field effect, we find generally that spin-triplet pairing mediated by a coexistence of 2 k F spin and 2 k F charge fluctuations can be strongly enhanced by applying magnetic field rather than triplet pairing due to a ferromagnetic spin fluctuations. Applying the above idea to (TMTSF) 2X compounds, a magnetic field induced singlet–triplet transition is consistent with above mechanism in (TMTSF) 2ClO 4.

Properties of superconductivity on a density wave background with small ungapped Fermi surface parts

We investigate the properties and the microscopic structure of superconductivity (SC) coexisting and sharing the common conducting band with density wave (DW). Such coexistence may take place when the nesting of the Fermi surface (FS) is not perfect, and in the DW state some quasiparticle states remain on the Fermi level and lead to the Cooper instability. The dispersion of such quasiparticle states strongly differs from that without DW, and so do the properties of SC on the DW background. The upper critical field ${H}_{c2}$ in such a SC state increases as the system approaches the critical pressure, where the ungapped quasiparticles and superconductivity just appear, and it may considerably exceed the usual ${H}_{c2}$ value without DW. The spin-density wave (SDW) background strongly suppresses the singlet SC pairing, while it does not affect so much the triplet SC transition temperature. The results obtained explain the experimental observations in layered organic metals ${(\text{TMTSF})}_{2}{\text{PF}}_{6}$ and $\ensuremath{\alpha}\text{\ensuremath{-}}{(\text{BEDT-TTF})}_{2}\text{KHg}{(\text{SCN})}_{4}$, where SC appears in the DW states under pressure and shows many unusual properties.

Some thermodynamic non-Fermi liquid properties of correlated electron systems. (...)Cu<sub><i>m</i></sub>O<sub><i>n-x</i><sub>

A mean-field Hamiltonian model has been used to investigate some thermodynamic properties of the normal states of non-Fermi liquid (NFL) systems,(...)CumOn-x . This Hamiltonian is like that of the Bardeen-Cooper-Schrieffer model [Phys. Rev. 108 (1957) 1175] but differs from the latter in (i) being multiband, (ii) the gap in energy being a function of the hopping integral and (iii) band energies of electrons being dependent upon spin orientation. The Hamiltonian is, therefore, similar to the Paring t-model [Physica 258 (9166) 30] but differs from it in not incorporating hybridization term and hybrid pair superconductivity. The analysis of the model yields magnetic energy spectrum for Cu (3d) bands` and non-magnetic energy spectrum for the O (2p) bands. Inverse temperature dependences of electronic specific heat Cv , entropy function (S) and pair susceptibility (&#935&#8593&#8595) are computed and exhibited. The specific heat dependence upon inverse temperature shows a linear form at very high temperature. It displays inverse-square-law temperature dependence, approximately, for lower temperatures. In the very low temperature range, the actual curve of the theoretical specific heat with temperature is rather like that of the Cp versus T-2 curve obtained for Bi4Cu4O16+y and Ti2Ba2Cn-1CunO2n+4 down to millikelvin temperature. This is in contradistinction to the linear temperature dependence (Cv = &#947T) of Fermi liquid systems. The specific entropy dependence on temperature shows correct physical response of systems to order (disorder) with varying temperatures. The pair susceptibility is linear at very high temperature and constant (X=X0) at moderate/low temperatures. The latter is as in Fermi liquid systems, but the former is an NFL manifestation. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 149-156

The effect of a superconducting surface layer on the optical properties of a dielectricphotonic composite

The effect of a strongly anisotropic superconducting surface layer on the transmittance,reflectance and absorptance of a one-dimensional, layered dielectric composite withperiodically alternating, isotropic constituents for linearly polarized, normally incidentelectromagnetic radiation is studied both analytically and numerically. The underlyingmodel of the electric permittivity of the superconducting constituent permits photonicexcitation at frequencies both below and above the superconductor pair breaking frequencyas well as thermal and normal scattering right up to the superconductor criticaltemperature. The optical properties addressed reveal traits such as band-like patterns ofthe transmittance and reflectance, but also step-like or smeared-out patterns of thereflectance and absorptance, displaying a marked reference to the particular type ofpolarization by virtue of the anisotropy of the superconducting layer covering thedielectric composite. Thus, in switching from transverse electric to transversemagnetic polarization, the maximum optical selectivity can become gigantic,given an appropriate thickness of the superconducting layer, with a moderatedependence on temperature. This fact offers unique possibilities regarding practicalapplications of such a novel photonic composite as an efficient polarization filter forelectromagnetic radiation tunable via the thickness of the covering layer and temperature.

Isotope effect in high-Tcsuperconductors

For high-${T}_{c}$ superconductors in which transition temperatures ${T}_{c}$ are reduced by doping, the oxygen isotope effect (OIE) coefficient in ${T}_{c}$ is shown to increase systematically with the pair-breaking rate and with the valence difference between the substituted and native ions. Moreover, the OIE in ${T}_{c}$ tends to zero as one approaches optimum (or ideal) stoichiometry at which the quality of the superconducting condensate is maximized. In materials with isovalent substitutions, e.g., Sr for Ba or Zn for Cu in $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$, the small OIE of the parent (unsubstituted) compound is magnified owing to pair-breaking disorder. In materials with heterovalent substitutions, e.g., La or Pr for Ba, where carrier densities are necessarily changed, pair breaking induces a much larger OIE. A seminal case is Pr-doped $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$, where data were previously misinterpreted owing to the false assumption that Pr substitutes only for Y. It is now clear, however, that the decrease in ${T}_{c}$ observed with Pr doping actually arises from pair breaking caused by Pr-on-Ba-site defects introduced during crystal growth. When $\mathrm{Pr}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ is grown correctly without such defects, ${T}_{c}$ remains unchanged (as in the case of most other rare-earth substitutions for Y). Invariance of ${T}_{c}$ under a 60% rare-earth mass increase provides strong evidence against phononic pairing mechanisms. The fact that ${T}_{c}$ drops when Pr substitutes for Ba but not for Y indicates that the superconducting hole condensate resides in the BaO layers, where pair breaking degrades ${T}_{c}$ and dramatically increases the OIE. Superconductive pairing modeled on Coulomb coupling between the hole (BaO) and the electron $(\mathrm{Cu}{\mathrm{O}}_{2})$ layers is shown to resolve the serious shortcomings inherent in approaches based on electron-phonon interactions and is found to be generally applicable. Moreover, the OIE in the magnetic penetration depth in alloys is shown to be constant, with degradation of ${T}_{c}$ up to 50%, and thus is unrelated to the OIE in ${T}_{c}$.

Magnetic flux periodicity of h/e in superconducting loops

Superconducting loops exhibit macroscopic quantum phenomena that have far-reaching implications; magnetic flux periodicity and flux quantization are the key to our understanding of fundamental properties of superconductors and are the basis for many applications. In superconducting rings, the electrical current responds to a magnetic flux by having a periodicity of h/2e, where the ratio of Planck’s constant and the elementary charge defines the magnetic flux quantum h/e. The well-known h/2e periodicity is a hallmark for electronic pairing in superconductors and is considered evidence for the existence of Cooper pairs. Here, we show that in contrast to this long-held belief, rings of many superconductors bear an h/e periodicity. These superconductors include the high-temperature superconductors, Sr2RuO4, the heavy-fermion superconductors, as well as all other unconventional superconductors with nodes (zeros) in the energy gap, and conventional s-wave superconductors with small gaps. As we show, the 50-year-old Bardeen–Cooper–Schrieffer theory of superconductivity implies that for loops of such superconductors the ground-state energies and consequently also the supercurrents are generically h/e periodic.