Gapless Region Research Articles

Small-q phonon-mediated superconductivity in organic kappa-BEDT-TTF compounds.

We propose a new picture for superconductivity in kappa-(BEDT-TTF)2X salts arguing that small- q electron-phonon scattering dominates the pairing. We reproduce the distinct X-shaped d-wave gap reported recently by magneto-optic measurements and we argue that the softness of the momentum structure of the gap and the near degeneracy of s- and d-wave gap states may be at the origin of the experimental controversy about the gap symmetry. We show that a magnetic field applied parallel to the planes may induce extended gapless regions on the Fermi surface accounting for the experimental signatures of a Fulde-Ferrel-Larkin-Ovchinikov state and it may induce gap symmetry transitions as well.

Closing ofa spin gap and ferromagnetism induced by magnetic impurities:finite-size effects and critical exponents

We consider the one-dimensional gas of electrons interacting via anattractive δ-function potential. The attractive potentialleads to the formation of Cooper-pair-like bound states with a spingap. Without destroying the integrability, we introduce a finiteconcentration of mixed-valence impurities with two magneticconfigurations of spin S and S + {{1}/{2}}, which hybridize withthe conduction states of the host. We derive the Bethe ansatzequations diagonalizing the system for the correlated host withimpurities and discuss the ground-state properties as functions ofthe concentration of impurities and the Kondo coupling. For asufficiently large density of electrons the spin gap is reduced bythe impurities and is closed at a critical concentration whichdepends on the impurity spin and the coupling strength. Aferromagnetic phase of unpaired spin-polarized itinerant electronsis induced for impurity concentrations larger than the critical one.The critical behaviour of the correlation functions is studied inthe gapped and gapless regions using the mesoscopic energy spectrumand conformal field theory.

Specific heat of anS=12Heisenberg ladder compoundCu2(C5H12N2)2Cl4under magnetic fields

Specific heat measurements down to 0.5 K have been performed on a single crystal sample of a spin-ladder-like compound ${\mathrm{Cu}}_{2}({\mathrm{C}}_{5}{\mathrm{H}}_{12}{\mathrm{N}}_{2}{)}_{2}{\mathrm{Cl}}_{4}$ under magnetic fields up to 12 T. The temperature dependence of the observed data in a magnetic field below 6 T is well reproduced by numerical results calculated for the $S=\frac{1}{2}$ two-leg ladder with ${J}_{\mathrm{rung}}{/J}_{leg}=5.$ In the gapless region above 7 T ${(H}_{\mathrm{c}1}),$ the agreement between experiment and calculation is good above about 2 K and a sharp and a round peak were observed below 2 K in a magnetic field around 10 T, but the numerical data show only a round peak, the magnitude of which is smaller than that of the observed one. The origin of the sharp peak and the difference between the experimental and numerical round peak are discussed.

Heat capacity of [formula omitted] in a magnetic field

Heat capacity measurements down to 0.5 K in a magnetic field up to 12 T have been performed on a single-crystal sample of a spin-ladder-like compound Cu 2( C 5 H 12 N 2) 2 Cl 4 . The singlet ground state with an energy gap becomes magnetic and gapless between 7 T ( H c1 ) and 13 T ( H c2 ) . In the temperature dependence of the heat capacity of this compound, we have observed a sharp and a round peak in the gapless region between H c1 and H c2 . The former peak most likely arises from the long-range order and the latter one is probably attributable to the low-energy excitation structure in a gapless spin-liquid system.

Low-energy behavior of the spin-tube and spin-orbital models

The low-energy effective Hamiltonian of three coupled spin chains with periodic boundary conditions (spin tube) is expressed, in the limit of strong interchain coupling, in terms of XXZ chains coupled by biquadratic exchange interaction. A similar class of models was proposed to describe the coupling of spins to orbital degrees of freedom in materials such as NaV2O5. We investigate these models by means of bosonization and renormalization group techniques, and find that the generic phase diagram comprises a gapless region and gapped regions consisting of a spin liquid phase and various antiferromagnetic phases. We discuss the properties of the spin liquid phase, in particular the nature of the ground state and of the elementary excitations above it. We then study the effect of a magnetic field, and conclude that a strong enough magnetic field can suppress the dimerized phase leading to a two component Luttinger liquid. The critical exponents at the transition gapful-gapless are calculated and shown to be non-universal in the spin tube case as well as in the generic spin orbital problem.

Extended gapless regions in disordereddx2−y2wave superconductors

A generalization of the Abrikosov-Gorkov equations for non-magnetic impurities in unconventional superconductors is proposed, including higher harmonics in the expansion of the momentum dependent gap function and a momentum dependent impurity scattering potential. This model is treated within a self-consistent calculation to obtain the electronic density of states, the optical conductivity, and the gap function in a two-dimensional d_{x^2-y^2}-wave superconductor. It is argued that momentum dependent scattering from the impurities may lead to extended gapless regions in the gap function centered around the nodes of the pure d_{x^2-y^2}-wave superconductor. The associated enhancement of the residual density of states may be responsible for the rapid decrease of T_c and the increase of the London penetration depth with hole doping observed in overdoped cuprate superconductors.

Enhancement of superconducting correlation due to interlayer tunneling

Interlayer single-particle tunneling between the CuO layers suppresses the in-plane short-range magnetic order (which is modeled as spin density wave (SDW) insulator). Doping over the SDW state kills perfect nesting of the Fermi surface (FS) in certain directions and hence the SDW gap reduces to zero in those directions of the FS. Coupling between the planes through interlayer tunneling ( t t ) further suppresses the in-plane magnetic SDW gap. Superconductivity arises in the gapless regions of the FS under the “modified spin-bag” mechanism. We show that the highest T c can only be obtained for non-zero t t based on this mechanism.

INFLUENCE OF NON-MAGNETIC IMPURITIES ON THE HIGH-Tc SUPERCONDUCTIVITY

In this paper, we have proved that the non -magnetic doping can also produce pair-breaking effect in the Anderson lattice model of the high-Tc cuprate superconductorts due the energy dependence of the order parameter. In the case of dilute doping, we have obtained a linear decreasing behavior of Tc with the increasing of non-magnetic impurity concentration in agreement with experimental results. Furthermore, we have also calculated the influence of doping on the superconducting energy gap in the density of states. The results indicate that the decreasing of the gap at T = 0 is much slower than the dropping of Tc with the increasing of non-magnetic impurities. Therefore, the gapless region may not appear before the system transforms into the normal state in different from the conventional BCS superconductors with magnetic impurities.

Critical behavior in quantum spin chains with composite spin.

Composite spin models are constructed such that, by varying two parameters, they interpolate between the spin-(1/2 antiferromagnetic Heisenberg chain and a number of spin-1 models. These include the usual Heisenberg model, the integrable spin-1 model, and the model with an exact valence-bond ground state. Finite-chain calculations are performed on the composite spin model to study its criticality, and to find if the integrable spin-1 model is a multicritical point with a finite gap generated away from it. We find indications for an extended gapless region.

Superconductivity in the dense Kondo system

Abstract An anisotropic s-symmetry superconductivity, possibly with a line gapless region, is shown to be most favorable under the strong on-site repulsive and the phonon-mediated inter-site attractive interaction. Spin-fluctuation-mediated indirect interaction does not seem to benefit triplet pairing.

On the phase diagram of the impure exciton ferromagnet

The influence of normal impurities on the exciton ferromagnet is studied and the phase diagram of the impure exciton ferromagnet is calculated. The main result is that normal impurities can produce a gapless region for spin down quasiparticle excitations while for spin up the gap is still present.

Theory of Electron-Spin Resonance in Gapless Superconductors

The transverse dynamic spin susceptibility for conduction electrons in dirty gapless superconductors, in particular, in the vortex state of type-II superconductors, is calculated. It is shown that in the gapless region the dynamic susceptibility consists of two terms, the regular term and the anomalous term. In the low-frequency region of experimental interest, the regular term reduces to the static spin susceptibility, which is determined, for example, by the Knight-shift measurement in superconductors, while the anomalous term has a pole, which is associated with a resonance of the spin of conduction electrons. The resonance linewidth ${T}_{2}^{\ensuremath{-}1}$ is determined from the imaginary part of the resonance frequency. It is shown that ${T}_{2}^{\ensuremath{-}1}$ behaves quite differently in the superconducting state depending on whether ${T}_{2}^{\ensuremath{-}1}$ in the normal state is primarily due to the spin-orbit scattering or due to the exchange scattering from the magnetic impurities.

Effect of Paramagnetic Impurities on Josephson Currents through Junctions with Normal-Metal Barriers

The present paper deals with a study of the effect of paramagnetic impurities on zero-bias Josephson currents through junctions with normal-metal barriers at $T=0\ifmmode^\circ\else\textdegree\fi{}$K. The ratio of the barrier supercurrent of the impure-SNS (superconductor-normal-metal-superconductor) junction to that of the pure-SNS junction is found to be equal to $1\ensuremath{-}\ensuremath{\zeta}$, where $\ensuremath{\zeta}$ is a measure of the impurity concentration. For $\ensuremath{\zeta}<1$, the Josephson current is nonzero and decreases with increase of impurity concentration, but in the gapless region (${\ensuremath{\omega}}_{g}=0$) when $\ensuremath{\zeta}>~1$, the current is zero for $\ensuremath{\zeta}=1$ and then becomes negative for $\ensuremath{\zeta}>1$. At $\ensuremath{\zeta}=0$, the result is in exact agreement with that of Ishii for the pure case.

Type II superconductors containing magnetic impurities

A theoretical study is made on the equilibrium as well as on the dynamical properties of type II superconductors containing magnetic impurities. The Kondo effect associated with the impurity spins is taken into account within the pole approximation, which has been used previously by Muller-Hartmann and Zittarz in their calculation of the superconducting transition temperature. In this approximation we have still the additive law of the different pair-breaking mechanisms for the transition temperature; the sum of the pair-breaking parameters due to magnetic impurities and due to magnetic fields is a universal function of the temperature. Since the pair-breaking parameter arising from magnetic impurities has the maximum atT≅T K , the upper critical fieldH c2 (T) reflects the Kondo effect in the system. The κ2(T) parameter, which describes the magnetization as well as the flux-flow resistivity of the vortex state, is obtained. WhenT K /T c0 >1, κ2(T) increases as the temperature decreases, but whenT K /T c0 <1, κ2(T) first increases as the temperature decreases, then passing a maximum and decreasing at low temperatures, which is in sharp contrast to that obtained previously where the impurity scattering was treated with the Born approximation (i.e., the Kondo effect was completely neglected.) A brief discussion of the density of states in the gapless region is also given, which reflects the Kondo effect in an interesting way.

Flux-flow resistance, ettingshausen effect, and thermal and magnetic properties of Nb 0.8-Mo 0.2 alloy

The specific heat and the magnetization have been measured on Nb 0.8-Mo 0.2 alloy in the temperature range from 1 K to 5 K. The analysis of these data gives the Ginzburg-Landau parameter κ = 4.13 at T c = 4.28 K. The critical fields, H c2(0) and H c(0), have been found to be 5437 Oe and 747 Oe, respectively. This alloy is found to be in the dirty limit of a type-II superconductor. According to the recent theory of Maki, these fundamental parameters together with the electrical resistivity in the normal state determine the type-II behaviors of the transport properties of this alloy with respect to their dependences on temperature and magnetic field. In the gapless region, the flow resistance and the entropy of the vortex motion deduced from Ettingshausen coefficients show their magnitudes and the temperature dependences in good agreement with the prediction of this microscopic theory. In addition the jump in the specific heat at the transition from the mixed state to the normal one has been measured at twelve values of the field up to 4566 Oe. This jump may be explained well in terms of the thermodynamical relation at that transition.

Thermal Conductivity in Pure Two-Band Superconductors in High Magnetic Fields

The theory proposed by Maki, for the electronic thermal conductivity in the gapless region of a pure type-II superconductor, is extended to include the presence of a second superconducting band so that it can be used to describe the mixed-state thermal conductivity in clean transition-metal superconductors near ${H}_{c2}$. The general features of Maki's one-band expression remain in the two-band expression.

Dynamical properties of gapless superconductors

The system of time-dependent equations is obtained for superconductors in the gapless region (strong magnetic fields). The thin films in a presence of uhf power are considered in more detail. It is shown that the whole picture is very different in comparison with the simple diffusion type extension of the Ginsburg—Landau theory. It is pointed out that a new characteristic time has to be introduced corresponding to processes of the energy relaxation.

Observation of Decrease of Supercurrent in the Gapless Region

The dependence of superfluid current density $J$ on superfluid velocity $v$ was measured in a hollow super-conducting cylinder of indium placed in an axial low-frequency magnetic field. In order to enter the $v$ region for which a decrease of $J$ as a function of $v$ is predicted, the interior of the cylinder was filled with a superconducting rod. The measured quantities were the flux ${\ensuremath{\varphi}}_{J}$ arising from $J$ and the magnitude ${H}_{e}$ of the low-frequency magnetic field which is related to $v$. The experimental results are graphs showing ${\ensuremath{\varphi}}_{J}$ as a function of ${H}_{e}$. At temperatures close to the transition temperature of the film, the ${\ensuremath{\varphi}}_{J}\ensuremath{-}{H}_{e}$ graphs were linear for small ${H}_{e}$, whereas for larger ${H}_{e}$, a maximum in ${\ensuremath{\varphi}}_{J}$ followed by a decrease was clearly observed. The temperature dependence and the maximum value of ${\ensuremath{\varphi}}_{J}$ were found---within experimental accuracy---to be in agreement with the predictions of the Ginzburg-Landau theory.

Thermal Conductivity in a Pure Type II Superconductor near the Upper Critical Field

The thermal conductivity, K , of a pure Nb (RRR=1900) has been studied as a function of longitudinal and transverse magnetic field between 1.8°K and the transition temperature (9.2°K). The thermal conductivity shows a deep minimum just above H c 1 and increases with infinite slope in the gapless region near H c 2 like Δ K / K n = C ( H c 2 - H ) 1/2 in good agreement with the Maki theory for both longitudinal and transverse field configurations. The temperature dependence of the coefficient C is compared with numerically calculated one from the revised Maki theory which includes both the impurity scattering and the phonon scattering, and a fairly good agreement is found between them, when density of states is assumed to be 1.6×10 33 states/cm 3 erg.

Thermal Conductivity of Pure Type-II Superconductors in High Magnetic Fields

The electronic contribution to the thermal conductivity in a pure type-II superconductor in the gapless region (i.e., in a field close to the upper critical field ${H}_{c2}$) is obtained. Use is made of the fact that the order parameter is described by the Abrikosov solution of the Ginzburg-Landau equation and $\frac{l}{{\ensuremath{\xi}}_{0}}\ensuremath{\gg}1$, where $l$ is the electronic mean free path and ${\ensuremath{\xi}}_{0}$ is the coherence distance. It is shown that the thermal conductivity drops rapidly in the superconducting region like ${({H}_{c2}\ensuremath{-}H)}^{\frac{1}{2}}$, and is strongly anisotropic.