Inhomogeneous Superconducting State Research Articles

Upper critical fields of quasi-low-dimensional superconductors with coexisting singlet and triplet pairing interactions in parallel magnetic fields

Quasi-low-dimensional type-II superconductors in parallel magnetic fields are studied when singlet pairing interactions and relatively weak triplet pairing interactions coexist. Singlet and triplet components of order parameter are mixed at high fields, and at the same time an inhomogeneous superconducting state called a Fulde-Ferrell-Larkin-Ovchinnikov state occurs. As a result, the triplet pairing interactions enhance the upper critical field of superconductivity remarkably even at temperatures far above the transition temperature of parallel spin pairing. It is found that the enhancement is very large even when the triplet pairing interactions are so weak that a high-field phase of parallel spin pairing may not be observed in practice. A possible relevance of the result in organic superconductors and a hybrid-ruthenate-cuprate superconductor is discussed.

Generalized Fulde-Ferrell-Larkin-Ovchinnikov state in heavy-fermion and intermediate-valence systems

Anomalous properties of the magnetization, the crystal dilatation, and other physical quantities observed in the mixed state of compounds such as UPd2Al3 and CeRu2 suggest the occurrence of a new state near H c2. In such compounds with large spin susceptibility and high H c2, a new inhomogeneous superconducting state is theoretically predicted to occur in high magnetic fields. In this inhomogeneous state which is shown to be a generalized Fulde-Ferrell-Larkin-Ovchinnikov state, the order parameter is spatially modulated, and planar nodes of the order parameter are periodically aligned perpendicular to the vortices. Various theoretical predictions are compared with experimental results on UPd2Al3 and CeRu2 related to this new superconducting high-field state.

Resistive transition and fluctuations of the conductivity in YBa 2Cu 3O 7, EuBa 2Cu 3O 7 and GdBa 2Cu 3O 7 superconductors : Effect of inhomogeneities

Systematic resistivity measurements in polycrystalline samples of the high- T c oxide superconductors RBa 2Cu 3O 7 (R = Y, Eu, Gd) are performed with several (low) current densities. Special attention is devoted to the temperature range close to the superconducting transition. The data allows the determination of temperature derivatives of the resistivity, which reveal the occurence of a two-step transition. This feature is typical of a granular system. Two scaling regimes for the fluctuation conductivity are also identified. Near the temperature where the grains become superconducting, the enhancement of the conductivity follows a power law with sample dependent exponents. Analysis of this result on the basis of the Aslamazov-Larkin theory indicates that a fractal topology might be adequate to describe the inhomogeneous superconducting state. In the second scaling regime, near the zero-resistance temperature, an apparently universal exponent is observed.

Induction of superconductivity by strong electric field

It is shown that strong electric field perpendicular to the surface of a solid with free charges creates the surface inhomogeneous superconducting state with critical parameters depending on the surface electrical potential only. The critical temperature and magnetic field of the surface inhomogeneous state can be high in the strong electric field.

Induction of Superconductivity by the Inner Contact Potential

AbstractThe inner contact potential changes the density of electron states and increases the value of the electron–electron interaction. A theory of the inhomogeneous superconducting state in these systems is presented. The critical temperature and magnetic field are calculated.

The critical parameters and structure of the surface superconducting state induced by external electric field

Electric field perpendicular to a surface of superconducting semiconductor or semimetal induces superconducting transition at temperature and in magnetic field higher than in the bulk. The magnetic moment and structure of the inhomogeneous surface superconducting state are calculated. All parameters depend on direction of magnetic field, magnitude of electric field, and temperature.

Surface superconductivity induced by an external electric field

A theory of surface superconductivity induced by an external electric field in superconducting semimetals, metals and semiconductors is presented. It is shown that the inhomogeneous surface superconducting state deeply penetrates into the bulk of the sample. The dependence of the critical surface temperature and magnetic field on the external electric field is calculated.

New instability model for the inhomogeneous gap states of a nonequilibrium superconductor

A new model based on the Rothwarf-Taylor-type rate equations taking the effect of relaxation phonons by decay of high-energy quasiparticles into account is proposed. This effect induces an instability toward the inhomogeneous superconducting state at a certain critical concentration significantly less than that of ${\ensuremath{\mu}}^{*}$ instability. The spatial scale of an instability is also estimated to be about 100 \ensuremath{\mu}m. The results are in good agreement with recent experimental observations.

On the fluctuation enhanced conductivity of a non-equilibrium superconductor

It is shown that simultaneous action of intense optical radiation and weak tunnel injection results in transition to the inhomogeneous superconducting state. The conductivity in the non-equilibrium normal state near the transition to the above-mentioned state is calculated vs the intensity of tunnel injection.

Rigorous study of the gap equation for an inhomogeneous superconducting state nearTc

A rigorous analytic study of the self-consistent gap equation (symobolically $\ensuremath{\Delta}={\mathcal{F}}_{T}[\ensuremath{\Delta}]$), for an inhomogeneous superconducting state, is presented in the Bogoliubov formulation. The gap function $\ensuremath{\Delta}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ is taken to simulate a planar normal-superconducting phase boundary: $\ensuremath{\Delta}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})={\ensuremath{\Delta}}_{\ensuremath{\infty}}tanh(\frac{\ensuremath{\alpha}{\ensuremath{\Delta}}_{\ensuremath{\infty}}z}{{v}_{F}})\ensuremath{\bigominus}(z)$, where ${\ensuremath{\Delta}}_{\ensuremath{\infty}}(T)$ is the equilibrium gap, ${v}_{F}$ is the Fermi velocity, and $\ensuremath{\bigominus}(z)$ is a unit step function. First a special space integral of the gap equation $\ensuremath{\propto}\ensuremath{\int}{0+}^{\ensuremath{\infty}}({\mathcal{F}}_{T}\ensuremath{-}\ensuremath{\Delta})(\frac{d\ensuremath{\Delta}}{\mathrm{dz}})dz$ is evaluated essentially exactly, except for a nonperturbative WKBJ approximation used in solving the Bogoliubov-de Gennes equations. It is then expanded near the transition temperature ${T}_{c}$ in power of ${\ensuremath{\Delta}}_{\ensuremath{\infty}}\ensuremath{\propto}{(1\ensuremath{-}\frac{T}{{T}_{c}})}^{\frac{1}{2}}$, demonstrating an exact cancellation of a subseries of "anomalous-order" terms. The leading surviving term is found to agree in order, but not in magnitude, with the Ginzburg-Landau-Gor'kov (GLG) approximation. The discrepancy is found to be linked to the slope discontinuity in our chosen $\ensuremath{\Delta}$. A contour-integral technique in a complex-energy plane is then devised to evaluate the local value of ${\mathcal{F}}_{T}\ensuremath{-}\ensuremath{\Delta}$ exactly. Our result reveals that near ${T}_{c}$ this method can reproduce the GLG result essentially everywhere, except within a BCS coherence length [not $\ensuremath{\xi}(T)$!] from a singularity in $\ensuremath{\Delta}$, where ${\mathcal{F}}_{T}\ensuremath{-}\ensuremath{\Delta}$ can have a singular contribution with an "anomalous" local magnitude, not expected from the GLG approach. This anomalous term precisely accounts for the discrepancy found in the special integral of the gap equation as mentioned above, and likely explains the ultimate origin of the anomalous terms found in the free energy of an isolated vortex line by Cleary.