Cooper Pair Interaction Research Articles

Cooper instability generated by attractive fermion–fermion interaction in the two-dimensional semi-Dirac semimetals

Cooper instability (CI) associated with superconductivity in the two-dimensional semi-Dirac semimetals is attentively studied in the presence of attractive Cooper-pairing interaction, which is the projection of an attractive fermion–fermion interaction. Performing the standard renormalization group analysis shows that the Cooper theorem is violated at zero chemical potential but instead CI can be generated only if the absolute strength of fermion–fermion coupling exceeds certain critical value and transfer momentum is restricted to a confined region, which is determined by the initial conditions. Rather, the Cooper theorem would be instantly restored once a finite chemical potential is introduced and thus a chemical potential-tuned phase transition is expected. Additionally, we briefly examine the effects of impurity scatterings on the CI at zero chemical potential, which in principle are harmful to CI although they can enhance the density of states of systems. Furthermore, the influence of competition between a finite chemical potential and impurities upon the CI is also simply investigated. These results are expected to provide instructive clues for exploring unconventional superconductors in the kinds of semimetals.

Superconductivity in two-dimensional disordered Dirac semimetals

In two-dimensional Dirac semimetals, Cooper pairing instability occurs only when the attractive interaction strength $|u|$ is larger than some critical value $|u_{c}|$ because the density of states vanishes at Dirac points. Disorders enhance the low-energy density of states but meanwhile shorten the lifetime of fermions, which tend to promote and suppress superconductivity, respectively. To determine which of the two competing effects wins, we study the interplay of Cooper pairing interaction and disorder scattering by means of renormalization group method. We consider three types of disorders, including random mass, random gauge potential, and random chemical potential, and show that the first two suppress superconductivity. In particular, the critical BCS coupling $|u_{c}|$ is increased to certain larger value if the system contains only random mass or random gauge potential, which makes the onset of superconductivity more difficult. In the case of random chemical potential, the effective disorder parameter flows to the strong coupling regime, where the perturbation expansion breaks down and cannot provide a clear answer concerning the fate of superconductivity. When different types of disorder coexist in one system, their strength parameters all flow to strong couplings. In the strong coupling regime, the perturbative renormalization group method becomes invalid, and one needs to employ other methods to treat the disorder effects. We perform a simple gap equation analysis of the impact of random chemical potential on superconductivity by using the Abrikosov-Gorkov diagrammatic approach, and also briefly discuss the possible generalization of this approach.

Effect of disorder on the competition between nematic and superconducting order in FeSe

Crystalline FeSe is known to display strong nematic order below a weak tetragonal-orthorhombic structural transition around K, and a superconducting transition at . Recently, it was shown that electron irradiation, which creates pointlike potential scattering defects, has the surprising effect of enhancing Tc while suppressing Ts. Here we discuss a possible scenario for such an effect, which postulates a competition between superconductivity and nematic order. The transition to the nematic state is modeled by a mean field theory of a d-wave Pomeranchuk instability, together with a Cooper pairing interaction in both one- and multiband models. The effect of nonmagnetic impurities on both orders is treated on equal footing within the Born approximation. We find evidence that disorder can indeed enhance Tc while suppressing the competing nematic order, but only in a multiband situation. We discuss our results in the context of experimental data on FeSe crystals.

Identifying the 'fingerprint' of antiferromagnetic spin fluctuations in iron pnictide superconductors

Cooper pairing in the iron-based high-Tc superconductors1,2,3 is often conjectured to involve bosonic fluctuations. Among the candidates are antiferromagnetic spin fluctuations1,4,5 and d-orbital fluctuations amplified by phonons6,7. Any such electron–boson interaction should alter the electron’s ‘self-energy’, and then become detectable through consequent modifications in the energy dependence of the electron’s momentum and lifetime8,9,10. Here we introduce a novel theoretical/experimental approach aimed at uniquely identifying the relevant fluctuations of iron-based superconductors by measuring effects of their self-energy. We use innovative quasiparticle interference (QPI) imaging11 techniques in LiFeAs to reveal strongly momentum-space anisotropic self-energy signatures that are focused along the Fe–Fe (interband scattering) direction, where the spin fluctuations of LiFeAs are concentrated. These effects coincide in energy with perturbations to the density of states N(ω) usually associated with the Cooper pairing interaction. We show that all the measured phenomena comprise the predicted QPI ‘fingerprint’ of a self-energy due to antiferromagnetic spin fluctuations, thereby distinguishing them as the predominant electron–boson interaction.

Muon spin rotation and relaxation inPr1−xNdxOs4Sb12: Paramagnetic states

Positive-muon ($\mu^+$) Knight shifts have been measured in the paramagnetic states of Pr$_{1-x}$Nd$_x$Os$_4$Sb$_{12}$ alloys, where $x =$ 0, 0.25, 0.45, 0.50, 0.55, 0.75, and 1.00. In Pr-substituted NdOs$_4$Sb$_{12}$ ($x \le$ 0.75), but not in NdOs$_4$Sb$_{12}$, Clogston-Jaccarino plots of $\mu^+$ Knight shift~$K$ versus magnetic susceptibility~$\chi$ exhibit an anomalous saturation of $K(\chi)$ at $\sim-$0.5% for large susceptibilities (low temperatures), indicating a reduction of the coupling strength between $\mu^+$ spins and $4f$ paramagnetism for temperatures $\lesssim$ 15~K. We speculate that itinerant Pr$^{3+}$ quadrupolar excitations, invoked to mediate the superconducting Cooper-pair interaction, might modify the $\mu^+$-$4f$ ion indirect spin-spin interaction.

Coexistence of p-wave cooper pairing and ferromagnetism

A two-band model for coexistence of p-wave superconductivity with localized ferromagnetism is studied using the equation of motion approach. It shows that ferromagnetic and superconducting states enhance each other but in a different way from that of the one-band model. The Curie temperature is not only determined by the exchange interactions between localized spins, but also can be increased with the coupling between electrons and spins, and with the p-wave Cooper-pairing interaction. These results are complementary to those of the one-band model, which suggest that the Curie temperature is unlikely to ever be below the superconducting transition temperature.

Feedback Effect on High-Energy Magnetic Fluctuations in the Model High-Temperature SuperconductorHgBa2CuO4+δObserved by Electronic Raman Scattering

We use electronic Raman scattering to study the model single-layer cuprate superconductor HgBa(2)CuO(4+δ). In an overdoped sample, we observe a pronounced amplitude enhancement of a high-energy peak related to two-magnon excitations in insulating cuprates upon cooling below the critical temperature T(c). This effect is accompanied by the appearance of the superconducting gap and a pairing peak above the gap in the Raman spectrum, and it can be understood as a hitherto-undetected feedback effect on the high-energy magnetic fluctuations due to the Cooper pairing interaction. This implies a direct involvement of the high-energy magnetic fluctuations in the pairing mechanism. All of these effects occur already above T(c) in two underdoped samples, demonstrating a related feedback mechanism associated with the pseudogap.

Role of surface Cooper pair interactions on critical temperature of ultra thin film superconductors

The superconductivity mechanism of Pb thin film on a Si substrate in the weak interaction regime is investigated. A discrete Fermi surface is constructed depend on the film thickness and electron density and crystallographic orientation. We consider two types of Cooper pair interactions, Cooper pair interaction at thin film surfaces and Cooper pair in the thin film volume. We have chosen the surface Cooper pair interaction, of ultra thin films superconductor proportional to the inverse of thin film thickness, while the volume Cooper pair interaction has been considered as a constant. By these assumptions, we have found oscillation feature of critical temperature T c and energy gap Δ in terms of thin film thickness similar to the experimental results for Pb / Si ( 111 ) thin film superconductor. However, by increasing number of Pb layers, the thin film T c goes to bulk T c . In contrast to the previous claimed constant value for the Δ b ( T = 0 ) / k B T c in bulk, we have found oscillation of this parameter in terms of thin film thickness similar to the T c oscillation.

Unified theory of superconductivity inLa2-xSrxCuO4 and Nd2-xCexCuO4

Taking the two-local-spin-mediated interaction as a Cooper pairinteraction, using the BCS (Bardeen-Cooper-Schrieffer) gap equationand the phase-coherence condition for quantum phase fluctuation,this paper explains basic experimental findings concerning bothp-type La2-xSrxCuO4 (LSCO) and n-typeNd2-xCexCuO4 (NCCO) at the same time, and predicts thatthe pseudogap should be clearly observed for underdoped NCCO.

Phase Diagrams of the Reentrant Superconducting Re(1)1?xRe(2)xX (X = Rh4B4) Alloys.Application to Er1?xHoxX, Er1?xGdxX, Er1?xTmxX, HoxLu1?xX and Sm1?xErxX

We consider a simplified version of the s–f model, supplemented by the intersite Cooper pair interaction between conduction electrons with opposite spins to investigate the ferromagnetic and superconducting properties of an alloy Re1-x(1)Re(2)xX (Re(1), Re(2) rare earth elements, X = Rh4B4) using the virtual crystal approximation (VCA). For a suitable choice of the model parameters we can reproduce the phase boundaries of the experimentally measured phase diagrams for Er1—xHoxX, Er1—xGdxX, Er1—xTmxX, HoxLu1—xX and Sm1—xErxX alloys.

Phase Diagrams of the Reentrant Superconducting Re(1)1xRe(2)xX (X = Rh4B4) Alloys.Application to Er1xHoxX, Er1xGdxX, Er1xTmxX, HoxLu1xX and Sm1xErxX

We consider a simplified version of the s–f model, supplemented by the intersite Cooper pair interaction between conduction electrons with opposite spins to investigate the ferromagnetic and superconducting properties of an alloy Re1-x(1)Re(2)xX (Re(1), Re(2) rare earth elements, X = Rh4B4) using the virtual crystal approximation (VCA). For a suitable choice of the model parameters we can reproduce the phase boundaries of the experimentally measured phase diagrams for Er1—xHoxX, Er1—xGdxX, Er1—xTmxX, HoxLu1—xX and Sm1—xErxX alloys.

The extended Hubbard model applied to phase diagram and the pressure effects in Bi2Sr2CaCu2O8+y superconductors

We use the two dimensional extended Hubbard Hamiltonian with the position of the attractive potential as a variable parameter, within a BCS type approach, to study the interplay between the superconductor transition temperature Tc and hole content for high temperature superconductors. This method gives some insight on the range and intensity of the Cooper pair interaction. It suggests why different compounds have different values for their measured coherence lengths, and describes the experimental results of the superconducting phase diagram Tc ´ n . The calculations may also be used to study the effect of the applied pressure with the assumption that it increases the attractive potential which is accompanied by an increase in the superconductor gap. In this way we obtain a microscopic interpretation for the intrinsic term and a general expansion for Tc in terms of the pressure which reproduces well the experimental measurements on the Bi2Sr2CaCu2O8+y superconductors.

A model for the correlations among critical temperature, hole content and pressure effects in Bi 2Sr 2CaCu 2O 8+ y

We use the two dimensional extended Hubbard Hamiltonian with the position of the attractive potential as a variable parameter in connection with a BCS-type approach to study the interplay between the superconductor transition temperature T c and hole content in high-temperature superconductors. This novel method gives some insight on the range and intensity of the Cooper pair interaction and on the measured coherence length. Furthermore, it describes well several experimental results of T c× n on different compounds and suggests that pressure causes an increase of the superconducting gap. This new idea is developed in order to study how T c is modified by the applied pressure. In this way we obtain a microscopic interpretation for the intrinsic term and a general expansion for T c in terms of the pressure. In order to demonstrate the method we apply it to the Bi 2Sr 2CaCu 2O 8+ y superconductors.

Reentrant Superconductivity in HoMo6S8

A simplified version of the s–f model, supplemented by the intersite Cooper pair interaction between conduction electrons with opposite spins, is used to investigate the competition between ferromagnetism and anisotropic superconductivity in a single-domain ferromagnet. The calculations of the temperature dependence of the magnetizations mf (localized 4f electrons), md (conduction electrons) and the superconducting order parameter show the existence of three critical temperatures: TC (Curie temperature), TS1 and TS2 (lower and upper superconducting transition temperatures). The critical temperatures fulfil the relation TS1 < TC < TS2. For T ∈ [0, TS1] the system is ferromagnetic and normal, for T ∈ [TS1, TC] ferromagnetic and superconducting, for T ∈ [TC, TS2] paramagnetic and superconducting and for T > TS2 paramagnetic and normal. The superconducting order parameter possesses a distinct maximum between TS1 and TS2 and vanishes for T < TS1 and T > TS2 in agreement with the recent experimental results for HoMo6S8. The calculated temperature dependence of the dc resistivity shows a typical reentrant behaviour, characteristic for such ferromagnetic superconductors as ErRh4B4 and HoMo6S8. Using a suitable choice of the model parameters we can obtain a reasonable fit of the recent experimental results for HoMo6S8, concerning the temperature dependence of the superconducting order parameter and dc resistivity.

Theoretical study of isotope effect in La-doped Y-123

The recent oxygen isotope effect measurement made in the system YBa2-x La x Cu3O7 (0≤x≤0.5) is analyzed using the “two-carrier” model which describes a superconducting system as a mass anisotropic system consisting of charge carriers with two different masses as a result of lattice defects or oxygen deficiency. The extent to which Ba, Cu, and O atoms participate in the phonon-mediated Cooper pairing interaction is elucidated. The relationship between the theoretically deduced mass anisotropic factor andT c agrees closely with the experimental results of Uemuraet al. [28]. Furthermore, the superconducting energy gap toT c ratio is found to be close to 3.5. Excellent agreement is also achieved between the theoretically calculated oxygen isotopic constant and the experimental results of Bornemann and Morris [12].

Cooper-pairing interaction due to magnetic fluctuations near the spin-density-wave phase transition.

An attractive d-wave interaction occurs for Cooper pairing due to magnetic fluctuations associated with both sides of the spin-density-wave phase transition, in the Hubbard model for both square and bcc lattices. This pairing interaction is not enhanced by the antiferromagnetic background that occurs in the spin-density-wave (SDW) state. The problem of magnetic Umklapp processes in the interaction for the SDW state is dealt with by using a two-component electron field to represent the two sublattices of the antiferromagnetism. A Landau-Fermi liquid is assumed for the electrons and fluctuations are treated in the random-phase approximation (RPA). We also discuss the qualitative form of the theory beyond the RPA.

Cooper-pairing interaction at the edge of an electron energy gap due to antiferromagnetism.

There is no effect of static antiferromagnetism (AF) on the phonon-mediated Cooper-pairing interaction represented by a structureless interaction in the gap equation when the spins of the AF are centered at ion sites. This result includes effects of all magnetic and nonmagnetic umklapp processes with correct phases and would apply in a simple way as well for any electron-electron interaction arising from phase-mode (phononlike) magnetic vibrations of a spin-density wave. In some cases other than these the s-wave pairing interaction for electron states near the edge of an energy gap due to AF may be reduced in strength by the static AF.