Cooper pairing in the presence of antiferromagnetism

With a BCS interaction, the free energy for usual BCS pairing of electrons but in the presence of antiferromagnetism is shown to be lower than for a different pairing scheme where pairs are formed from electron eigenstates of the antiferromagnet. In both pairing schemes, super-conductivity in the presence of antiferromagnetism is always a mixture of spin-singlet-even-parity-orbital and spin-triplet-odd-parity-orbital electron pairs.     

One-dimensional Cooper pairing

We study electron pairing in a one-dimensional (1D) fermion gas at zero temperature under zero- and finite-range, attractive, two-body interactions. The binding energy of Cooper pairs (CPs) with zero total or center-of-mass momentum (CMM) increases with attraction strength and decreases with interaction range for fixed strength. The excitation energy of 1D CPs with nonzero CMM display novel, unique properties. It satisfies a dispersion relation with two branches: a phonon-like linear excitation for small CP CMM; this is followed by roton-like quadratic excitation minimum for CMM greater than twice the Fermi wavenumber, but only above a minimum threshold attraction strength. The expected quadratic-in-CMM dispersion in vacuo when the Fermi wavenumber is set to zero is recovered for any coupling. This paper completes a three-part exploration initiated in 2D and continued in 3D.     

Cooper pairing and superfluidity in the Emery model

The energy E of the system as a function of the gauge phase Φ is calculated by exact diagonalization in a two-dimensional Cu₄O₈ cluster and by the slave-boson method for large systems. It is shown that motion of carriers with charge 2e, i.e., Cooper pairs, is observed for certain values of the parameters in the Hamiltonian. This motion is identified from the onset of a characteristic maximum of E(Φ) at Φ≈Φ₀/2, where Φ₀ is the flux quantum. The phase diagram is constructed and the range of values of the model parameters where the effect is observed is determined. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 2, 78–82 (25 January 1996)     

Generalization of the Cooper pairing mechanism for spin-triplet in superconductors

A generalization of the Cooper pairing mechanism is proposed which allows for a triplet state of lower energy. This is achieved by incorporating spin into the canonical commutation relations and by modifying the δ potential contact interaction. The gap equation contain as solutions both singlet and triplet states. It is shown that the triplet state is lower in energy than the singlet state which may explain the spin-triplet superconductivity observed.     

Impurity effects on lowest-energy Cooper pairing in an antiferromagnet

Isotropic scattering of electrons from nonmagnetic impurities does not suppress lowest-energy Cooper pairing in an antiferromagnet at all, and effects of non-isotropic scattering are expected to be small in magnitude. For this state, impurities substituted for magnetic ions affect the superconductivity mainly through their effects on the antiferromagnetism. Effects of nonmagnetic impurities on lowest-energy Cooper pairing in an antiferromagnet are just as though the pairing were s-wave in a nonmagnetic superconductor: in this state anisotropy of the pairing is purely a spin-density anisotropy and not a charge-density anisotropy. The Cooper pairing scheme which has lowest free energy in a perfect-crystal antiferromagnet also has lowest energy in a dirty antiferromagnet.     

Correlations and spin susceptibility of lowst-energy Cooper pairing in an antiferromagnet

Lowest-energy Cooper pairing of electron eigenfunctions in an antiferromagnetic metal is transformed to $\text{k}$-wave or nonmagnetic-Bloch-function space, where the pairing is resolved into wave-vector and spin components. The spin susceptibility is calculated using an eight-component field in Bloch function space.     

A reflection on the contrast between the Cooper pairing in iron-based and conventional superconductors

In this Perspective article we review retrospectively the streamline of our work on iron-based superconductors, and reflect on the mechanism of Cooper pairing in conventional and unconventional, such as iron-based superconductors. The main theme of this review is the concept of effective interaction and renormalization group.     

Lowest excitation energy of 9Be

Variational calculations employing explicitly correlated Gaussian functions and explicitly including the nuclear motion [i.e., without assuming the Born-Oppenheimer (BO) approximation] have been performed to determine the lowest singlet transition energy in the 9Be atom. The non-BO wave functions were used to calculate the alpha2 relativistic corrections (alpha=1/137.035,999,679). With those corrections and with the alpha3 and alpha4 QED corrections determined previously by others, we obtained 54,677.35 cm(-1) for the 3(1)S-->2(1)S transition energy. This result falls within the error bracket for the experimental transition of 54,677.26(10) cm(-1). This is the first time an electronic transition of Be has been calculated from first principles with the experimental accuracy.     

The elementary method in pairing energy

The elementary method in pairing energy calculations presented in [1] for like-nucleons has been extended to the system of protons and neutrons. It has been shown that the sophisticated results coming from the non-trivial orthogonal symmetrySO(5) in this case can be obtained with the help of the same elementary method which has been applied to the system of like-nucleons.     

Nodeless d-wave superconducting pairing due to residual antiferromagnetism in underdoped Pr2-xCexCuO4-delta

We investigate the doping dependence of the penetration depth versus temperature in electron-doped Pr(2-x)Ce(x)CuO(4-delta) using a model which assumes the uniform coexistence of (mean-field) antiferromagnetism and superconductivity. Despite the presence of a d(x2-y2) pairing gap in the underlying spectrum, we find nodeless behavior of the low-T penetration depth in the underdoped case, in accord with experimental results. As doping increases, a linear-in-T behavior of the penetration depth, characteristic of d-wave pairing, emerges as the lower magnetic band crosses the Fermi level and creates a nodal Fermi surface pocket.     

Density dependence of the energy of N Cooper pairs

We approach the analytical resolution of Richardson’s equations from which the exact energy of N Cooper pairs can be obtained, through an expansion in the dimensionless parameter associated to sample volume. We first derive the explicit solutions of these Richardson’s equations for the lowest N’s, up to fourth order in this parameter. From them, we deduce a compact expression of the N-pair energy, that we recover using a more general procedure. Our results support the recently found fact that the expression of the N-pair energy obtained at the lowest order stays valid up to the dense limit, the next order term being here shown to be underextensive due to a set of non-trivial cancellations.     

Non-empirical pairing energy density functional

We perform systematic calculations of pairing gaps in semi-magic nuclei across the nuclear chart using the Energy Density Functional method and a non-empirical pairing functional derived, without further approximation, at lowest order in the two-nucleon vacuum interaction, including the Coulomb force. The correlated single-particle motion is accounted for by the SLy4 semi-empirical functional. Rather unexpectedly, both neutron and proton pairing gaps thus generated are systematically close to experimental data. Such a result further suggests that missing effects, i.e. higher partial waves of the NN interaction, the NNN interaction and the coupling to collective fluctuations, provide an overall contribution that is sub-leading as for generating pairing gaps in nuclei. We find that including the Coulomb interaction is essential as it reduces proton pairing gaps by up to 40%.     

Kinetic energy driven pairing in cuprate superconductors

Pairing occurs in conventional superconductors through a reduction of the electronic potential energy accompanied by an increase in kinetic energy. In the underdoped cuprates, optical experiments show that pairing is driven by a reduction of the electronic kinetic energy. Using the dynamical cluster approximation we study superconductivity in the two-dimensional Hubbard model. We find that pairing is indeed driven by the kinetic energy and that superconductivity evolves from an unconventional state with partial spin-charge separation, to a superconducting state with quasiparticle excitations.     

Disordering effects in superconductors with anisotropic pairing: From Cooper pairs to compact bosons

In the weak-coupling BCS-theory approximation, normal impurities do not influence the superconducting transition temperature T _c in the case of isotropic s pairing. In the case of d pairing they result in a rapid destruction of the superconducting state. This is at variance with many experiments on the disordering of high-T _c superconductors, assuming that d pairing is realized in them. As the interelectronic attraction in a Cooper pair increases, the system transforms continuously from a BCS-type superconductor with “loose” pairs to a picture of superconductivity of “compact,” strongly coupled bosons. Near such a transition substantial deviations can be expected from the universal disorder dependence of T _c , as determined by the Abrikosov-Gor’kov equation, and T _c becomes more stable against disordering. Since high-T _c super-conducting systems fall into the transitional region from BCS-type pairs to compact bosons, these results can explain their relative stability against disordering. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 3, 258–262 (10 February 1997)     

On the role of the Coulomb interaction in the mechanism of d-wave Cooper pairing of charge carriers in high-T c superconductors

The question of the effect of the structure of the anisotropic quasi-two-dimensional electron spectrum of high-T _c superconductors on the character of the screening of the Coulomb interaction and the symmetry of the superconducting order parameter is studied. Calculations of the polarization operator of electrons are performed on the basis of the single-particle band spectrum extracted from angle-resolved photoemission spectroscopy data. It is shown that the static screened Coulomb repulsion has a minimum at small momentum transfers. This corresponds to an effective electron-electron attraction in the -wave channel of Cooper pairing of the charge carriers on account of their interaction with the long-wavelength charge-density fluctuations. This attraction together with the anisotropic electron-phonon interaction increase the critical superconducting transition temperature T _c with increasing hole density and can give quite high values of T _c while at the same time suppressing the isotope effect, in qualitative agreement with the experimental data for underdoped hole-type cuprate metal-oxide compounds. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 10, 703–710 (25 May 1999)