Lowest energy Cooper pairing in the presence of antiferromagnetism

Cooper pairing of electron eigenstates of an antiferromagnet involves considerable complexity in spin space and in phases of the order parameters. With a BCS interaction the pairing scheme with lowest free energy has anisotropic spin-matrix order parameter $\textcolor{red}{}\text{(}\text{k}\text{); however}\textcolor{red}{}{}^{\mathrm{+}}\text{(}\text{k}\text{)}\textcolor{red}{}\text{(}\text{k}\text{)=|△|}{}^2\textcolor{red}{}$. Magnitude of the anisotropic order parameter satisfies the simple BCS gap equation but with electron energies of the antiferromagnet eigenstates appearing instead of Bloch state energies of the nonmagnetic crystal.     

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.     

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.     

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)     

Possible pairing of spatially separated electrons and holes in the presence of peierls transition

We investigate a model of two quasi-one-dimensional systems with electron and hole conductivity. We find that in general, Peierls ordering suppresses the possible excitonic pairing of the spatially separated electrons and holes.     

Quantum antiferromagnetism in quasicrystals

The antiferromagnetic Heisenberg model is studied on a two-dimensional bipartite quasiperiodic lattice. Using the stochastic series expansion quantum Monte Carlo method, the distribution of local staggered magnetic moments is determined on finite square approximants with up to 1393 sites, and a nontrivial inhomogeneous ground state is found. A hierarchical structure in the values of the moments is observed which arises from the self-similarity of the quasiperiodic lattice. The computed spin structure factor shows antiferromagnetic modulations that can be measured in neutron scattering and nuclear magnetic resonance experiments. This generic model is a first step towards understanding magnetic quasicrystals such as the recently discovered Zn-Mg-Ho icosahedral structure.     

Kinetic antiferromagnetism in the triangular lattice

We show that the motion of a single hole in the infinite-U Hubbard model with frustrated hopping leads to weak metallic antiferromagnetism of kinetic origin. An intimate relationship is demonstrated between the simplest versions of this problem in one and two dimensions, and two of the most subtle many body problems, namely, the Heisenberg Bethe ring in one dimension and the two-dimensional triangular lattice Heisenberg antiferromagnet.     

Field-induced antiferromagnetism in the Kondo insulator

The Kondo lattice model, augmented by a Zeeman term, serves as a useful model of a Kondo insulator in an applied magnetic field. A variational mean field analysis of this system on a square lattice, backed up by quantum Monte Carlo calculations, reveals an interesting separation of magnetic field scales. For Zeeman energy comparable to the Kondo energy, the spin gap closes and the system develops transverse staggered magnetic order. The charge gap, however, remains robust up to a higher hybridization energy scale, at which point the canted antiferromagnetism is exponentially suppressed and the system crosses over to a nearly metallic regime. Quantum Monte Carlo simulations support this mean field scenario. An interesting rearrangement of spectral weight with magnetic field is found.     

Room-temperature antiferromagnetism in CuMnAs

We report on an experimental and theoretical study of CuMn-V compounds. In agreement with previous works we find low-temperature antiferromagnetism with Néel temperature of 50 K in the cubic half-Heusler CuMnSb. We demonstrate that the orthorhombic CuMnAs is a room-temperature antiferromagnet. Our results are based on X-ray diffraction, magnetization, transport, and differential thermal analysis measurements, and on density-functional theory calculations of the magnetic structure of CuMn-V compounds. In the discussion part of the paper we make a prediction, based on our density-functional theory calculations, that the electronic structure of CuMn-V compounds makes a transition from a semimetal to a semiconductor upon introducing the lighter group-V elements.