V. I. Belyavsky

Mirror nesting of the Fermi contour and zero line of the superconducting order parameter

The superconducting order parameter that emerges owing to pairing of charge carriers with a large total momentum of the pair during screened Coulomb repulsion in a degenerate quasi-two-dimensional electronic system is determined as a function of the momentum of relative motion of the pair. In view of the kinematic constraint associated with Fermi filling, the ordered state exists in a limited domain of the momentum space, the shape and size of this domain being determined by the total momentum of the pair. The order parameter is not a constant-sign function of the momentum and reverses its sign on a certain line in a kinematically allowed domain. Superconducting instability arises for an arbitrarily small value of the repulsive interaction for certain momenta of the pair, for which the mirror nesting condition is satisfied; this results in the formation of a pair Fermi contour, i.e., the line of coincidence of segments of the Fermi contour with the isoline of the kinetic energy of relative motion of the pair. The temperature dependence of the superconducting order parameter is studied. Owing to the proximity effect in the momentum space, superconducting ordering is extended to the kinematically forbidden domain.

Biordered superconductivity and strong pseudogap state

Interrelation between the two-particle and mean-field problems is used to describe the strong pseudogap and superconducting states in cuprates. We present strong pseudogap state as off-diagonal short-range order (ODSRO) originating from quasi-stationary states of the pair of repulsing particles with large total momentum (K - pair). Phase transition from the ODSRO state into the off-diagonal long-range ordered (ODLRO) superconducting state is associated with Bose-Einstein condensation of the K - pairs. A checkerboard spatial order observable in the superconducting state in the cuprates is explained by a rise of the K - pair density wave. A competition between the ODSRO and ODLRO states leads to the phase diagram typical of the cuprates. Biordered superconducting state of coexisting condensates of Cooper pairs with zero momentum and K - pairs explains some properties of the cuprates observed below Tc: Drude optical conductivity, unconventional isotope effect and two-gap quasiparticle spectrum with essentially different energy scales.

Mirror nesting and electron-hole asymmetry at repulsive superconducting pairing

The dependence of the superconducting order parameter Δ(k) on the momentum of the relative motion of a pair with a large total momentum K is numerically studied for the case of repulsive pairing with allowance for the kinematic and insulator constraints on the momentum transfer at scattering. The Fermi contour with nesting and mirror nesting, which is typical of cuprates and optimal for repulsion-induced superconductivity, lies in an extended vicinity of the saddle points of the dispersion law. A deviation from the mirror nesting cuts off the logarithmic singularity from below and bounds the pre-exponent in Δ(k). The effective coupling constant is determined by the degree of the electron-hole asymmetry. The suppression of the contribution of small momentum transfer processes by the impurity and electron-phonon scattering favors an increase in the order parameter amplitude. The nesting of the Fermi contour causes a Peierls singularity in the Coulomb interaction. The self-consistency equation allows the solutions that may be both antisymmetric and symmetric with respect to the momentum inversion. The maximum-amplitude antisymmetric solution in the case of a singlet pairing can be realized only for K ≠ 0.

Mirror Nesting of the Fermi Contour and Superconducting Pairing from the Repulsive Interaction

We consider the necessary conditions of superconducting pairing at repulsive interaction between particles composing a pair with large total momentum: (1) the existence of, at least, one negative eigenvalue of the repulsion potential and (2) mirror nesting of the Fermi contour. Under these conditions, we represent the solution of the self-consistency equation continuously depending on the momentum of the relative motion of the pair. The corresponding superconducting order parameter changes its sign on a line crossing the Fermi contour inside the domain of definition of the relative motion pair momentum. We argue that repulsive-induced superconducting pairing with large total pair momentum maybe just the case relating to high-temperature superconducting cuprates.

Macroscopic description of superconducting pairing under repulsive interaction

The order parameter of a quasi-two-dimensional electron system in which superconducting pairing with large momentum and repulsive interaction occurs represents an alternating function of the momentum of the relative motion of a pair. This function vanishes at points on the Fermi contour (FC) segments inside each equivalent domain of kinematic constraint. The superfluid density is proportional to the area of such a domain. When the pairing interaction is repulsive, the order parameter can be described by a two-component complex function of coordinates that represents a solution to a system of two Ginzburg-Landau differential equations. The characteristic size of a pair, which is determined by the effective mass rather than the velocity of an electron near the FC, as well as the penetration depth and the correlation length for the fluctuations of the order parameter are obtained. The order parameter forms incommensurable quasi-periodic structures that arise under long-wavelength fluctuations of the phase and correspond to antiferromagnetically ordered current circulations. The pairing channel considered provides a qualitative description for the characteristic features of superconductivity in cuprates.

Topological d-wave superconductor

The hypothetical topologically nontrivial superconducting state of a two-dimensional electron system is discussed in connection with the problem of high-temperature superconductivity of cuprates. Direct numerical solution of the self-consistency equation exhibits two nearly degenerate order parameters which can be formally referred to

Superconductivity in Homologous Series of Cuprates: Deep Oscillations of the Pairing Coulomb Potential

d_{x^2 - y^2 }

Topology of the Fermi surface and the coexistence of orbital antiferromagnetism and superconductivity in cuprates

and dxy orbital symmetry. Spontaneous breaking of the time-reversal symmetry can mix these states and form fully gapped chiral d + id superconducting state.