Coexistence of spin‐singlet s‐ and d‐wave and spin‐triplet p‐wave order parameters in anisotropic superconductors

Abstract

A two-dimensional model of an anisotropic superconductor with a relatively wide partially filled conduction band and a dispersion relation implying singularities in the density of states is considered. Employing the conformal transformation method and choosing the Fourier harmonics as the complete and orthogonal basis for 4v C irreducible representations the symmetry of the superconducting order parameter is identified. Detailed numerical calculations are carried out for the two-dimensional tight-binding band model and compared with the results obtained within the BCS-type approximation. Diagrams of stable superconducting states in the coordinates V coincide, whereas the tight-binding results and some obtained within the BCS-type approximation are dissimilar. The influence of the attractive or repulsive onsite interaction on the stability of the s-wave order parameter is explained. The developed and widely illustrated formalism can be easily applied to some more composed models.

Simple analytical model of the effect of high pressure on the critical temperature and other thermodynamic properties of superconductors

“…Also, in reference to the quoted ab-initio results, one might introduce a number of various fluctuations (peaks) in the density of states in the form , where x i is the distance of the i -th fluctuation from the Fermi level and x i as well as χ i can be either positive or negative 80 . Such an approach should make possible to improve the accuracy of the description of thermodynamic properties of some simple and composed superconducting systems 7,21–23,26 . However, the most promising case seems to be the one when just two fluctuations are included.…”

“…As a closing remark, let us emphasize that although the approach presented in this paper corresponds to the Van Hove Scenario, it is obtained in a quite general manner by applying the more general conformal transformation method, that includes the Van Hove Scenario as its special case 3,7,8,20,27,35,41,88 .…”

On New Families of Integrals in Analytical Studies of Superconductors within the Conformal Transformation Method

“…Let us also emphasize that although the case = 0 corresponds to the Van Hove Scenario, the case > 0 can be properly discussed in the conformal transformation method only [7,[21][22][23]30]. One should then include additional functions 2 ( ), for = 1, 2, .…”

“…These include 2 Advances in Condensed Matter Physics high-copper-oxide quasi two-dimensional superconducting systems and various doped superconducting compounds such as spinel-and perovskite-type structures of superconducting compounds of a trivalent rare-earth and a divalent alkali-earth ion. Other classes of superconducting materials that have been actively studied in recent years include novel superconducting compounds of MgB 2 with a C, Al, or Sc substitution, or organic superconductors with a controlled bandwidth and band filling [7,11,[15][16][17][18][19][20][21][22]. Theoretical description of such superconducting systems requires to take into account spin-fluctuations or strong-correlation effects.…”

New classes of integrals inherent in the mathematical structure of extended equations describing superconducting systems

“…Other classes of superconducting materials that have been actively studied in recent years include novel superconducting compounds of MgB 2 with a C, Al or Sc substitution, or organic superconductors with a controlled bandwidth and band filling. 5,6,[10][11][12][13][17][18][19][20] Over the past few years, research on superconducting systems and their applications has been gaining new momentum after the seminal discovery of superconductivity in fluorine-doped LaOFeP. 14 This has brought iron-based superconductors containing quasi-2D FeAs or FeSe layers to the front line of the modern superconductivity research.…”