Critical Current Density in d-Wave Hubbard Superconductors

In this work, the Generalized Hubbard Model on a square lattice is applied to evaluate the electrical current density of high critical temperature d-wave superconductors with a set of Hamiltonian parameters allowing them to reach critical temperatures close to 100 K. The appropriate set of Hamiltonian parameters permits us to apply our model to real materials, finding a good quantitative fit with important macroscopic superconducting properties such as the critical superconducting temperature (Tc) and the critical current density (Jc). We propose that much as in a dispersive medium, in which the velocity of electrons can be estimated by the gradient of the dispersion relation ∇ε(k), the electron velocity is proportional to ∇E(k) in the superconducting state (where E(k)=(ε(k)-μ)2+Δ2(k) is the dispersion relation of the quasiparticles, and k is the electron wave vector). This considers the change of ε(k) with respect to the chemical potential (μ) and the formation of pairs that gives rise to an excitation energy gap Δ(k) in the electron density of states across the Fermi level. When ε(k)=μ at the Fermi surface (FS), only the term for the energy gap remains, whose magnitude reflects the strength of the pairing interaction. Under these conditions, we have found that the d-wave symmetry of the pairing interaction leads to a maximum critical current density in the vicinity of the antinodal k-space direction (π,0) of approximately 1.407236×108 A/cm², with a much greater current density along the nodal direction (π2,π2) of 2.214702×109 A/cm². These results allow for the establishment of a maximum limit for the critical current density that could be attained by a d-wave superconductor.