Binding energy of a Cooper pairs with non-zero center of mass momentum in d-wave superconductors

TL;DR

This paper calculates the binding energy of Cooper pairs with non-zero total momentum in d-wave layered cuprate superconductors, revealing anisotropic depairing properties through numerical solutions of self-consistent equations.

Contribution

It introduces a detailed calculation of the binding energy for finite-momentum Cooper pairs in d-wave superconductors, including anisotropic depairing momentum analysis.

Findings

Numerical solutions for gap functions x(q), y(q), x(q), y(q) along different q directions.

Anisotropic depairing momentum and current in d-wave superconductors.

Quantitative analysis of Cooper pair binding energy with finite total momentum.

Abstract

The binding energy of Cooper pairs has been calculated for the case of d-wave symmetry of the superconducting gap in layered cuprate superconductors. We assume that Cooper pairs are formed by the short range potential and then derive the binding energy in the form Delta_kq = \Delta_x(q)cos(k_xa) + \Delta_y(q)cos(k_ya) + \Omega_x(q)sin(k_xa) + \Omega_y(q)sin(k_ya), where q is a total momentum of the pair. Numerical solutions of the self-consistent system of the integral equations for quantities \Delta_x(q), \Delta_y(q) and \Omega_x(q), \Omega_y(q) along different lines in q_x, q_y plane have been obtained. Anisotropy of the depairing total momentum (or depairing current) has been calculated.