Exact solution for finite center-of-mass momentum Cooper pairing

Cooper’s proof that the Fermi surface of a metal is unstable to a weak attractive potential between two quasi-particles laid the foundation for a subsequent comprehensive theory of superconductivity in elemental metals by Bardeen, Cooper and Schrieffer. The resulting bound state of the two quasi-particles, termed a “Cooper pair”, contains zero center-of-mass momentum and constitutes the basic building block of a superconductor.But Is there an analog of the Cooper argument for finite center-of-mass momentum pairing?

In this talk, authors choose the interaction form with d-wave symmetry. The main finding is the stability of a finite center-of-mass momentum pair over a uniform solution with zero center of mass momentum (Q = 0) above a critical interaction strength. Furthermore, they construct a variational ansatz for the ground state wave function of the many-body problem. These results provide inspiration for explaining the presence of Pair Density Waves (PDWs) in various superconducting materials.

[1]Bardeen, John, Leon N. Cooper, and John Robert Schrieffer. "Theory of superconductivity." Physical review 108.5 (1957): 1175.

[2]Setty, Chandan, et al. "Exact solution for finite center-of-mass momentum Cooper pairing." arXiv preprint arXiv:2209.10568 (2022).