Enhanced stability of bound pairs at nonzero lattice momenta

TL;DR

This paper investigates how the stability of bound pairs in a two-body lattice system depends on their total momentum, revealing increased stability at nonzero momenta and potential hot spots for pairing.

Contribution

It derives exact pairing conditions for different symmetries and shows how pair stability varies with momentum, especially near the Brillouin zone boundary.

Findings

Pair stability increases with total momentum K.

Pairs form more easily along the (π,0) direction.

Stable pairs appear near the Brillouin zone boundary.

Abstract

A two-body problem on the square lattice is analyzed. The interaction potential consists of strong on-site repulsion and nearest-neighbor attraction. Exact pairing conditions are derived for s-, p-, and d-symmetric bound states. The pairing conditions are strong functions of the total pair momentum K. It is found that the stability of pairs increases with K. At weak attraction, the pairs do not form at the $\Gamma$-point but stabilize at lattice momenta close to the Brillouin zone boundary. The phase boundaries in the momentum space, which separate stable and unstable pairs are calculated. It is found that the pairs are formed easier along the $(\pi,0)$ direction than along the $(\pi,\pi)$ direction. This might lead to the appearance of ``hot pairing spots" on the Kx and Ky axes.