Triplet character of 2D-fermion dimers arising from $s$-wave attraction via spin-orbit coupling and Zeeman splitting

TL;DR

This paper investigates how spin-orbit coupling and Zeeman splitting influence two-dimensional fermion dimers, revealing a dominant triplet pairing component and distinctive wave function features that suggest unconventional superfluidity.

Contribution

It provides exact solutions for two-particle bound states showing a dominant triplet component and maps out conditions for bound state existence under various spin-orbit couplings.

Findings

Triplet component dominates in bound states over a wide parameter range.

Bound states exhibit p-wave features in their wave functions.

Existence of bound states depends on center-of-mass momentum and system parameters.

Abstract

We theoretically study spin-$1/2$ fermions confined to two spatial dimensions and experiencing isotropic short-range attraction in the presence of both spin-orbit coupling and Zeeman spin splitting - a prototypical system for developing topological superfluidity in the many-body sector. Exact solutions for two-particle bound states are found to have a triplet contribution that dominates over the singlet part in an extended region of parameter space where the combined Zeeman- and center-of-mass-motion-induced spin-splitting energy is large. The triplet character of dimers is purest in the regime of weak $s$-wave interaction strength. Center-of-mass momentum is one of the parameters determining the existence of bound states, which we map out for both two- and one-dimensional types of spin-orbit coupling. Distinctive features emerging in the orbital part of the bound-state wave function, including but not limited to its $p$-wave character, provide observable signatures of unconventional pairing.