Rashbon bound states associated with a spherical spin-orbit coupling in an ultracold Fermi gas with an $s$-wave interaction

TL;DR

This paper explores how spherical spin-orbit coupling influences rashbon bound states and superfluid transition temperatures in ultracold Fermi gases, revealing the dominance of rashbons in certain interaction regimes and their mixed parity nature.

Contribution

It extends the NSR strong-coupling theory to include spherical spin-orbit coupling, analyzing rashbon formation and superfluid transition in a unified framework.

Findings

Rashbon bound states dominate the superfluid transition in specific parameter regions.

The spin-orbit coupling induces parity mixing in bound states.

The superfluid transition temperature depends on both interaction strength and spin-orbit coupling.

Abstract

We investigate the formation of rashbon bound states and strong-coupling effects in an ultracold Fermi gas with a spherical spin-orbit interaction, $H_{\rm so}=\lambda{\bf p}\cdot{\bf \sigma}$ (where ${\bf \sigma}=(\sigma_x,\sigma_y,\sigma_z)$ are Pauli matrices). Extending the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink (NSR) to include this spin-orbit coupling, we determine the superfluid phase transition temperature $T_{\rm c}$, as functions of the strength of a pairing interaction $U_s$, as well as the spin-orbit coupling strength $\lambda$. Evaluating poles of the NSR particle-particle scattering matrix describing fluctuations in the Cooper channel, we clarify the region where rashbon bound states dominate the superfluid phase transition in the $U_{s}$-$\lambda$ phase diagram. Since the antisymmetric spin-orbit interaction $H_{\rm so}$ breaks the inversion symmetry of the system, rashbon bound states naturally have, not only a spin-singlet and even-parity symmetry, but also a spin-triplet and odd-parity symmetry. Thus, our results would be also useful for the study of this parity mixing effect in the BCS-BEC crossover regime of a spin-orbit coupled Fermi gas.