Spin-orbit-assisted electron pairing in one-dimensional waveguides

Understanding and controlling the transport properties of interacting fermions is a key forefront in quantum physics across a variety of experimental platforms. Motivated by recent experiments in one-dimensional (1D) electron channels written on the LaAlO3/SrTiO3 interface, we analyze how the presence of different forms of spin-orbit coupling (SOC) can enhance electron pairing in 1D waveguides. We first show how the intrinsic Rashba SOC felt by electrons at interfaces such as LaAlO3/SrTiO3 can be reduced when they are confined in one dimension. Then, we discuss how SOC can be engineered, and show using a mean-field Hartree-Fock-Bogoliubov model that SOC can generate and enhance spin-singlet and -triplet electron pairing. Our results are consistent with two recent sets of experiments [Briggeman, Nat. Phys. 17, 782787 (2021)10.1038/s41567-021-01217-z; Sci. Adv. 6, eaba6337 (2020)10.1126/sciadv.aba6337] that are believed to engineer the forms of SOC investigated in this work, which suggests that metal-oxide heterostructures constitute attractive platforms to control the collective spin of electron bound states. However, our findings could also be applied to other experimental platforms involving spinful fermions with attractive interactions, such as cold atoms.