Charge- 4e superconductivity in a Hubbard model

A phase of matter in which fermion quartets form a superconducting condensate, rather than the paradigmatic Cooper pairs, is a recurrent subject of experimental and theoretical studies. However, a comprehensive microscopic understanding of charge-$4e$ superconductivity as a quantum phase is lacking. Here, we study a two-orbital tight-binding model with attractive Hubbard-type interactions. Such a model naturally provides the Bose-Einstein condensate as a limit for electron quartets and supports charge-$4e$ superconductivity, as we show by mapping it to a spin-1/2 chain in this perturbative limit. Using density matrix renormalization group calculations for the one-dimensional case, we further establish that the ground state is indeed a superfluid phase of $4e$ charge carriers and that this phase can be stabilized well beyond the perturbative regime. Importantly, we demonstrate that $4e$ condensation dominates over $2e$ condensation even for nearly decoupled orbitals, which is a more likely scenario in electronic materials. Our model paves the way for both experimental and theoretical exploration of $4e$ superconductivity and provides a natural starting point for future studies beyond one dimension or more intricate $4e$ states.