Nonstandard Hubbard model and electron pairing

TL;DR

This paper introduces a non-standard Hubbard model with a new Wannier function treatment, revealing a novel pairing mechanism driven by long-range interactions that could impact understanding of superconductivity and metal-insulator transitions.

Contribution

It develops a perturbative approach to define Wannier functions for arbitrary potentials, deriving a Hubbard Hamiltonian with new tunneling terms and uncovering a long-range interaction-induced pairing mechanism.

Findings

Long-range interactions induce electron pairing without an insulating state.

Density-induced tunneling suppresses single-electron motion, favoring pair coherence.

Implications for flat bands, superconductivity, and metal-insulator transitions.

Abstract

We present a non-standard Hubbard model applicable to arbitrary single-particle potential profiles and inter-particle interactions. Our approach involves a novel treatment of Wannier functions, free from the ambiguities of conventional methods and applicable to finite systems without periodicity constraints. To ensure the consistent evaluation of Wannier functions, we develop a perturbative approach, utilizing the barrier penetration coefficient as a perturbation parameter. With the newly defined Wannier functions as a basis, we derive the Hubbard Hamiltonian, revealing the emergence of density-induced and pair tunneling terms alongside standard contributions. Our investigation demonstrates that long-range inter-particle interactions can induce a novel mechanism for repulsive particle pairing. This mechanism relies on the effective suppression of single-particle tunneling due to density-induced tunneling. Contrary to expectations based on the standard Hubbard model, an increase in inter-particle interaction does not lead to an insulating state. Instead, our proposed mechanism implies the coherent motion of correlated electron pairs, similar to bound states within a multi-well system, resistant to decay from single-electron tunneling transitions. These findings carry significant implications for various phenomena, including the formation of flat bands, the emergence of superconductivity in twisted bilayer graphene, and the possibility of a novel metal-insulator transition.