I will present new mechanisms of electron pairing that is assisted by a third electron. Starting with a two-band Hubbard model with purely repulsive interaction, I will show explicitly and rigorously that two conduction electrons can attract and form a bound state due to the involvement of a third electron in a filled band. Two scenarios may occur, depending on the microscopic details. First, two conduction electrons may bind with the excited state of a valence electron to reduce the electrostatic repulsion. The resulting charge-2e composite object is dubbed a "trimer". Wigner crystallization of trimers lead to a pair density wave, while the condensation of trimers leads to BEC-BCS superconductivity [1]. Alternatively, even when a trimer has a large energy cost, it may induce an attraction between free electrons at low energy and produce (strong-coupling) superconductivity [2, 3]. In this scenario, the pairing glue is provided by the polarization of the valence electron lattice. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.
[1] K. Slagle and L. Fu, Phys. Rev. B 102, 235423 (2020) [2] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021) [3] V. Crepel and L. Fu, PNAS 119, e2117735119 (2022)
