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 . 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.
 K. Slagle and L. Fu, Phys. Rev. B 102, 235423 (2020)  V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021)  V. Crepel and L. Fu, PNAS 119, e2117735119 (2022)