biostudies-literatureLiu YBNational Natural Science Foundation of China (National Science Foundation of China)7926https://www.ebi.ac.uk/biostudies/studies/S-EPMC10692084biostudies-literatureUnknown14(1)The material realization of charge-4e/6e superconductivity (SC) is a big challenge. Here, we propose to realize charge-4e SC in maximally-twisted homobilayers, such as 45^∘-twisted bilayer cuprates and 30^∘-twisted bilayer graphene, referred to as twist-bilayer quasicrystals (TB-QC). When each monolayer hosts a pairing state with the largest pairing angular momentum, previous studies have found that the second-order interlayer Josephson coupling would drive chiral topological SC (TSC) in the TB-QC. Here we propose that, above the T_c of the chiral TSC, either charge-4e SC or chiral metal can arise as vestigial phases, depending on the ordering of the total- and relative-pairing-phase fields of the two layers. Based on a thorough symmetry analysis to get the low-energy effective Hamiltonian, we conduct a combined renormalization-group and Monte-Carlo study and obtain the phase diagram, which includes the charge-4e SC and chiral metal phases.Nature communicationsCharge-4e superconductivity and chiral metal in 45°-twisted bilayer cuprates and related bilayers.PMC1069208411674025Wu CLiu YBYang FZhou JfalseCharge-4e superconductivity and chiral metal in 45°-twisted bilayer cuprates and related bilayers.The material realization of charge-4e/6e superconductivity (SC) is a big challenge. Here, we propose to realize charge-4e SC in maximally-twisted homobilayers, such as 45^∘-twisted bilayer cuprates and 30^∘-twisted bilayer graphene, referred to as twist-bilayer quasicrystals (TB-QC). When each monolayer hosts a pairing state with the largest pairing angular momentum, previous studies have found that the second-order interlayer Josephson coupling would drive chiral topological SC (TSC) in the TB-QC. Here we propose that, above the T_c of the chiral TSC, either charge-4e SC or chiral metal can arise as vestigial phases, depending on the ordering of the total- and relative-pairing-phase fields of the two layers. Based on a thorough symmetry analysis to get the low-energy effective Hamiltonian, we conduct a combined renormalization-group and Monte-Carlo study and obtain the phase diagram, which includes the charge-4e SC and chiral metal phases.2023-01-01T00:00:00Z2023 Dec2025-04-04T09:39:39.576Z2025-04-04T09:39:39.576ZS-EPMC106920843804076410.1038/s41467-023-43782-2