Charge-4e superconductivity and chiral metal in the 45°-twisted bilayer cuprates and similar materials

Abstract The material realization of the charge-4e/6e superconductivity (SC) is a big challenge. Here we propose realization of the charge-4e SC and chiral metal in a class of materials made through stacking a homo-bilayer with the largest twist angle, dubbed as the twist-bilayer quasi-crystal (TB-QC), exampled by the 45\degree-twisted bilayer cuprates and 30\degree-twisted bilayer graphene. When each mononlayer hosts a pairing state with the largest pairing angular momentum, previous studies yield 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 phase, either the total- or relative- pairing phase of the two layers can be unilateral quasi- ordered or ordered. In the form case, a Cooper pair from the top layer pairs with a Cooper pair from the bottom layer to form the charge-4e SC; in the latter case, a time-reversal symmetry breaking chiral metal phase is formed. Based on a thorough symmetry analysis, we arrive at the low-energy effective Hamiltonian describing the pairing- phase fluctuations. Our combined renormalization group and Monte-Carlo studies reveal the presence of the charge-4e SC and chiral metal phases in the phase diagram, characterized by various temperature-dependent quantities and spatial-dependent correlations.