Charge 4e superconductivity and chiral metal in the $45^\circ$-twisted bilayer cuprates and similar bilayers

TL;DR

This paper proposes a theoretical framework for realizing charge-4e superconductivity and chiral metal phases in twisted bilayer cuprates and similar materials, supported by symmetry analysis and numerical studies.

Contribution

It introduces a new mechanism for charge-4e superconductivity and chiral metal phases in twist-bilayer systems with large twist angles, expanding the understanding of unconventional superconductivity.

Findings

Phase diagram includes charge-4e SC and chiral metal phases.

Charge-4e SC emerges from unilateral pairing phase order.

Chiral topological superconductivity driven by interlayer coupling.

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 through stacking a homo-bilayer with the largest twist angle, forming the twist-bilayer quasi-crystal (TB-QC), exampled by the 45$^\circ$-twisted bilayer cuprates and 30$^\circ$-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, either the total- or relative- pairing phase of the two layers can be unilateral quasi-ordered or ordered, leading to the charge-4e SC or the chiral metal phase. 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.