Abstract

The origin of superconductivity in twisted bilayer graphene – whether phonon-driven or electron-driven – remains unresolved, in part due to the absence of a quantitative and efficient model for electron-phonon coupling (EPC). In this work, we develop a first-principles-based microscopic theory to calculate EPC in twisted bilayer graphene for arbitrary twist angles without requiring a periodic moiré supercell. Our approach combines a momentum-space continuum model for both electronic and phononic structures with a generalized Eliashberg-McMillan theory beyond the adiabatic approximation. Using this framework, we find that the EPC is strongly enhanced near the magic angle. The superconducting transition temperature induced by low-energy phonons peaks at 1.1° around 1 K, and remains finite for a range of angles both below and above the magic angles. We predict that superconductivity persists up to ∼1.4°, where superconductivity has been recently observed despite the dispersive electronic bands. Beyond a large density of states, we identify a key condition for strong EPC: resonance between the electronic bandwidth and the dominant phonon frequencies. We also show that the EPC strength of a specific phonon corresponds to the modification of the moiré potential. In particular, we identify several Γ-phonon branches that contribute most significantly to the EPC, which are experimentally detectable via Raman spectroscopy.

Abstract

The origin of superconductivity in twisted bilayer graphene – whether phonon-driven or electron-driven – remains unresolved, in part due to the absence of a quantitative and efficient model for electron-phonon coupling (EPC). In this work, we develop a first-principles-based microscopic theory to calculate EPC in twisted bilayer graphene for arbitrary twist angles without requiring a periodic moiré supercell. Our approach combines a momentum-space continuum model for both electronic and phononic structures with a generalized Eliashberg-McMillan theory beyond the adiabatic approximation. Using this framework, we find that the EPC is strongly enhanced near the magic angle. The superconducting transition temperature induced by low-energy phonons peaks at 1.1° around 1 K, and remains finite for a range of angles both below and above the magic angles. We predict that superconductivity persists up to ∼1.4°, where superconductivity has been recently observed despite the dispersive electronic bands. Beyond a large density of states, we identify a key condition for strong EPC: resonance between the electronic bandwidth and the dominant phonon frequencies. We also show that the EPC strength of a specific phonon corresponds to the modification of the moiré potential. In particular, we identify several Γ-phonon branches that contribute most significantly to the EPC, which are experimentally detectable via Raman spectroscopy.

Abstract

The origin of superconductivity in twisted bilayer graphene – whether phonon-driven or electron-driven – remains unresolved, in part due to the absence of a quantitative and efficient model for electron-phonon coupling (EPC). In this work, we develop a first-principles-based microscopic theory to calculate EPC in twisted bilayer graphene for arbitrary twist angles without requiring a periodic moiré supercell. Our approach combines a momentum-space continuum model for both electronic and phononic structures with a generalized Eliashberg-McMillan theory beyond the adiabatic approximation. Using this framework, we find that the EPC is strongly enhanced near the magic angle. The superconducting transition temperature induced by low-energy phonons peaks at 1.1° around 1 K, and remains finite for a range of angles both below and above the magic angles. We predict that superconductivity persists up to ∼1.4°, where superconductivity has been recently observed despite the dispersive electronic bands. Beyond a large density of states, we identify a key condition for strong EPC: resonance between the electronic bandwidth and the dominant phonon frequencies. We also show that the EPC strength of a specific phonon corresponds to the modification of the moiré potential. In particular, we identify several Γ-phonon branches that contribute most significantly to the EPC, which are experimentally detectable via Raman spectroscopy.

Abstract

The origin of superconductivity in twisted bilayer graphene – whether phonon-driven or electron-driven – remains unresolved, in part due to the absence of a quantitative and efficient model for electron-phonon coupling (EPC). In this work, we develop a first-principles-based microscopic theory to calculate EPC in twisted bilayer graphene for arbitrary twist angles without requiring a periodic moiré supercell. Our approach combines a momentum-space continuum model for both electronic and phononic structures with a generalized Eliashberg-McMillan theory beyond the adiabatic approximation. Using this framework, we find that the EPC is strongly enhanced near the magic angle. The superconducting transition temperature induced by low-energy phonons peaks at 1.1° around 1 K, and remains finite for a range of angles both below and above the magic angles. We predict that superconductivity persists up to ∼1.4°, where superconductivity has been recently observed despite the dispersive electronic bands. Beyond a large density of states, we identify a key condition for strong EPC: resonance between the electronic bandwidth and the dominant phonon frequencies. We also show that the EPC strength of a specific phonon corresponds to the modification of the moiré potential. In particular, we identify several Γ-phonon branches that contribute most significantly to the EPC, which are experimentally detectable via Raman spectroscopy.