Variational Solution for Electron-Phonon Coupling in Twisted Bilayer Graphene

Superconductivity in twisted bilayer graphene (TBG) emerges when the system is tuned to the magic angle, where flat bands appear, leading to strong electronic correlations. However, the exact mechanism driving this superconductivity remains not fully understood. Recent experimental findings have revealed a close relationship between superconductivity and the emergence of band replica features in nano-ARPES experiments. To explain the origin of these band replicas, we utilize a variational non-Gaussian transformation approach to simulate TBG and its variants with non-perturbative electron-phonon couplings. This method allows us to determine the ground-state and excited-state wavefunctions, reproducing the experimentally observed replica features. More importantly, our results reveal how the substrate potential of the hBN layer and finite bandwidth competes with electron-phonon coupling, suppressing the formation of band replicas. These competitions further address the experimentally observed trends, which are correlated with superconductivity. These findings shed new light on the underlying physics of unconventional superconductivity in moire systems and especially the cooperation between phonons and strong correlations.