Robust and reentrant superconductivity in magic-angle twisted trilayer graphene

The recent discovery of superconductivity in magic-angle twisted trilayer graphene (MATTG) has sparked significant interest. Here we focus on MATTG, where the low energy flat bands and linearly dispersive Dirac bands coexist and can be decoupled by external fields. Using a continuum model, we examine the low-energy electronic structures and superconductivity for various external fields and small lateral shifts. We find that small lateral shifts play a crucial role by interacting with magnetic fields to increase the density of states in the flat bands, resulting in an anomalous superconducting phenomenon that strengthens with increasing magnetic field strength. Electric displacement fields and sublattice polarization, even though both break the $C_2{M}_h$ symmetry, contribute in opposite ways to the robustness of superconductivity. The interplay of these mechanisms can give rise to reentrant superconductivity under specific parameter settings. Our findings provide insights into the external field-regulated robustness and reentrant superconductivity in the MATTG system.