Twisted Trilayer Graphene, Quasiperiodic Superconductor

Abstract

Twisted multilayer moir\'e materials are generically quasiperiodic on the moir\'e scale due to the interference of different misaligned moir\'e periodicities. Spatial inhomogeneities such as these can be detrimental to superconductivity; nonetheless, superconductivity has been observed in quasiperiodic twisted trilayer graphene (TTG). Here, we systematically study the superconducting properties of TTG. We reveal that an interplay between quasiperiodicity and topology drives TTG into a critical regime, enabling it to host superconductivity with rigid phase stiffness for a wide range of twist angles, rather than at a fine-tuned value. The criticality in the normal state is due to the Dirac fermions coupled by quasiperiodic tunneling simulating 3D topological superconductor surface states. This critical-metal regime is marked by multifractal wave functions across the spectrum and scale-invariant transport reminiscent of the integer quantum Hall plateau transition. We demonstrate this with large-scale wave function and Kubo conductivity calculations. These observations lead to a clear experimental implication: stronger interlayer coupling in TTG further stabilizes both the criticality and superconductivity, allowing superconductivity to be seen across a wider range of angles with experimentally accessible pressures.