Twisted Trilayer Graphene, Quasiperiodic Superconductor

Twisted multilayer graphene is generically quasiperiodic on the moiré scale, due to the incommensurate twist angle mismatch. In this work, we show that quasiperiodic twisted trilayer graphene (TTLG) hosts robust superconductivity with rigid phase stiffness, not relying on fine-tuning to magic angles. The superconductivity can be further enhanced by stronger interlayer coupling, which is experimentally accessible by applying pressure. The enhancement of superconductivity is explained by wave function criticality of the normal states, which effectively simulate topological superconductor surface states. In particular, we demonstrate that TTLG behaves like as a critical metal, with fractal wave function statistics at all energies linked to the plateau transition of the integer quantum Hall effect. We demonstrate the criticality by large-scale wave function and Kubo conductivity calculations based on the kernel polynomial method.

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