Universal wave function statistics and superconductivity in quasiperiodic twisted trilayer graphene

Twisted multilayer graphene (TMG) was recently discovered to host superconductivity and offers a much richer playground to study moiré physics, with more knobs to tune including multiple twist angles. The low-energy physics of TMG is described by multi-cone Dirac fermions coupled with matrix-value fields, which are effectively topological when inter-valley scattering is suppressed. The topology protection prevents the wave functions from being Anderson (or Wannier) localized by quasiperiodicity; the latter is natural in TMG with 3 or more layers due to inevitable interlayer twist-angle differences. Here we focus on quasiperiodic twisted trilayer graphene (TTG). We employ two different models, with and without a collinear approximation for the moiré wavevectors [1]. We show that quasiperiodic TTG behaves like a dirty surface of a bulk class-AIII topological insulator, and exhibits "spectrum-wide quantum criticality" [2] that is robust in the absence of exotic surface-coupling scenarios [3]. This implies that superconductivity can be enhanced without fine-tuning to magic angles, as was previously shown in a model of quasiperiodic TBLG [4]. We will also explore how the chiral symmetry breaking terms affects the wave function statistics and superconductivity.

[1] Ziyan Zhu, Stephen Carr, Daniel Massatt, Mitchell Luskin, and Efthimios Kaxiras, PRL 125, 116404 (2020)

[2] Björn Sbierski, Jonas F. Karcher, and Matthew S. Foster, PRX 10, 021025 (2020)

[3] Alexander Altland, Piet W. Brouwer, Johannes Dieplinger, Matthew S. Foster, Mateo Moreno-Gonzalez, and Luka Trifunovic, PRX 14, 011057 (2024)

[4] Xinghai Zhang, Justin H. Wilson, and Matthew S. Foster, arXiv:2406.06676.