- Series
- Math Physics Seminar
- Time
- Friday, February 20, 2026 - 11:00am for 1 hour (actually 50 minutes)
- Location
- Skyles 006
- Speaker
- Vieri Mastropietro – Universita' di Roma “La Sapienza”, Department of Physics, Rome, Italy – vieri.mastropietro@uniroma1.it
- Organizer
- Federico Bonetto
We consider a lattice model of twisted bilayer graphene (TBG) for incommensurate twist angles, focusing on the role of large-momentum-transfer Umklapp terms. These terms, which nearly connect the Fermi points of different layers, are typically neglected in effective continuum descriptions but could, in principle, destroy the Dirac cones; they are indeed closely analogous to those appearing in fermions within quasi-periodic potentials, where they play a crucial role. We prove that, for small but finite interlayer coupling, the semimetallic phase is stable provided the angles belong to a fractal set of large measure (which decreases with the hopping strength) characterized by a number theoretic Diophantine condition. In particular, this set excludes the (zero measure) commensurate angles. Our method combines a Renormalization Group (RG) analysis of the imaginary-time, zero temperature Green’s functions, with number theoretic properties, and is similar to the technique used in the Lindstedt series approach to Kolmogorov-Arnold-Moser (KAM) theory. The convergence of the resulting series allows us to rule out non-perturbative effects. The result provides a partial justification of the effective continuum description of TBG in which such large-momentum interlayer hopping processes are neglected.
Work in collaboration with Ian Jauslin
Available on zoom at:
https://gatech.zoom.us/j/92212527205?jst=4