Valley Jahn-Teller effect in Twisted Bilayer Graphene

Two sheets of graphene—a honeycomb lattice of carbon atoms—laid slightly askew to one another induce surprising insulating and superconductive behavior not seen in individual sheets. Up until now, most researchers have focused on how interactions among electrons in this “twisted bilayer graphene” might produce these states, but they have largely ignored the role of phonons—quantized mechanical vibrations in the atomic lattice. Here, we show how phonons could produce the observed insulating states.

When the two graphene layers are slightly rotated by a small angle, a so-called moiré pattern forms, introducing a long-wavelength modulation of the atomic lattice. Using sophisticated calculations, we find that this modulation affects not only the electronic properties of the system but also the collective lattice vibrations, or phonons. In particular, we find a set of phonon modes—dubbed moiré phonons—whose vibration intensity is modulated by this pattern. Among these moiré phonons, we find a special set that strongly couples to the electrons. When the lattice is statically deformed following the vibration of these modes, insulating states at any integer filling (i.e., whenever one electron is added per unit cell) occur, exactly where they have been observed experimentally.

The suggested electron-phonon origin for the insulating states of the twisted graphene bilayer is a game changer. The additional consequence is that superconductivity in the nearby metallic states has the same origin, leading to detailed predictions about pairing symmetries. In our view, these theoretical discoveries push the established field of apparently strongly correlated insulating and superconducting states of magic bilayers out of its present track and into a new direction.

Full paper here

Dated: October 15, 2019