Correlated Insulators, Semimetals, and Superconductivity in Twisted Trilayer Graphene

Abstract

Motivated by recent experiments indicating strong superconductivity and intricate correlated insulating and flavor-polarized physics in mirror-symmetric twisted-trilayer graphene, we study the effects of interactions in this system close to the magic angle, using a combination of analytical and numerical methods. We identify asymptotically exact correlated many-body ground states at all integer filling fractionsνof the flat bands. To determine their fate when moving away from these fine-tuned points, we apply self-consistent Hartree-Fock numerics and analytic perturbation theory, with good agreement between the two approaches. This allows us to construct a phase diagram for the system as a function ofνand the displacement field, the crucial experimental tuning parameter of the system, and study the spectra of the different phases. The phase diagram is dominated by a correlated semimetallic intervalley coherent state and an insulating sublattice-polarized phase around charge neutralityν=0, with additional spin polarization being present at quarter (ν=−2) or three-quarter (ν=+2) fillings of the quasiflat bands. We further study the superconducting instabilities emerging from these correlated states, both in the absence and in the additional presence of electron-phonon coupling, also taking into account possible Wess-Zumino-Witten terms. In the experimentally relevant regime, we find triplet pairing to dominate, possibly explaining the observed violation of the Pauli limit. Our results have several consequences for experiments as well as future theoretical work and illustrate the rich physics resulting from the interplay of almost-flat bands and dispersive Dirac cones in twisted-trilayer graphene.

Alternate abstract:

Plain Language Summary

The remarkable physics of twisted bilayer graphene—two sheets of graphene stacked at slight angles to one another—has inspired many incarnations of twisted materials in the last few years. A recent notable example is mirror-symmetric twisted trilayer graphene, where three layers of graphene are stacked with alternating twist angles. It exhibits robust superconductivity, alongside various other correlated phases, and can be efficiently tuned with an electric field, making trilayer graphene an exciting platform for exploring strongly correlated physics. Here, we study the phase diagram of this system to better understand the nature of its correlated insulating, semimetal, and superconducting phases.

We numerically and analytically study the phase diagram as a function of the electric field, the type of electron tunneling between adjacent graphene layers, and the number of electrons per unit cell. We show that the ground state of the system in the absence of an electric field decouples into a product of the ground state of graphene and that of twisted bilayer graphene. Our results further establish the dominance of insulating and semimetallic phases in the presence of an electric field, which are unique to the trilayer system. We use our resulting phase diagram for the correlated normal states to constrain the form of the superconductor, considering different pairing mechanisms.

Our results provide a possible origin for several previously unexplained aspects of trilayer experiments and shed light on the energetics at play in the system. Furthermore, the properties of the correlated phases we find are expected to be useful for the interpretation of future experiments and, as such, help elucidate the complex physics in mirror-symmetric twisted trilayer graphene.