p-wave superconductivity induced from valley symmetry breaking in twisted trilayer graphene

We show that the e-e interaction induces a strong breakdown of valley symmetry in twisted trilayer graphene, just before the superconducting instability develops in the hole-doped material. We analyze this effect by means of an atomistic self-consistent Hartree-Fock approximation, which is a sensible approach as the Fock part becomes crucial to capture the breakdown of symmetry. This effect allows us to reproduce the experimental observation of the Hall density, including the reset at 2-hole doping. Moreover, the breakdown of valley symmetry has important consequences for the superconductivity, as it implies a reduction of symmetry down to the C₃ group. We observe that the second valence band has a three-fold van Hove singularity, which is pinned to the Fermi level at the experimental optimal doping for superconductivity. We further find that the C₃ configuration of the saddle points leads to a version of Kohn-Luttinger superconductivity where the dominant pairing amplitude has p-wave symmetry[1]. We stress that the breakdown of symmetry down to C₃ may be shared by other materials with valley symmetry breaking, so that it may be an essential ingredient to capture there the right order parameter of the superconductivity.

[1] J. Gonzalez and T. Stauber, arXiv:2110.11294