Yaar Vituri

Recent experiments in ABC trilayer graphene detected superconductivity on the border of a phase transition to a symmetry-broken phase. In this work, we use unrestricted Hartree-Fock to study the nature of this phase. We find a close competition between two incommensurate intervalley coherent (IVC) phases: an IVC crystal where the ordering occurs at multiple wave vectors, and an IVC spiral with a single ordering wave vector.

Probing the superconducting order parameter symmetry is a crucial step towards understanding the pairing mechanism in unconventional superconductors. Inspired by the recent discoveries of superconductivity in various van der Waals materials and the availability of the relative twist angle as a continuous tuning knob in these systems, we propose a general setup for probing the order parameter symmetry of two-dimensional superconductors in twisted Josephson junctions.

The lowest-order Josephson coupling, J1(θ)cos(ϕ), between two d-wave superconductors with a phase difference ϕ across the junction vanishes when their relative orientation is rotated by θ=π/4. However, in the presence of inhomogeneity, J1(r) is nonzero locally, with a sign that fluctuates in space. We show that such a random J1 generates a global second-harmonic Josephson coupling, J2cos(2ϕ), with a sign that favors ϕ=±π/2, i.e., spontaneous breaking of time-reversal symmetry.