Spin-valley antiferromagnetism and topological superconductivity in the trilayer graphene Moire super-lattice

Abstract

Exotic correlated insulating phases emerge in the ABC-stacked trilayer graphene-boron nitride Moire super-lattice at both quarter and half-filling. A single-band minimal model with valley contrasting staggered-flux is proposed to capture the relevant band structure, where the conspiracy of perfect Fermi-surface nesting and van Hove singularity strongly enhance the valley fluctuation, leading to inter-valley spiral (IVS) order at half filling. In this paper, we consider a strong coupling U(1)${}_v\times$SU(2)${}_s$ symmetric spin-valley model to obtain the correlated insulating state and the pairing instability near quarter filling. A significant ingredient in the strong coupling model is the Dzyaloshinsky-Moriya like interaction inherited from the flux, which breaks not only the valley SU(2)${}_v$ symmetry but also the sub-valley spatial reflection symmetry. We discuss all the possible long-range orders stabilized by the effective spin-valley-exchange interactions, and it turns out that the flux remarkably enhance the ferro-spin inter-valley 120${}^{\circ }$ order, which shares the same valley feature as the IVS order. Upon doping, the leading pairing instability lies in the inter-valley channel with a trigonally warped $p\pm ip$-wave form factor in the presence of the sub-valley reflection symmetry breaking. Depending on the sign of Hund's coupling, the total pairing state could be either spin singlet or triplet. While the spin singlet chiral topological pairing state $(p\pm ip{)}_{\uparrow \downarrow }-(p\pm ip{)}_{\downarrow \uparrow }$ is necessarily chiral, the spin triplet topological pairing state could be chiral $(p\pm ip{)}_{\uparrow \uparrow }+(p\pm ip{)}_{\downarrow \downarrow }$, or helical $(p\pm ip{)}_{\uparrow \uparrow }+(p\mp ip{)}_{\downarrow \downarrow }$.

arXiv comment11 pages, 6 figures, revised version

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