Topological superconductivity, ferromagnetism, and valley-polarized phases in moire systems: Renormalization group analysis for twisted double bilayer graphene

Abstract

Recent experiments have observed possible spin- and valley-polarized insulators and spin-triplet superconductivity in twisted double bilayer graphene, a moire structure consisting of a pair of Bernal-stacked bilayer graphene. Besides the continuously tunable band widths controlled by an applied displacement field and twist angle, these moire bands also possess van Hove singularities near the Fermi surface and a field-dependent nesting which is far from perfect. Here we carry out a perturbative renormalization group analysis to unbiasedly study the competition among all possible instabilities in twisted double bilayer graphene and related systems with a similar van Hove fermiology in the presence of weak but finite repulsive interactions. Our key finding is that there are several competing magnetic, valley, charge, and superconducting instabilities arising from interactions in twisted double bilayer graphene, which can be tuned by controlling the displacement field and the twist angle. In particular, we show that spin- or valley-polarized uniform instabilities generically dominate under moderate interactions smaller than the band width, whereas $p$-wave spin-triplet topological superconductivity and exotic spin-singlet modulated paired state become important as the interactions decrease. Realization of our findings in general moire systems with a similar van Hove fermiology should open up new opportunities for manipulating topological superconductivity and spin- or valley-polarized states in highly tunable platforms.

arXiv comment11 pages, 6 figures

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• Parquet renormalization group analysis of weak-coupling instabilities with multiple high-order Van Hove points inside the Brillouin zone
• Spin-valley locked instabilities in moire transition metal dichalcogenides with conventional and higher-order Van Hove singularities
• Electric-field-tunable electronic nematic order in twisted double-bilayer graphene
• Pair density wave and loop current promoted by van Hove singularities in moiré systems
• Evolution of Superconductivity in Twisted Graphene Multilayers
• ${\phi }_0$-Josephson junction in twisted bilayer graphene induced by a valley-polarized state
• Unconventional Self-Similar Hofstadter Superconductivity from Repulsive Interactions
• Pair density wave and reentrant superconducting tendencies originating from valley polarization
• $\text{Ab initio}$ four-band Wannier tight-binding model for generic twisted graphene systems
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• Renormalization group analysis of weakly interacting van der Waals Fermi system