Nematic superconductivity in magic-angle twisted bilayer graphene from atomistic modeling

Abstract

Twisted bilayer graphene (TBG) develops large moiré patterns at small twist angles with flat energy bands hosting domes of superconductivity. The large system size and intricate band structure have however hampered investigations into the superconducting state. Here, using full-scale atomistic modelling with local electronic interactions, we find at and above experimentally relevant temperatures a highly inhomogeneous superconducting state with nematic ordering on both atomic and moiré length scales. The nematic state has a locally anisotropic real-valued d-wave pairing, with a nematic vector winding throughout the moiré pattern, and is three-fold degenerate. Although d-wave symmetric, the superconducting state has a full energy gap, which we tie to a π-phase interlayer coupling. The superconducting nematicity is further directly detectable in the local density of states. Our results show that atomistic modeling is essential and also that very similar local interactions produce very different superconducting states in TBG and the high-temperature cuprate superconductors.

Superconductivity in monolayer and few-layer graphene. II. Topological edge states and Chern numbers

“…One of the main pressing questions to be answered is the nature of the superconducting state in different graphene systems. Many different methods, including mean-field theory [35,40,41,62], renormalization group [36][37][38][39]63], Monte Carlo [43,[64][65][66], and others, have predicted both spin-singlet and spin-triplet order parameters, beyond conventional s pairing, such as d-, p-and f -wave states [12,16,25,35,36,[66][67][68][69][70][71][72][73]. Understanding the type of order parameter developed by these systems may help in making progress in understanding the underlying mechanism giving rise to superconductivity, be it phonon based [6,28,71] and enhanced by the formation of flat bands in the multilayer graphene spectrum, such as in twisted bilayer [74] or rhombohedral graphene [28], or electron-electron interaction induced and also enhanced by the flat band formation [8,33,75].…”

Phonon softening in nanostructured phonon–mediated superconductors (review)

“…Moreover, in twisted FLG, depending on the angle between the layers, the number of phonon modes increases dramatically, leading to significant modification of the phonon spectrum and to the appearance of low-energy ZA phonon modes with frequencies of the order of a few terahertz [455]. Finally, the electron-phonon coupling in graphene is sufficiently strong to explain the appearance of the superconductivity around 1 K in twisted bilayer graphene for the magic angle θ ≈ 1.05 • [456][457][458] and in twisted trilayer graphene for the magic angle θ ≈ 1.6 [459,460].…”

Twisted Bilayer Graphene: A Journey Through Recent Advances and Future Perspectives

“…Some recent studies have suggested that the superconducting state in TBG may exhibit unconventional characteristics, such as odd-frequency pairing and non-trivial topology. [104,105] Hence, superconductivity in TBG is a fascinating phenomenon arising from this material system's unique electronic properties. [99] Copyright 2019, The Authors, published by The American Association for the Advancement of Science.…”

“…Some recent studies have suggested that the superconducting state in TBG may exhibit unconventional characteristics, such as odd‐frequency pairing and non‐trivial topology. [ 104,105 ] Hence, superconductivity in TBG is a fascinating phenomenon arising from this material system's unique electronic properties. The experimental observations of superconductivity in TBG have matched the theoretical predictions, and ongoing research continues to shed light on this intriguing phenomenon's mechanisms and potential applications.…”