Electrostatic fate of N-layer moiré graphene
Twisted N-layer graphene (TNG) moiré structures have recently been shown to exhibit robust superconductivity similar to twisted bilayer graphene (TBG). In particular for N = 4 and N = 5, the phase diagram features a superconducting pocket that extends beyond the nominal full filling of the flat band. These observations are seemingly at odds with the canonical understanding of the low-energy theory of TNG, wherein the TNG Hamiltonian consists of one flat-band sector and accompanying dispersive bands. Using a self-consistent Hartree-Fock treatment, we explain how the phenomenology of TNG can be understood through an interplay of in-plane Hartree and inhomogeneous layer potentials, which cause a reshuffling of electronic bands. We extend our understanding beyond the case of N = 5 realized in experiment so far. We describe how the Hartree and layer potentials control the phase diagram for devices with N > 5 and tend to preclude exchange-driven correlated phenomena in this limit. To circumvent these electrostatic constraints, we propose a flat-band paradigm that could be realized in large-N devices by taking advantage of two nearly flat sectors acting together to enhance the importance of exchange effects.
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© 2023 American Physical Society.
We are grateful to Alex Thomson, Jason Alicea, and Étienne Lantagne-Hurtubise for helpful discussions and collaboration on related projects. We would also like to thank the HPC Service of ZEDAT, Freie Universität Berlin, for computing time. Work at Freie Universität Berlin was supported by Deutsche Forschungsgemeinschaft through CRC 183 (Project No. C02) and a joint ANR-DFG project (TWISTGRAPH). C.L. was supported by start-up funds from Florida State University and the National High Magnetic Field Laboratory. The National High Magnetic Field Laboratory is supported by the National Science Foundation through NSF/DMR-1644779 and the State of Florida. S.N-P. acknowledges the support of NSF (Award No. DMR-1753306) and the Office of Naval Research (Award No. N142112635).