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Abstract Twisted bilayer graphene (TBG) has drawn significant interest due to recent experiments which show that TBG can exhibit strongly correlated behavior such as the superconducting and correlated insulator phases. Much of the theoretical work on TBG has been based on analysis of the Bistritzer–MacDonald model which includes a phenomenological parameter to account for lattice relaxation. In this work, we use a newly developed continuum model which systematically accounts for the effects of structural relaxation. In particular, we model structural relaxation by coupling linear elasticity to a stacking energy that penalizes disregistry. We compare the impact of the two relaxation models on the corresponding many-body model by defining an interacting model projected to the flat bands. We perform tests at charge neutrality at both the Hartree–Fock and coupled cluster singles and doubles level of theory and find the systematic relaxation model gives quantitative differences from the simplified relaxation model.
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Electronic Observables for Relaxed Bilayer Two-Dimensional Heterostructures in Momentum Space
Momentum space transformations for incommensurate two-dimensional electronic structure calculations are fundamental for reducing computational cost and for representing the data in a more physically motivating format, as exemplified in the Bistritzer--MacDonald model [Proc. Natl. Acad. Sci. USA, 108 (2011), pp. 12233--12237]. However, these transformations can be difficult to implement in more complex systems such as when mechanical relaxation patterns are present. In this work, we aim for two objectives. First, we strive to simplify the understanding and implementation of this transformation by rigorously writing the transformations between the four relevant spaces, which we denote real space, configuration space, momentum space, and reciprocal space. This provides a straightforward algorithm for writing the complex momentum space model from the original real space model. Second, we implement this for twisted bilayer graphene with mechanical relaxation effects included. We also analyze the convergence rates of the approximations and show the tight-binding coupling range increases for smaller relative twists between layers, demonstrating that the 3-nearest neighbor coupling of the Bistritzer--MacDonald model is insufficient when mechanical relaxation is included for very small angles. We quantify this and verify with numerical simulation.
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- Award ID(s):
- 1906129
- PAR ID:
- 10472345
- Publisher / Repository:
- SIAM
- Date Published:
- Journal Name:
- Multiscale Modeling & Simulation
- Volume:
- 21
- Issue:
- 4
- ISSN:
- 1540-3459
- Page Range / eLocation ID:
- 1344 to 1378
- Subject(s) / Keyword(s):
- momentum space, real space, 2D, electronic structure, density of states, conductivity, heterostructure, mechanical relaxation, moir\'e patterns
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1137/21M1451208
