Large scale tight-binding methods for 2D moiré heterostructures: hBN encapsulated multilayer graphene

  The advent of 2D moiré heterostructures, starting with the discovery of flat bands and strong correlations in magically twisted bilayer graphene (TBLG), has shown that there is still a lot of room for uncovering exciting new physics when the layer, twist and strain degrees of freedom are explored. From a theoretical and computational perspective, the 2D moiré heterostructures have in common an increasingly large supercell, with as many as 104 atoms per supercell, leading to increasing difficulties in accurately modeling them. In this case, ab-initio methods are beyond the reach of current computing resources, while continuum effective models might not be valid anymore. In the first part of the presentation I will introduce two tight-binding open-source softwares, Pybinding ^[1] and Quantum-Kite ^[2], that can be deployed in the description of moiré systems. These are based on spectral expansions of the Green’s functions and allow for the description of opto-electronic properties of moiré systems in the presence of disorder, vacancies, magnetic field, with possibilities to model systems with as many as 10¹⁰ degrees of freedom.

  In the second part of the presentation I will exemplify the use of the methods and softwares for the description of electronic properties of hBN encapsulated multilayer graphene. Recent experimental and theoretical works [3] have shown that the combination of marginally aligned graphene/hBN heterostructures will lead to secondary Dirac points, mini-bands and gaps in the spectrum ^[4]. In this presentation we will instead explore the electronic properties of encapsulated graphene multilayer configurations, where the hBN and graphene layers are aligned, paying special attention to the role of precise stacking of the encapsulating hBN layers ^[5]. We find that for selected moiré-stacking configurations an robust gap at the secondary Dirac point, in combination with an applied perpendicular electric field gives rise in encapsulated bernal stacked bilayer graphene to flat bands with bandwidth below 10meV without the need of interlayer twisting. Similar to TBLG, attainable bandwidths are below energy scales related to the Coulomb interaction and thus strongly-correlated electronic states are expected.

*Ref:
 ^[1] Pybinding website: https://docs.pybinding.site/en/stable/
 ^[1] Quantum-Kite website: https://quantum-kite.com/
 ^[3] Z. Wang, Y. B. Wang, J. Yin, E. Tóvári, Y. Yang, L. Lin, M. Holwill, J. Birkbeck, D. J. Perello, Shuigang Xu, J. Zultak, R. V. Gorbachev, A. V. Kretinin, T. Taniguchi, K. Watanabe, S. V. Morozov, M. Anđelković, S. P. Milovanović, L. Covaci, F.M. Peeters, A. Mishchenko, A. K. Geim, K. S. Novoselov, Vladimir I. Fal’ko, Angelika Knothe, C. R. Woods, Science Advances 12, eaay8897 (2019)
 ^[4] M. Anđelković, S. P. Milovanović, L. Covaci, F. M. Peeters, Nano Lett. 20, 979 (2020)
 ^[5] R. Smeyers, L. Covaci, M. V. Milošević, arXiv:2211.16351 (2022)