Continuum models for twisted bilayer graphene: Effect of lattice deformation and hopping parameters

Abstract

We analyze a description of twisted graphene bilayers, that incorporates the deformation of the layers using state of the art interlayer atomic potentials, and a modification of the hopping parameters between layers in the light of the classic Slonczewski-Weiss-McClure parametrisation. We obtain narrow bands in all cases, but that their nature can be rather different. We will show how to describe the results by equivalent continuum models. Even though such models can be constructed, their complexity can vary, requiring many coupling parameters to be included, and the full in-layer dispersion must be taken into account. The combination of all these effects will have a large impact on the wave functions of the flat bands, and that modifications in details of the underlying models can lead to significant changes. A robust conclusion is that the natural strength of the interlayer couplings is higher than usually assumed, leading to shifts in the definition of the magic angles. The structure at the edges of the narrow bands, at the Γ point of the Brillouin Zone is also strongly dependent on parametrization. As a result, the existence, and size, of band gaps between the flat bands and the neighboring ones are changed. Hence, the definition of Wannier functions, and descriptions based on local interactions are strongly dependent on the description of the model at the atomic scale. * Francisco. Guinea@imdea.org † Niels.Walet@manchester.ac.uk; https://www.research.manchester.ac.uk/portal/niels.walet.html AA AB FIG. 1. Examples of a graphene bilayer in (approximate) AA and AB alignment. arXiv:1903.00364v2 [cond-mat.str-el]

The emergence of one-dimensional channels in marginal-angle twisted bilayer graphene

“…We study results for a pair of flat (fixed distance d = 3.46Å) graphene layers, which we have relaxed under influence of the "LKC" (LCBOPI+KC) potential model discussed in detail in ref. [33]. Since we are mainly interested in the channel states in this paper, we shall not use the complex many-body screening discussed in that reference, but we shall only study the exponential Koster-Slater hopping of the form Note that this has been enhanced by a factor of 1.3 relative to our previous work, in order that the first magic angle occurs at 1.05 • for the flat LKC relaxed lattice.…”

“…As always, we start with the case of rigid graphene sheets, without any relaxation. We do not perform tight-binding calculation, but rather construct a continuum model from the tight-binding Hamiltonian using a method recently developed by us [33]. This generalizes the now ubiquitous continuum model of twisted bilayer graphene [36,39,40] to include more than a single triangle of couplings-these couplings are due to the momentum transferred by the misalignment of the two layers.…”

“…This example is for the LCBOPI+KC potential, see Ref. [33]. a) Stream-line representation (in green) of the in-plane movement of atoms in the top layer on relaxation.…”

Electron transitions for Dirac Hamiltonians with flat bands under electromagnetic radiation: Application to the α−T3 graphene model

“…Our results show many useful relationships between transition probabilities, times and parameters of the model. This can serve to combine experimental and theoretical results to fine tune the parameters of the Hamiltonian, which is a problem that is still a work in progress 36 , as well as a tool to have quantum control of the system.…”

Perfect one-dimensional chiral states in biased twisted bilayer graphene

“…The real TBG is not a simple stack of rigid graphene layers as assumed in the previous section, but it has a spontaneous lattice relaxation and resulting AB/BA domain formation [31][32][33]35,[45][46][47][48][49][50][51][52][53] . Such a structural deformation modifies the electronic band structure 19,20,35,44,50,[52][53][54] . Here we calculate the energy band structures in the presence of the lattice strain using the tight-binding method 50 .…”