Full Slonczewski-Weiss-McClure parametrization of few-layer twistronic graphene

Abstract

We use a hybrid k • p theory -tight binding (HkpTB) model to describe interlayer coupling simultaneously in both Bernal and twisted graphene structures. For Bernal-aligned interfaces, HkpTB is parametrized using the full Slonczewski-Weiss-McClure (SWMcC) Hamiltonian of graphite 1 , which is then used to refine the commonly used minimal model for twisted interfaces 2,3 , by deriving additional terms that reflect all details of the full SWMcC model of graphite. We find that these terms introduce some electron-hole asymmetry in the band structure of twisted bilayers, but in twistronic multilayer graphene, they produce only a subtle change of moiré miniband spectra, confirming the broad applicability of the minimal model for implementing the twisted interface coupling in such systems.

ARPES Signatures of Few-Layer Twistronic Graphenes

“…The large number of atoms in a moirécell complicate the application of ab initio approaches, leading to the development of various multiscale approaches 13 such as large-scale density functional theory, 14−16 tight-binding and continuum models. 3,17,18 Although these give qualitatively similar predictions, the details of the dispersions, and hence their properties, depend on the simulation methodology and parameter set used. Experimental studies are therefore vital to validate and refine the theoretical models and to understand the electronic band structure changes which underlie the emergent twistronic effects.…”

“…The high density of states within this flat band results in strong, and gate-tunable, electron correlation effects, ,, as also observed in twisted-bilayer transition-metal dichalcogenides , and in twisted few-layer graphenes. − However, there are challenges to modeling these systems. The large number of atoms in a moiré cell complicate the application of ab initio approaches, leading to the development of various multiscale approaches such as large-scale density functional theory, − tight-binding and continuum models. ,, Although these give qualitatively similar predictions, the details of the dispersions, and hence their properties, depend on the simulation methodology and parameter set used. Experimental studies are therefore vital to validate and refine the theoretical models and to understand the electronic band structure changes which underlie the emergent twistronic effects.…”

Semimetallic and semiconducting graphene-hBN multilayers with parallel or reverse stacking

“…Starting from a hybrid k.p theory-tight binding approach 27 for the differently stacked 3D graphene/hBN crystals in Fig. 1 we derive the low-energy effective Hamiltonians for the electrons on the graphene layers subject to perturbations from the adjacent hBNs 2,28,29 .…”

Mixed-Stacking Few-Layer Graphene as an Elemental Weak Ferroelectric Material

“…Below, we use the full Slonczewski–Weiss–McClure (SWMcC) model of graphite films discussed in ref . This model accounts for couplings sketched in Figure , which include both the closest and next-neighbor hoppings, and it is implemented in the framework of a hybrid k · p -tight-binding model, using a Hamiltonian, scriptH , specified in the Supporting Information. The diagonalization of scriptH gives the dispersions, ε β ( p ), and wave functions, ψ β, p α L , of bands β in the multilayer, which we use to compute both on-layer electron densities, n L , and electric polarization: P z = e d ∑ L = 1 n + m + 3 L n L ; goodbreak0em1em⁣ n L = 4 ∑ β , α L , boldp [ false| ψ β , boldp α L false| 2 Θ false[ E normalF − ε β ( p ) false] − 1 4 ] Here e is the electron charge, d ≈ 3.35 Å the interlayer distance, and “ L ” the layer index, and α L = A L , B L sublattice indices.…”

“…Below, we use the full Slonczewski–Weiss–McClure (SWMcC) model of graphite films discussed in ref . This model accounts for couplings sketched in Figure , which include both the closest and next-neighbor hoppings, and it is implemented in the framework of a hybrid k · p -tight-binding model, using a Hamiltonian, , specified in the Supporting Information. The diagonalization of gives the dispersions, ε β ( p ), and wave functions, ψ β, p α L , of bands β in the multilayer, which we use to compute both on-layer electron densities, n L , and electric polarization: Here e is the electron charge, d ≈ 3.35 Å the interlayer distance, and “ L ” the layer index, and α L = A L , B L sublattice indices.…”