Accurate two-band tight-binding Hamiltonians for hexagonal two-dimensional materials for strong-field physics

Two-dimensional (2D) hexagonal materials are promising for a variety of applications ranging from valleytronics, spin-current sources, topology, and more. They are recently extensively studied for high-field nonlinear phenomena including Floquet physics, lightwave-driven photogalvanic currents, and high harmonic generation (HHG). For strong-field phenomena, which are typically induced by off-resonant intense driving lasers, two-band tight-binding (TB) descriptions of the system are highly popular because they provide a combination of computational efficiency and accuracy. They are especially appealing since they yield continuous analytic expressions for the band energies and dipole matrix elements, avoiding issues with gauge freedom that can arise in more complex ab-initio theory. However, implementations commonly utilize only up to 2nd nearest-neighbor (NN) terms, which can produce qualitatively wrong band structures in vast regions of the Brillouin zone (BZ). While this approximation is valid for low energy excitations near K/K′, in strong-field conditions it can lead to wrong physical behavior. Here we develop accurate two-band TB Hamiltonians for hexagonal monolayers with up to 14 NN terms that are fitted to ab-initio bands in various systems (graphene, hexagonal-boron-nitride, WS₂, WSe₂, WTe₂, MoS₂, MoSe₂, MoTe₂), and reproduce the band structure across the entire BZ, including in regions with inverted curvature near Γ. We employ these models in semi-conductor Bloch equations simulations of HHG, showing that the angular-dependence of HHG yields substantially differs if choosing the full model, or a 2nd-order TB model that correctly captures bands only near K/K′. Our work provides accessible model parameters and analytic expressions for a variety of systems, which should facilitate accurate and efficient simulations of strong-field phenomena in 2D solids. It should also motivate more careful assessment of HHG features before applying various HHG spectroscopy techniques.