Abstract: Finding a tight-binding (TB) model for a desired solid is always a challenge that is of great interest when, e.g., studying transport properties. A method is proposed to construct TB models for solids using machine learning (ML) techniques. The approach is based on the LCAO method in combination with Slater-Koster (SK) integrals, which are used to obtain optimal SK parameters. The lattice constant is used to generate training examples to construct a linear ML model. We successfully used this method to find a TB model for BiTeCl, where spin-orbit coupling plays an essential role in its topological behavior.

Abstract: By using density functional theory (DFT) calculations, we predict a puckered, dynamically stable Janus single-layer black arsenic-phosphorus (b-AsP), which is composed of two different atomic sublayers, arsenic and phosphorus atoms. The calculated phonon spectrum reveals that Janus single-layer b-AsP is dynamically stable with either pure or coupled optical phonon branches arising from As and P atoms. The calculated Raman spectrum indicates that due to the relatively strong P-P bonds, As atoms have no contribution to the highfrequency optical vibrations. In addition, the orientation-dependent isovolume heat capacity reveals anisotropic contributions of LA and TA phonon branches to the low-temperature thermal properties. Unlike pristine single layers of b-As and b-P, Janus single-layer b-AsP exhibits additional out-of-plane asymmetry which leads to important consequences for its electronic, optical, and elastic properties. In contrast to single-layer b-As, Janus single-layer b-AsP is found to possess a direct band gap dominated by the P atoms. Moreover, real and imaginary parts of the dynamical dielectric function, including excitonic effects, reveal the highly anisotropic optical feature of the Janus single-layer. A tight-binding (TB) model is also presented for Janus single-layer b-AsP, and it is shown that, with up to seven nearest hoppings, the TB model reproduces well the DFT band structure in the low-energy region around the band gap. This TB model can be used in combination with the Green's function approach to study, e.g., quantum transport in finite systems based on Janus single-layer b-AsP. Furthermore, the linear-elastic properties of Janus single-layer b-AsP are investigated, and the orientation-dependent in-plane stiffness and Poisson ratio are calculated. It is found that the Janus single layer exhibits strong in-plane anisotropy in its Poisson ratio much larger than that of single-layer b-P. This Janus single layer is relevant for promising applications in optical dichroism and anisotropic nanoelasticity.

Abstract: Using the simplified linear combination of atomic orbitals (LCAO) method in combination with ab initio calculations, we construct a tight-binding (TB) model for two different crystal structures of monolayer gallium: a(100)- and b(010)-Gallenene. The analytical expression for the Hamiltonian and numerical results for the overlap matrix elements between different orbitals of the Ga atoms and for the Slater and Koster (SK) integrals are obtained. We find that the compaction of different structures affects significantly the formation of the orbitals. The results for a(100)-Gallenene can be very well explained with an orthogonal basis set, while for b(010)-Gallenene we have to assume a non-orthogonal basis set in order to construct the TB model. Moreover, the transmission properties of nanoribbons of both monolayers oriented along the AC and ZZ directions are also investigated and it is shown that both AC- and ZZ-b(010)-Gallenene nanoribbons exhibit semiconducting behavior with zero transmission while those of a(100)-Gallenene nanoribbons are metallic.

Abstract: Starting from the simplified linear combination of atomic orbitals method in combination with first-principles calculations, we construct a tight-binding (TB) model in the two-centre approximation for borophene and hydrogenated borophene (borophane). The Slater and Koster approach is applied to calculate the TB Hamiltonian of these systems. We obtain expressions for the Hamiltonian and overlap matrix elements between different orbitals for the different atoms and present the SK coefficients in a nonorthogonal basis set. An anisotropic Dirac cone is found in the band structure of borophane. We derive a Dirac low-energy Hamiltonian and compare the Fermi velocities with that of graphene.