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Register a new userA tight-binding model of an ambient-pressure molecular Dirac electron system
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By deriving a tight-binding model, we demonstrate a mechanism of forming a nodal line of Dirac points in a single-component molecular conductor [Pt(dmtd)$_2$] [Zhou {it et al.}, Chem. Commun. {bfseries 55}, 3327 (2019)], consisting of HOMO and LUMO. The nodal line is obtained as the intersection of two surfaces, where one corresponds to the HOMO-LUMO band crossing and another is vanishing of the HOMO-LUMO couplings due to their different symmetries. The latter property is essential for the Dirac electron in molecular conductors. The nature of the open nodal line is discussed in terms of the parity of the wavefunctions at eight TRIMs (time reversal invariant momenta).
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We extend a tight-binding method to include the effects of spin-orbit coupling, and apply it to the study of the electronic properties of the actinide elements Th, U, and Pu. These tight-binding parameters are determined for the fcc crystal structure using the equivalent equilibrium volumes. In terms of the single particle energies and the electronic density of states, the overall quality of the tight-binding representation is excellent and of the same quality as without spin-orbit coupling. The values of the optimized tight-binding spin-orbit coupling parameters are comparable to those determined from purely atomic calculations.
We present a three-band tight-binding (TB) model for describing the low-energy physics in monolayers of group-VIB transition metal dichalcogenides $MX_2$ ($M$=Mo, W; $X$=S, Se, Te). As the conduction and valence band edges are predominantly contributed by the $d_{z^{2}}$, $d_{xy}$, and $d_{x^{2}-y^{2}}$ orbitals of $M$ atoms, the TB model is constructed using these three orbitals based on the symmetries of the monolayers. Parameters of the TB model are fitted from the first-principles energy bands for all $MX_2$ monolayers. The TB model involving only the nearest-neighbor $M$-$M$ hoppings is sufficient to capture the band-edge properties in the $pm K$ valleys, including the energy dispersions as well as the Berry curvatures. The TB model involving up to the third-nearest-neighbor $M$-$M$ hoppings can well reproduce the energy bands in the entire Brillouin zone. Spin-orbit coupling in valence bands is well accounted for by including the on-site spin-orbit interactions of $M$ atoms. The conduction band also exhibits a small valley-dependent spin splitting which has an overall sign difference between Mo$X_{2}$ and W$X_{2}$. We discuss the origins of these corrections to the three-band model. The three-band TB model developed here is efficient to account for low-energy physics in $MX_2$ monolayers, and its simplicity can be particularly useful in the study of many-body physics and physics of edge states.
For a previously published study of the titanium hcp (alpha) to omega (omega) transformation, a tight-binding model was developed for titanium that accurately reproduces the structural energies and electron eigenvalues from all-electron density-functional calculations. We use a fitting method that matches the correctly symmetrized wavefuctions of the tight-binding model to those of the density-functional calculations at high symmetry points. The structural energies, elastic constants, phonon spectra, and point-defect energies predicted by our tight-binding model agree with density-functional calculations and experiment. In addition, a modification to the functional form is implemented to overcome the collapse problem of tight-binding, necessary for phase transformation studies and molecular dynamics simulations. The accuracy, transferability and efficiency of the model makes it particularly well suited to understanding structural transformations in titanium.
We investigated the precise crystal structures and electronic states in a quasi-two-dimensional molecular conductor ${alpha}$-(BETS)$_2$I$_3$ at ambient pressure. The electronic resistivity of this molecular solid shows metal-to-insulator (MI) crossover at $T_{MI}$=50 K. Our x-ray diffraction and $^{13}$C nuclear magnetic resonance experiments revealed that ${alpha}$-(BETS)$_2$I$_3$ maintains the inversion symmetry below $T_{MI}$. First-principles calculations found a pair of anisotropic Dirac cones at a general k-point, with the degenerate contact points at the Fermi level. The origin of the insulating state in this system is a small energy gap of ~2 meV opened by the spin-orbit interaction. The Z$_2$ topological invariants indicate that this system is a weak topological insulator. Our results suggest that ${alpha}$-(BETS)$_2$I$_3$ is a promising material for studying the bulk Dirac electron system in two dimensions.
We study the different ways of introducing light-matter interaction in first-principle tight-binding (TB) models. The standard way of describing optical properties is the velocity gauge, defined by linear coupling to the vector potential. In finite systems a transformation to represent the electromagnetic radiation by the electric field instead is possible, albeit subtleties arise in periodic systems. The resulting dipole gauge is a multi-orbital generalization of Peierls substitution. In this work, we investigate accuracy of both pathways, with particular emphasis on gauge invariance, for TB models constructed from maximally localized Wannier functions. Focusing on paradigmatic two-dimensional materials, we construct first-principle models and calculate the response to electromagnetic fields in linear response and for strong excitations. Benchmarks against fully converged first-principle calculations allow for ascertaining the accuracy of the TB models. We find that the dipole gauge provides a more accurate description than the velocity gauge in all cases. The main deficiency of the velocity gauge is an imperfect cancellation of paramagnetic and diamagnetic current. Formulating a corresponding sum rule however provides a way to explicitly enforce this cancellation. This procedure corrects the TB models in the velocity gauge, yielding excellent agreement with dipole gauge and thus gauge invariance.
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