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Concept# Tight binding

Summary

In solid-state physics, the tight-binding model (or TB model) is an approach to the calculation of electronic band structure using an approximate set of wave functions based upon superposition of wave functions for isolated atoms located at each atomic site. The method is closely related to the LCAO method (linear combination of atomic orbitals method) used in chemistry. Tight-binding models are applied to a wide variety of solids. The model gives good qualitative results in many cases and can be combined with other models that give better results where the tight-binding model fails. Though the tight-binding model is a one-electron model, the model also provides a basis for more advanced calculations like the calculation of surface states and application to various kinds of many-body problem and quasiparticle calculations.
Introduction
The name "tight binding" of this electronic band structure model suggests that this quantum mechanical model describes the properties of tigh

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We theoretically study the topological properties of the tight-binding model on the breathing kagome lattice with antisymmetric spin-orbit coupling (SOC) between nearest neighbors. We show that the system hosts nontrivial topological phases even without second-nearest-neighbor hopping and that the weakly dispersing band of the kagome lattice can become topological. The main results are presented in the form of phase diagrams, where the Z(2)( )topological index is shown as a function of SOC (intrinsically allowed and Rashba) and lattice trimerization. In addition, exact diagonalization is compared with effective low-energy theories around the high-symmetry points. We find that the weakly dispersing band has a very robust topological property associated with it. Moreover, the Rashba SOC can produce a topological phase rather than hinder it, in contrast to the honeycomb lattice. Finally, we consider the case of a fully spin polarized (ferromagnetic) system, breaking time-reversal symmetry. We find a phase diagram that includes systems with finite Chern numbers. In this case too, the weakly dispersing band is topologically robust to trimerization.

2019We present an open-source program irvsp, to compute irreducible representations of electronic states for all 230 space groups with an interface to the Vienna ab-initio Simulation Package. This code is fed with plane-wave-based wavefunctions (e.g. WAVECAR) and space group operators (listed in OUTCAR), which are generated by the VASP package. This program computes the traces of matrix presentations and determines the corresponding irreducible representations for all energy bands and all the k-points in the three-dimensional Brillouin zone. It also works with spin-orbit coupling (SOC), i.e., for double groups. It is in particular useful to analyze energy bands, their connectivities, and band topology, after the establishment of the theory of topological quantum chemistry. Accordingly, the associated library -irrep_bcs.a - is developed, which can be easily linked to by other ab-initio packages. In addition, the program has been extended to orthogonal tight-binding (TB) Hamiltonians, e.g. electronic or phononic TB Hamiltonians. A sister program is presented as well. Program summary Program title: irvsp CPC Library link to program files: http://doi.org/10.1763/y9ds5nnm2f.1 Licensing provisions: GNU Lesser General Public License Programming language: Fortran 90/77 Nature of problem: Determining irreducible representations for all energy bands and all the k-points in 230 space groups. It is in particular useful to analyze energy bands, their connectivities, and band topology. Solution method: By computing the traces of matrix presentations of space group operators for the eigen-wavefunctions at a certain k-point in a given space group, one can determine irreducible representations for them. (C) 2020 Elsevier B.V. All rights reserved.

Xiao Dong, Quansheng Wu, Oleg Yazyev

The 8-Pmmn borophene, a boron analog of graphene, hosts tilted and anisotropic massless Dirac fermion quasiparticles owing to the presence of a distorted graphenelike sublattice. First-principles calculations show that stacked 8-Pmmn borophene is transformed into fused three-dimensional borophene under pressure, being accompanied by partial bond breaking and bond reformation. Strikingly, fused 8-Pmmn borophene inherits the Dirac band dispersion resulting in an unusual semimetal-semimetal transition. A simple tight-binding model derived from graphene qualitatively reveals the underlying physics due to the maximum preservation of the graphenelike substructure after the phase transition, which contrasts greatly to the transformation of graphite into diamond associated with the semimetal-insulator transition.