Z. Popović | Searcharxiv

arXiv2021

Irreducible and site symmetry induced representations of single/double ordinary/gray layer groups

Considered are eighty sets of layer groups, each set consisted of four groups: ordinary single and double, and gray single and double layer group. Structural properties of layer groups (factorization onto cyclic subgroups and existence of grading according to the sequence of halving subgroups) enable efficient symbolic computation (by POLSym code) of the relevant properties, real and complex irreducible and allowed (half-)integer (co-)representations in particular. This task includes, as the first step, classification of the irreducible domains based on the group action in Brillouin zone combined with torus topology. Also, the band (co-)representations induced from the irreducible (co-)representations of Wyckoff position stabilizers (site symmetry groups) are decomposed onto the irreducible components. These, and other layer group symmetry related theoretical data relevant for physics, layered materials in particular, are tabulated and made available through the web site.

cond-mat.mes-hall↗

arXiv2012

Electronic structure of the substitutional vacancy in graphene: Density-functional and Green's function studies

We study the electronic structure of graphene with a single substitutional vacancy using a combination of the density-functional, tight-binding, and impurity Green's function approaches. Density functional studies are performed with the all-electron spin-polarized linear augmented plane wave (LAPW) method. The three $sp^2 σ$ dangling bonds adjacent to the vacancy introduce localized states (V$σ$) in the mid-gap region, which split due to the crystal field and a Jahn-Teller distortion, while the $p_z π$ states introduce a sharp resonance state (V$π$) in the band structure. For a planar structure, symmetry strictly forbids hybridization between the $σ$ and the $π$ states, so that these bands are clearly identifiable in the calculated band structure. As for the magnetic moment of the vacancy, the Hund's-rule coupling aligns the spins of the four localized V$σ_1 \uparrow \downarrow$, V$σ_2 \uparrow $, and the V$π\uparrow$ electrons resulting in a S=1 state, with a magnetic moment of $2 μ_B$, which is reduced by about $0.3 μ_B$ due to the anti-ferromagnetic spin-polarization of the $π$ band itinerant states in the vicinity of the vacancy. This results in the net magnetic moment of $1.7 μ_B$. Using the Lippmann-Schwinger equation, we reproduce the well-known $\sim 1/r$ decay of the localized V$π$ wave function with distance and in addition find an interference term coming from the two Dirac points, previously unnoticed in the literature. The long-range nature of the V$π$ wave function is a unique feature of the graphene vacancy and we suggest that this may be one of the reasons for the widely varying relaxed structures and magnetic moments reported from the supercell band calculations in the literature.

cond-mat.mes-hall↗