Electronic structure of vacancy resonant states in graphene: A critical review of the single-vacancy case

Abstract

The resonant behaviour of vacancy states in graphene is well-known but some ambiguities remain concerning in particular the nature of the so-called zero energy modes. Other points are not completely elucidated in the case of low but finite vacancy concentration. In this article we concentrate on the case of vacancies described within the usual tight-binding approximation. More precisely we discuss the case of a single vacancy or of a finite number of vacancies in a finite or infinite system.

Nodal adsorbate bound states in armchair graphene nanoribbons: Fano resonances and adsorbate recognition in weak disorder

“…2 (lower figures) shows that | | 2 weights more, in general, on the B site. This trend is in agreement with that for a vacancy [41]. The very large on-site potential V 0 for the vacancy has pushed the wave function of its zero-energy state to the B (A) site entirely when the vacancy is at an A (B) site.…”

“…The positions of the nodal adsorbate are at the centers of the yellow triangular structures in the contours. Similar triangular structures have been obtained, but in the local density of states at zero energies around a vacancy in bulk graphene [41,42]. For the sake of our following discussions, we denote the nodal-adsorbate site to be an A site.…”

Review on graphene spintronic, new land for discovery

“…However, we need more exact predictions for better understanding of graphene structures. Especially in the case of a structure with one or more adsorbed dopants [55,108,109] or vacant finite graphene (mentioned before) [54,110], which are a very important part of new discovery tools. Moreover, calculations give us more information about inside the structure, like spin density [74], and magnet moment etc.…”

Atomistic T -matrix theory of disordered two-dimensional materials: Bound states, spectral properties, quasiparticle scattering, and transport

“…The only difference between the QP scattering rate in Eqs. (32) and (33) and the inverse transport relaxation time is the factor 1 − cos θ kk in the square brackets, which accounts for the fact that the transport is insensitive to small-angle scattering while the QP lifetime is equally sensitive to all scattering processes. For isotropic scattering, the two scattering times become identical as the angular integral of the cos θ kk term vanishes.…”

“…The present work is thus complementary to our previous first-principles T -matrix study of the LDOS and quasiparticle interference in 2D materials. 26 In comparison with analytic and tight-binding based T -matrix studies of defects in, e.g., graphene [27][28][29][30][31][32][33][34] and black phosphorus, 35 our first-principles method permits for parameter-free modeling of realistic defects in disordered materials. It furthermore goes beyond other first-principles studies of defects and their transport-limiting effects based on the Born approximation, [36][37][38][39][40] which we here demonstrate breaks down for point defects in 2D materials.…”