Weik, Norman and Schindler, Johannes and Bera, Soumya and Solomon, Gemma C. and Evers, Ferdinand (2016) Graphene with vacancies: Supernumerary zero modes. PHYSICAL REVIEW B, 94 (6): 064204. ISSN 2469-9950, 2469-9969
Full text not available from this repository.Abstract
The density of states rho(E) of graphene is investigated within the tight-binding (Huckel) approximation in the presence of vacancies. They introduce a nonvanishing density of zero modes n(zm) that act as midgap states, rho(E) = n(zm)delta(E) + smooth. As is well known, the actual number of zero modes per sample can, in principle, exceed the sublattice imbalance, N-zm >= vertical bar N-A - N-B vertical bar, where N-A, N-B denote the number of carbon atoms in each sublattice. In this paper, we establish a stronger relation that is valid in the thermodynamic limit and that involves the concentration of zero modes, n(zm) > vertical bar c(A) - c(B)vertical bar, where c(A) and c(B) denote the concentration of vacancies per sublattice; in particular, n(zm) is nonvanishing even in the case of balanced disorder, N-A/ N-B = 1. Adopting terminology from benzoid graph theory, the excess modes associated with the current carrying backbone (percolation cluster) are called supernumerary. In the simplest cases, such modes can be associated with structural elements such as carbon atoms connected with a single bond, only. Our result suggests that the continuum limit of bipartite hopping models supports nontrivial "supernumerary" terms that escape the present continuum descriptions.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ANDERSON TRANSITIONS; TRANSPORT; EIGENVALUES; PERCOLATION; SYMMETRIES; STATES; |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics > Chair Professor Grifoni > Group Ferdinand Evers |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 05 Apr 2019 09:13 |
| Last Modified: | 05 Apr 2019 09:13 |
| URI: | https://pred.uni-regensburg.de/id/eprint/3459 |
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